A Bibliography of Publications of George Marsaglia

Nelson H. F. Beebe Department of Mathematics University of Utah Salt Lake City, UT 84112 USA

Tel: +1 801 581 5254 FAX: +1 801 581 4148

          E-mail: beebe@math.utah.edu (Internet)
     WWW URL: https://www.math.utah.edu/~beebe/

02 November 2023 Version 1.78

Abstract

This bibliography records publications of George Marsaglia.

Title word cross-reference

1, 2, 3 [184]. 1/2πTan^{−1}(λ) [11]. 10^{2857} [133]. 1040 million [155]. 64 [172]. A [28, 29]. A + B [28, 29]. Γ [100]. n! [107]. π [180]. rank(A + B) = rank(A) + rank(B) [77]. t [91]. Tan^{−1}(λ) [11]. X + Y, X/Y [103].

*good* [138].

-bit [172]. -distribution [91].

128-bit [175]. 1962 [188]. 1965 [189]. 1969 [190]. 1971 [191]. 1984 [195]. 1988 [196, 197].

2011 [203]. 20th [196, 197].

42 [79, 80].

64-bit [138, 146].

= [191].

Abnormality [83]. Accumulated [42, 52, 50]. Acknowledgement [79, 80]. Ada [167]. Administrator [136]. Algorithm [102, 176, 101]. American [199]. analyse [191]. Analysis [158, 203, 33, 191]. Anderson [132, 147]. Ann [79, 80]. application [170]. Applications [191, 171, 84, 143, 191]. approximation [94, 107, 190]. Approximations [66, 70]. April [196, 197]. Area [102]. associated [16]. Asymptotic [156]. Atlanta [195]. Attack [164]. August [199, 189].

Based [160, 156]. Battery [124, 126]. Behavior [176]. Between [20, 106]. Binary [72, 74, 79, 80, 93]. biologic [68]. Bit [183, 172, 175, 138, 146]. Blood [58, 42, 52, 50]. Bounds [35, 59].

C [127, 130]. C309 [102]. C69 [90]. Carleton [192]. Carlo [168, 141, 169, 174, 177]. Cautionary [169]. CDROM [124]. central [4, 5]. Centre [191]. certain [156, 171]. characterization [84, 103]. Choosing [75, 119, 143]. Circle [131]. Circulants [19]. Circular [45, 46, 55]. Circulation [73]. claims [152]. class [111]. Classes [2]. classical [104]. Classroom [49]. Cleve [176]. clustered [16]. clustered-rocket [16]. Collection [102]. Combination [60, 160]. Combinations [66, 62, 63, 70]. Comment [178]. Compartment [33]. Compatibility [3]. Computationally [197]. Computer [41, 54, 194, 201, 202, 30, 57, 94, 193, 195]. Computers [23, 137, 44]. Computing [203, 197, 196]. concentration [89]. Conditional [27, 36]. conditions [82]. Conference [203, 188, 189]. Congruential [76, 160, 175, 166, 67, 71]. Consideration [73]. construction [8]. continuous [100]. Contributions [198]. Convenient [37]. Convex [102]. Corner [176]. correlation [96]. correlations [200]. Correspondence [119]. course [199]. Courts [136]. Covariance [27, 28, 29, 36]. Covariances [27, 36]. criteria [156]. Cross [73]. Crossings [40, 51]. Cryptanalysis [163]. CUDA [185]. Cumulative [26, 48]. CURAND [185]. Current [97].

Darling [132, 147]. Decimal [151]. decision [188, 189, 101]. decreasing [95]. Density [40, 15, 51, 95]. dependent [4, 5]. derivation [107]. Determinants [49]. deviation [185]. DIEHARD [126, 124]. difference [104]. differential [104]. differential-difference [104]. Difficult [139]. Difficult-to-pass [139]. Digits [72, 180, 74, 79, 80, 93]. direct [171]. Discrete [149, 30, 162]. distance [106]. distributed [9, 176]. Distribution [3, 28, 29, 39, 50, 85, 140, 147, 148, 10, 31, 84, 91, 100, 103, 121].

Distributions [17, 20, 162]. Diverted [42]. does [77]. Dose [42, 52, 50]. DUPER [78]. during [50, 52].

easily [95]. easy [184]. Editor [161]. Effect [26, 48, 89]. effectiveness [199]. Efficient [173]. Element [110]. Elementary [20]. Encyclopedia [193, 194, 201, 202]. END [130]. Engineering [194, 201]. enhanced [171]. Enough [115]. Equalities [81]. equations [104]. errors [168]. essays [198]. Evaluating [140, 147, 148]. evaluation [121]. exact [94]. exact-approximation [94]. exceeding [155]. Exchange [73, 68, 18, 61]. Expansions [151]. Experimental [187]. explanation [89]. Exploration [187]. Exponential [25, 85, 34, 13]. exponentially [9]. Expressing [12, 28, 29]. Extension [84]. Extracorporeal [52, 56, 50].

Fairfax [196]. fall [32, 65]. family [171]. Fast [25, 21, 149, 186, 34, 38, 86, 95]. Ferrokinetics [68, 69, 58]. finding [11]. Fit [150, 156, 132]. flights [16]. Florida [136]. forms [6, 10]. Fourier [158]. fourth [189]. fractional [125]. Function [60, 15, 100, 121]. Functions [3, 60, 66, 188, 189, 70, 95].

Gamma [128, 134, 84, 88, 103]. Gaussian [112]. General [7, 6, 57]. generalized [82]. generates [176]. Generating [25, 13, 14, 21, 22, 30, 31, 37, 39, 91, 96, 128, 134, 34, 9, 15, 24, 38, 86, 88, 94, 129, 135, 90]. Generation [117, 149, 159, 87, 92, 101]. Generator [167, 133, 160, 108, 109, 114, 127, 138, 154, 185]. Generators [145, 158, 47, 97, 99, 116, 119, 142, 187, 160, 161, 173, 171, 172, 175, 166, 168, 200, 62, 63, 67, 71, 111, 113, 120, 122, 143, 179, 170, 186]. George [182]. Georgia [195]. given [90]. goddess [132]. goddess-of-fit [132]. good [168, 200]. Goodness [150, 156]. Goodness-of-Fit [150]. GPGPU [185].

having [15]. held [188, 189, 190]. Hemochromatosis [83]. Hidden [168]. High [203]. histograms [101]. honor [198]. hyperplane [171]. hyperspheres [181]. Hypotheses [157]. Hypothesis [7, 6].

Idempotent [6]. Idiopathic [83]. IH [83]. II [14]. Implementation [167, 178]. implemented [95]. Implementing [119]. Improvements [86]. Improving [22]. including [124]. incomplete [100]. Independence [157]. Independent [72, 74, 79, 80, 93, 125]. Inequalities [81]. information [188, 189]. Ingram [198]. integer [125]. Intensive [197]. Interface [195, 196, 197]. internal [18, 61]. International [203]. interpolation [118]. inverse [121]. inverses [82]. investigating [61]. Involving [45, 46, 55]. Iron [83, 68, 18, 61, 89]. Irradiation [52, 56, 50]. Iterated [4, 5].

July [190]. June [188]. Jury [137].

Key [164]. Key-Search [164]. kinetics [89]. KISS [114, 154, 183]. Kolmogorov [140].

Lack [85]. Lancaster [190]. lattice [165, 166]. Lehmer [171, 172]. less [152]. Lesson [169]. Letter [115, 161]. Leukemia [56]. Liblice [188]. limit [4, 5]. limits [4, 5]. Line [26, 48, 62, 63]. Linear [7, 60, 66, 76, 166, 6, 15, 70]. Long [133, 122]. Longest [133]. Longest-period [133]. Losses [26, 48]. lot [181]. Lukacs [84].

Maclaren [163, 164]. Maine [199]. mainly [32, 65]. Man [69, 58, 68, 18, 89]. March [195]. Marsaglia [182, 181, 173, 145, 165, 166, 167, 124, 170, 162, 163, 164, 187]. Math [79, 80]. Mathematical [199, 73]. Mathematics [191, 113]. Matrices [35, 81, 98, 6, 59, 82, 96]. Matrix [27, 28, 29, 36]. McGill [78]. mean [90]. Means [27, 36]. Measure [131, 11]. Memoranda [136]. Memory [85]. Method [178, 22, 37, 41, 54, 128, 134, 57, 88, 94, 95, 129, 135, 141, 61, 162]. Methods [197, 86, 174, 177]. model [68]. Moment [40, 51]. Monkey [116, 170]. Monkeying [150]. Monster [133]. Monte [168, 141, 169, 174, 177]. Montreal [191]. Monty [128, 129]. mother [120]. Multi [33]. Multi-Compartment [33]. Multidimensional [161]. multipliers [172, 175]. multivariate [8].

nature [18]. near [188]. nearly [15]. Networking [203]. nombres [191]. non [166]. non-linear [166]. Normal [58, 14, 20, 21, 22, 27, 28, 29, 36, 37, 39, 54, 64, 112, 131, 148, 153, 176, 8, 11, 24, 31, 38, 43, 53, 86, 90, 121]. normally [176]. Note [145, 3, 85, 99, 8]. Notes [49]. November [203]. Number [145, 158, 167, 47, 97, 99, 116, 117, 119, 124, 133, 142, 159, 160, 191, 173, 199, 171, 172, 175, 166, 168, 200, 62, 63, 67, 71, 78, 87, 92, 98, 108, 109, 111, 113, 122, 127, 138, 143, 154, 179, 170, 185, 186, 101]. Numbers [64, 165, 32, 65, 130, 176, 184]. Numerical [104, 191]. numérique [191].

Obituary [182]. October [192]. Office [136]. Offset [131]. Olkin [198]. One [28, 29, 62, 63, 66, 70, 133]. One-line [62, 63]. One-Sided [66, 70]. opinion [143]. Optimal [60]. Optimality [162]. Orono [199]. Other [151, 157]. Ottawa [192].

package [78]. packing [181]. Pair [22]. Panels [137]. Parallel [184]. parking [181]. partitioned [82]. parts [125]. pass [139]. PC [108]. Performance [203]. Period [133, 122]. periods [155]. physical [171]. Physics [169]. Pi [151, 152]. Plane [20]. planes [32, 65]. Plasma [89, 68]. point [75]. points [106]. Poisson [100]. Polar [22]. polygonal [11]. portable [122]. Prague [188, 189]. prediction [173]. Previously [133]. priority [79, 80]. Probabilities [110]. Probability [131, 198, 11, 16]. Problems [45, 46, 55, 137]. Procedure [25, 21, 34, 24, 38]. Procedures [14]. Proceedings [203, 196, 191, 195, 190, 192]. Processes [2, 156, 188, 189, 1]. Producing [41, 54, 57]. Proof [49]. Property [85]. Proposed [99]. Pseudo [64, 159, 166]. Pseudo-Random [159, 166]. Pseudorandom [161, 172, 175, 165, 170, 185, 186]. Python [128, 129].

quadratic [6, 10]. Query [64].

Radiation [42, 52, 50]. radioiron [89]. Random [181, 145, 158, 167, 25, 47, 2, 14, 21, 22, 23, 26, 32, 41, 44, 64, 65, 72, 74, 79, 80, 87, 92, 93, 97, 99, 105, 112, 115, 116, 117, 119, 124, 125, 130, 133, 142, 149, 159, 160, 110, 173, 171, 166, 168, 200, 188, 189, 34, 9, 12, 13, 15, 24, 30, 38, 48, 57, 62, 63, 67, 71, 78, 86, 91, 94, 98, 106, 108, 109, 111, 113, 120, 122, 127, 129, 135, 138, 143, 152, 154, 176, 179, 184, 101]. random-number [78, 138, 154]. Randomness [124, 126, 139, 151, 157, 180]. Rank [35, 82, 59]. Ranks [81, 10]. Rapid [121]. Ratios [43, 53, 153]. RBC [83]. Re [138]. rectangles [106]. Refutation [152]. regions [11]. Regularities [67, 71]. Related [40, 192, 51]. Relations [20]. Remark [19, 15]. Remarks [119, 11]. Representation [60]. RES [83]. Research [191]. Result [49]. Results [159]. Reticuloendothelial [83]. RNG [146]. RNGs [144, 155]. rocket [16]. rug [123].

sample [8, 90]. sampling [95]. Savage [132]. SC’11 [203]. Science [194, 201, 202, 196, 197, 195, 193]. scientific [143]. Scrambled [187]. Search [164, 118]. Seattle [203]. Seeds [143]. Selecting [137]. Selection [110]. September [189, 191]. Sequences [76, 98]. Sets [102]. Short [49, 199]. Shunt [42]. Sided [66, 70]. Simple [134, 183]. Simplex [17]. Simulating [118, 162]. simulations [168]. Singular [27, 36]. Sixteenth [195]. small [24]. social [143]. Society [199]. solution [104]. Some [16, 45, 46, 55, 122, 139, 159, 11, 104]. Specified [110]. sphere [75]. Spherical [45, 46, 55]. splittable [186]. squaring [101]. squeeze [88]. Standard [185]. State [136]. Statist [79, 80]. statistical [188, 189, 174, 177]. Statistics [192, 196, 197, 195, 198]. Still [54]. Stirling [107]. Stochastic [2, 33, 156, 1]. Storage [203]. Structure [76, 98]. structures [1]. Study [180, 172, 175]. Subsets [110]. such [152]. Sum [35, 59]. sums [43, 53]. SUPER [78, 154]. SUPER-DUPER [78]. Supercomputers [105, 112]. support [171]. suppression [171]. surface [75]. symmetric [95]. Symposium [195, 192, 196, 197, 190, 191]. System [83, 163]. Systems [33, 164].

Tables [10, 11, 131]. Tail [39, 31]. Targets [45, 46, 55]. Technical [119, 143]. Techniques [143]. Terms [28, 29, 12]. Test [99, 150, 181, 165, 166, 132, 170]. Tests [116, 126, 139, 157, 124]. their [11, 62, 63]. Theme [197]. theorem [4, 5]. théorie [191]. Theory [170, 191, 156, 199, 188, 189, 16, 190]. third [188]. thought [152]. three [10]. Times [133]. Too [183]. Topics [192].

Touted [133]. Transactions [188, 189]. transferrin [61]. Transmission [26, 48]. Transport [83]. Treatment [56]. tree [101]. Two [35, 160, 10, 61]. types [61].

Uniform [158, 47, 17, 20, 160, 12, 53]. Uniformity [161]. unimodal [95]. Union [102]. Universal [167, 109, 146]. University [192, 191]. unreasonable [199]. Use [137, 11, 62, 63, 78]. utilizing [61].

Variable [39, 12, 15]. Variables [25, 2, 14, 21, 22, 23, 27, 36, 37, 41, 54, 72, 105, 112, 128, 134, 149, 153, 34, 4, 5, 9, 12, 13, 24, 30, 31, 38, 43, 44, 53, 57, 74, 79, 80, 86, 91, 93, 94, 125, 129, 135]. variance [90]. variates [88]. very [122]. very-long-period [122]. View [97]. Virginia [196].

WA [203].

Xorshift [145, 144, 179, 187].

Zaman [173]. Ziggurat [178, 135, 176].

References

Marsaglia:1948:SSP

[1] George Marsaglia. The structures of stochastic processes. Thesis (M.A.), The Ohio State University, Columbus, OH, USA, 1948. ?? pp.

Marsaglia:1951:SPC

[2] George Marsaglia. Stochastic Processes and Classes of Random Variables. Ph.D. thesis, The Ohio State University, Columbus, OH, USA,

     1951. 46 pp. URL http://ezproxy.lib.utah.edu/docview/302068737?
     accountid=14677.

Marsaglia:1953:NCD

[3] George Marsaglia. A note on the compatibility of distribution functions. Report 85, Institute of Statistics, University of North Carolina, Chapel Hill, NC, USA, November 12, 1953. ii + 2 pp. URL http://www.dtic.

     mil/get-tr-doc/pdf?AD=AD0029405.

Marsaglia:1954:ILCa

[4] George Marsaglia. Iterated limits and the central limit theorem for dependent variables. Special Report 93, Institute of Statistics, University of North Carolina, Chapel Hill, NC, USA, February 1954. ii + 7

pp. URL http://www.dtic.mil/docs/citations/AD0035146;   http:
//www.dtic.mil/dtic/tr/fulltext/u2/035146.pdf;   http://www.
dtic.mil/get-tr-doc/pdf?AD=AD0035146.

Marsaglia:1954:ILCb

[5] George Marsaglia. Iterated limits and the central limit theorem for dependent variables. Proceedings of the American Mathematical Society, 5(6): 987–991, December 1954. CODEN PAMYAR. ISSN 0002-9939 (print), 1088-6826 (electronic).

Graybill:1957:IMQ

[6] Franklin A. Graybill and George Marsaglia. Idempotent matrices and quadratic forms in the general linear hypothesis. Annals of mathematical statistics, 28(3):678–686, September 1957. CODEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic). URL http://projecteuclid.org/

euclid.aoms/1177706879.

Marsaglia:1957:GLH

[7] George Marsaglia. The general linear hypothesis. Statistical paper 2, Departments of Economics, Statistics & Commerce, University of Rangoon,

Rangoon, Burma, ???? 1957. URL http://www.worldcat.org/title/
general-linear-hypothesis/oclc/27397695.

Marsaglia:1957:NCM

[8] George Marsaglia. A note on the construction of a multivariate normal sample. IEEE Transactions on Information Theory, 3(2):149, June 1957. CODEN IETTAW. ISSN 0018-9448 (print), 1557-9654 (electronic).

Marsaglia:1960:GED

[9] George Marsaglia. On generating exponentially distributed random variables. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, ???? 1960. ?? pp.

Marsaglia:1960:TDQ

[10] George Marsaglia. Tables of the distribution of quadratic forms of ranks two and three. Report 213, Boeing Scientific Research Laboratories, Seattle, WA, USA, ???? 1960. ?? pp.

Marsaglia:1960:TSR

[11] George Marsaglia. Tables of 1/2πTan^{−1}(λ) and Tan^{−1}(λ) for λ = .0001, .0002, …, .9999, with some remarks on their use in finding the normal probability measure of polygonal regions. Report D1-82-0078, Boeing Scientific Research Laboratories, Seattle, WA, USA, ???? 1960. ?? pp.

Marsaglia:1961:ERV

[12] G. Marsaglia. Expressing a random variable in terms of uniform random variables. Annals of mathematical statistics, 32(3):894–898, September 1961. CODEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic).

URL http://projecteuclid.org/euclid.aoms/1177704983;   http:
//www.jstor.org/stable/2237849.

Marsaglia:1961:GER

[13] G. Marsaglia. Generating exponential random variables. Annals of mathematical statistics, 32(3):899–900, September 1961. CO-DEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic).

URL http://projecteuclid.org/euclid.aoms/1177704984;   http:
//www.jstor.org/stable/2237850.

Marsaglia:1961:PGN

[14] George Marsaglia. Procedures for generating normal random variables, II. Mathematical note 243, Boeing Scientific Research Laboratories, Seattle, WA, USA, October 1961.

Marsaglia:1961:RGR

[15] G. Marsaglia. Remark on generating a random variable having a nearly linear density function. Mathematical Note 242, Boeing Scientific Research Laboratories, Seattle, WA, USA, 1961.

Marsaglia:1961:SPT

[16] George Marsaglia. Some probability theory associated with clusteredrocket flights. Planetary and Space Science, 4(??):194–201, January 1961. CODEN PLSSAE. ISSN 0032-0633 (print), 1873-5088 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0032063361901325.

Marsaglia:1961:UDS

[17] George Marsaglia. Uniform distributions over a simplex. Mathematical note ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, December 1961.

Hosain:1962:NII

[18] F. Hosain, G. Marsaglia, W. Noyes, and C. A. Finch. The nature of internal iron exchange in man. Transactions of the Association of American Physicians, 75(??):59–63, ???? 1962. ISSN 0066-9458.

Mann:1962:RC

[19] H. B. Mann and G. Marsaglia. A remark on circulants. Mathematical note ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, ???? 1962. ?? pp.

Marsaglia:1962:ERB

[20] George Marsaglia. Elementary relations between uniform and normal distributions in the plane. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, August 1962. ?? pp. URL http://www.dtic.

mil/docs/citations/AD0288501.

Marsaglia:1962:FPG

[21] G. Marsaglia, M. D. Maclaren, and T. A. Bray. A fast procedure for generating normal random variables. Mathematical note 282, Boeing Scientific Research Laboratories, Seattle, WA, USA, August

1962. URL http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&
doc=GetTRDoc.pdf&AD=AD0296195.

Marsaglia:1962:IPM

[22] George Marsaglia. Improving the polar method for generating a pair of normal random variables. Technical report D1-82-0203, Boeing Scientific Research Laboratories, Seattle, WA, USA, September 1962. URL http:/

/www.dtic.mil/docs/citations/AD0288931.

Marsaglia:1962:RVC

[23] George Marsaglia. Random variables and computers. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, May 1962. ?? pp.

URL http://www.dtic.mil/docs/citations/AD0278358.

Marsaglia:1962:SPG

[24] George Marsaglia and T. A. Bray. A small procedure for generating normal random variables. Mathematical note 283, Boeing Scientific Research Laboratories, Seattle, WA, USA, November 1962. ?? pp.

MacLaren:1963:FPG

[25] M. D. MacLaren, G. Marsaglia, and T. A. Bray. A fast procedure for generating exponential random variables. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, January 1963. ?? pp.

Marsaglia:1963:CER

[26] George Marsaglia. The cumulative effect of random losses in a transmission line. Mathematical note D1-82-0236, Boeing Scientific Research Laboratories, Seattle, WA, USA, February 1963. ii + 14

pp. URL http://www.dtic.mil/docs/citations/AD0403722;   http:
//www.dtic.mil/get-tr-doc/pdf?AD=AD0403722. Mathematical Note

number 289.

Marsaglia:1963:CMC

[27] George Marsaglia. Conditional means and covariances of normal variables with singular covariance matrix. Mathematical note 288, Boeing Scientific Research Laboratories, Seattle, WA, USA, February 1963. URL http://

www.dtic.mil/docs/citations/AD0299080.

Marsaglia:1963:ENDa

[28] George Marsaglia. Expressing the normal distribution with covariance matrix A + B in terms of one with covariance matrix A. Mathematical note ??, Boeing Scientific Research Laboratories, Seattle, WA, USA,

February 1963. ?? pp. URL http://www.dtic.mil/docs/citations/
AD0299120.

Marsaglia:1963:ENDb

[29] George Marsaglia. Expressing the normal distribution with covariance matrix A + B in terms of one with covariance matrix A. Biometrika, 50(3/4):535–538, December 1963. CODEN BIOKAX. ISSN 0006-3444 (print), 1464-3510 (electronic). URL http://www.jstor.org/stable/

2333924.

Marsaglia:1963:GDR

[30] G. Marsaglia. Generating discrete random variables in a computer. Communications of the ACM, 6(1):37–38, January 1963. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:1963:GVT

[31] George Marsaglia. Generating variables from the tail of the normal distribution. Report 0399324, Boeing Scientific Research Laboratories, Seattle, WA, USA, September 1963. 6 pp. URL http://www.dtic.

mil/docs/citations/AD0423993;   http://www.stormingmedia.us/
39/3993/0399324.html.

Marsaglia:1963:RNF

[32] George Marsaglia. Random numbers fall mainly in the planes. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, August 1963.

9 pp. URL http://www.dtic.mil/docs/citations/AD0685578.

Marsaglia:1963:SAM

[33] George Marsaglia. Stochastic analysis of multi-compartment systems. Mathematical note 313, Boeing Scientific Research Laboratories, Seattle, WA, USA, July 1963. 22 pp.

MacLaren:1964:FPG

[34] M. D. MacLaren, G. Marsaglia, and T. A. Bray. A fast procedure for generating exponential random variables. Communications of the ACM, 7(5):298–300, May 1964. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:1964:BRS

[35] George Marsaglia. Bounds for the rank of the sum of two matrices. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, April

1964. 13 pp. URL http://www.dtic.mil/docs/citations/AD0600471.

Marsaglia:1964:CMC

[36] George Marsaglia. Conditional means and covariances of normal variables with singular covariance matrix. Journal of the American Statistical Association, 59(308):1203–1204, December 1964. CODEN JSTNAL. ISSN 0162-1459 (print), 1537-274X (electronic). URL http://www.jstor.org/

stable/2282635.

Marsaglia:1964:CMG

[37] G. Marsaglia and T. A. Bray. A convenient method for generating normal variables. SIAM Review, 6(3):260–264, ???? 1964. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic). URL http://www.jstor.

org/stable/2027592.

Marsaglia:1964:FPG

[38] G. Marsaglia, M. D. MacLaren, and T. A. Bray. A fast procedure for generating normal random variables. Communications of the ACM, 7(1): 4–10, January 1964. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:1964:GVT

[39] George Marsaglia. Generating a variable from the tail of the normal distribution. Technometrics, 6(1):101–102, February 1964. CODEN TCMTA2. ISSN 0040-1706 (print), 1537-2723 (electronic). URL http://www.jstor.

org/stable/1266749.

Marsaglia:1964:MCR

[40] George Marsaglia, Albert W. Marshall, and Frank Proschan. Moment crossings as related to density crossings. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, July 1964. ?? pp. URL http:

//www.dtic.mil/docs/citations/AD0603582.

Marsaglia:1964:MPR

[41] George Marsaglia. A method for producing random variables in a computer. Mathematical note 342, Boeing Scientific Research Laboratories, Seattle, WA, USA, February 1964. 13 pp. URL http://www.dtic.mil/

docs/citations/AD0601118.

Marsaglia:1964:RDA

[42] George Marsaglia. The radiation dose accumulated by blood diverted through a shunt. Mathematical note 357, Boeing Scientific Research Laboratories, Seattle, WA, USA, July 1964. 8 pp.

Marsaglia:1964:RNV

[43] George Marsaglia. Ratios of normal variables and ratios of sums of variables. Mathematical note D1-82-0348, Mathematics Research Laboratory, Boeing Scientific Research Laboratories, Seattle, WA, USA, April 1964. iii

+ 13 + 3 pp. URL http://www.dtic.mil/docs/citations/AD0600972;
 http://www.dtic.mil/dtic/tr/fulltext/u2/600972.pdf;   http:
//www.dtic.mil/get-tr-doc/pdf?AD=AD0600972.

Marsaglia:1964:RVC

[44] George Marsaglia. Random variables and computers. In Kožešník [188], pages 499–512. LCCN ???? In memory of RNDr. Antonin Spacek.

Marsaglia:1964:SPIa

[45] George Marsaglia. Some problems involving circular and spherical targets. Report ??, Boeing Scientific Research Laboratories, Seattle, WA,

USA, April 1964. 19 pp. URL http://www.dtic.mil/docs/citations/
AD0600566.

Marsaglia:1964:SPIb

[46] George Marsaglia. Some problems involving circular and spherical targets. Operations Research, 13(1):18–27, January/February 1964. CODEN OPREAI. ISSN 0030-364X (print), 1526-5463 (electronic). URL http:/

/www.jstor.org/stable/167951.

MacLaren:1965:URN

[47] M. Donald MacLaren and George Marsaglia. Uniform random number generators. Journal of the ACM, 12(1):83–89, January 1965. CODEN JACOAH. ISSN 0004-5411 (print), 1557-735X (electronic).

Marsaglia:1965:CER

[48] G. Marsaglia. The cumulative effect of random losses in a transmission line. Journal of the Franklin Institute, 280(5):443–450, November 1965. CODEN JFINAB. ISSN 0016-0032 (print), 1879-2693 (electronic).

Marsaglia:1965:CNS

[49] George Marsaglia. Classroom notes: Short proof of a result on determinants. American Mathematical Monthly, 72(2):173, February 1965. CO-DEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Marsaglia:1965:DRD

[50] G. Marsaglia and E. D. Thomas. Distribution of radiation dose accumulated by blood during extracorporeal irradiation. Radiation Research, ?? (??):??, ???? 1965. CODEN RAREAE. ISSN 0033-7587 (print), 1938-5404 (electronic).

Marsaglia:1965:MCR

[51] G. Marsaglia, A. W. Marshall, and F. Proschan. Moment crossings as related to density crossings. Journal of the Royal Statistical Society. Series B (Methodological), 27(1):91–93, January 1965. CODEN JSTBAJ. ISSN 0035-9246.

Marsaglia:1965:RDA

[52] George Marsaglia and E. Donnall Thomas. The radiation dose accumulated by blood during extracorporeal irradiation. Radiation Research, 25 (2):269–276, June 1965. CODEN RAREAE. ISSN 0033-7587 (print),

1938-5404 (electronic). URL http://www.jstor.org/stable/3571970.

Marsaglia:1965:RNV

[53] George Marsaglia. Ratios of normal variables and ratios of sums of uniform variables. Journal of the American Statistical Association, 60(309):193– 204, March 1965. CODEN JSTNAL. ISSN 0162-1459 (print), 1537-274X

(electronic). URL http://www.jstor.org/stable/2283145.

Marsaglia:1965:SAM

[54] George Marsaglia. Still another method for producing normal variables in a computer. Mathematical note ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, January 1965. 8 pp. URL http://www.dtic.

mil/docs/citations/AD0612430.

Marsaglia:1965:SPI

[55] George Marsaglia. Some problems involving circular and spherical targets. Operations Research, 13(1):18–27, January/February 1965. CODEN OPREAI. ISSN 0030-364X (print), 1526-5463 (electronic). URL http:/

/pubsonline.informs.org/doi/pdf/10.1287/opre.13.1.18.

Thomas:1965:TLE

[56] E. D. Thomas, R. B. Epstein, J. W. Eschbach Jr., D. Prager, C. D. Buckner, and G. Marsaglia. Treatment of leukemia by extracorporeal irradiation. The New England Journal of Medicine, 273(1):6–12, July 1, 1965. CODEN NEJMAG. ISSN 0028-4793 (print), 1533-4406

(electronic). URL http://www.ncbi.nlm.nih.gov/pubmed/14297099;
 http://www.nejm.org/doi/full/10.1056/NEJM196507012730102.

Marsaglia:1966:GMP

[57] G. Marsaglia. A general method for producing random variables in a computer. In Proceedings of the Fall Joint Computer Conference, San Francisco, November 1966, pages 169–173. Spartan Books, Washington, DC, USA, 1966. LCCN TK7885.A1 J74 1966 Fall.

Hosain:1967:BFN

[58] Fazle Hosain, George Marsaglia, and Clement A. Finch. Blood ferrokinetics in normal man. Journal of Clinical Investigation, 46(1):1–9, January 1967. CODEN JCINAO. ISSN 0021-9738 (print), 1558-8238 (electronic).

URL http://www.ncbi.nlm.nih.gov/pmc/articles/PMC297014/.

Marsaglia:1967:BRS

[59] George Marsaglia. Bounds on the rank of the sum of matrices. In Kožešník [189], pages 455–462. LCCN ????

Marsaglia:1967:ORF

[60] George Marsaglia. Optimal representation of a function as a linear combination of functions. Report 0841156, Boeing Scientific Research Laboratories, Seattle, WA, USA, March 1967. 14 pp. URL http://www.dtic.

mil/docs/citations/AD0651148;   http://www.stormingmedia.us/
84/8411/0841156.html.

Morgan:1967:MII

[61] E. H. Morgan, G. Marsaglia, E. R. Giblett, and C. A. Finch. A method of investigating internal iron exchange utilizing two types of transferrin.

Journal of Laboratory and Clinical Medicine, 63(3):370–381, March 1967. CODEN JLCMAK. ISSN 0022-2143 (print), 1532-6543 (electronic).

Marsaglia:1968:OLRa

[62] George Marsaglia and T. A. Bray. One-line random number generators and their use in combinations. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, March 1968. 12 pp. URL http://www.

dtic.mil/docs/citations/AD0667956.

Marsaglia:1968:OLRb

[63] George Marsaglia and T. A. Bray. One-line random number generators and their use in combinations. Communications of the ACM, 11(11): 757–759, November 1968. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:1968:QPR

[64] George Marsaglia. Query 27: Pseudo random normal numbers. Technometrics, 10(2):401–402, May 1968. CODEN TCMTA2. ISSN 0040-1706 (print), 1537-2723 (electronic). URL http://www.jstor.org/stable/

1267057.

Marsaglia:1968:RNF

[65] George Marsaglia. Random numbers fall mainly in the planes. Proceedings of the National Academy of Sciences of the United States of America, 61(1):25–28, September 15, 1968. CODEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (electronic). A popularized account of this work appeared as “Are random numbers really random?” [Scientific Research (Philadelphia, PA), 3 (1968), 21–??]. This widely-cited paper describes the hyperplane problem that linear congruential generators suffer from, although careful choice of multipliers can minimize its importance: see [158, 172, 171, 175].

Marsaglia:1969:OSA

[66] George Marsaglia. One-sided approximations by linear combinations of functions. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, September 1969. 18 pp. URL http://www.dtic.mil/docs/

citations/AD0695796.

Marsaglia:1969:RCR

[67] George Marsaglia. Regularities in congruential random number generators. Report ??, Boeing Scientific Research Laboratories, Seattle, WA,

USA, May 1969. 8 pp. URL http://www.dtic.mil/docs/citations/
AD0689295.

Cook:1970:FBM

[68] J. D. Cook, G. Marsaglia, J. W. Eschbach, D. D. Funk, and C. A. Finch. Ferrokinetics: a biologic model for plasma iron exchange in man. Journal of Clinical Investigation, 49(2):197–205, February 1970. CODEN JCI-NAO. ISSN 0021-9738 (print), 1558-8238 (electronic). URL http:/

/www.ncbi.nlm.nih.gov/pmc/articles/PMC322461/;   http://www.
pubmedcentral.gov/articlerender.fcgi?artid=322461.

Finch:1970:FM

[69] C. A. Finch, K. Deubelbeiss, J. D. Cook, J. W. Eschbach, L. A. Barker, D. D. Funk, G. Marsaglia, R. S. Hillman, S. Slichter, J. W. Adamson, A. Ganzoni, and E. R. Giblett. Ferrokinetics in man. Medicine (Baltimore), 49(1):17–54, January 1970. CODEN MEDIAV. ISSN 0025-7974 (print), 1536-5964 (electronic). URL http://journals.lww.com/

md-journal/Citation/1970/01000/Ferrokinetics_in_Man.2.aspx.

Marsaglia:1970:OSA

[70] G. Marsaglia. One-sided approximations by linear combinations of functions. In Talbot [190], pages 233–242. ISBN 0-12-682250-6. LCCN QA221 .A66.

Marsaglia:1970:RCR

[71] George Marsaglia. Regularities in congruential random number generators. Numerische Mathematik, 16(1):8–10, 1970. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic).

Marsaglia:1970:RVI

[72] George Marsaglia. Random variables with independent binary digits. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA,

January 1970. 15 pp. URL http://www.dtic.mil/docs/citations/
AD0705642.

Marsaglia:1971:MCC

[73] George Marsaglia and E. D. Thomas. Mathematical consideration of cross circulation and exchange. Transfusion, 11(4):216–219, July/August 1971. CODEN TRANAT. ISSN 0041-1132 (print), 1537-2995 (electronic).

Marsaglia:1971:RVI

[74] George Marsaglia. Random variables with independent binary digits. Annals of mathematical statistics, 42(6):1922–1929, December 1971. CODEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic).

URL http://projecteuclid.org/euclid.aoms/1177693058;   http:
//www.jstor.org/stable/2240118.

Marsaglia:1972:CPS

[75] George Marsaglia. Choosing a point from the surface of a sphere. Annals of mathematical statistics, 43(2):645–646, April 1972. CO-DEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic).

URL http://projecteuclid.org/euclid.aoms/1177692644;   http:
//www.jstor.org/stable/2240001.

Marsaglia:1972:SLC

[76] George Marsaglia. The structure of linear congruential sequences. In Zaremba [191], pages 249–285. ISBN 0-12-775950-6. LCCN QA297 .A67.

Marsaglia:1972:WD

[77] G. Marsaglia and G. P. H. Styan. When does rank(A + B) = rank(A) + rank(B)? Canadian mathematical bulletin = Bulletin canadien de mathématiques, 15(3):451–452, ???? 1972. CODEN CMBUA3. ISSN 0008-4395 (print), 1496-4287 (electronic).

Marsaglia:1973:HUM

[78] George Marsaglia, K. Ananthanarayanan, and A. Zaman. How to use the McGill random-number package SUPER-DUPER. Technical report, School of Computer Science, McGill University, Montreal, Quebec, Canada, 1973.

Marsaglia:1974:APRa

[79] George Marsaglia. Acknowledgement of priority to: “Random variables with independent binary digits” (Ann. Math. Statist. 42 (1971), 1922– 1929). Annals of Probability, 2(4):747, August 1974. CODEN AP-BYAE. ISSN 0091-1798 (print), 2168-894X (electronic). URL http://

projecteuclid.org/euclid.aop/1176996619.

Marsaglia:1974:APRb

[80] George Marsaglia. Acknowledgement of priority to: “Random variables with independent binary digits” (Ann. Math. Statist. 42 (1971), 1922– 1929). Annals of Statistics, 2(4):848, 1974. CODEN ASTSC7. ISSN 0090-5364 (print), 2168-8966 (electronic). URL http://projecteuclid.

org/euclid.aos/1176342776.

Marsaglia:1974:EIR

[81] George Marsaglia and George P. H. Styan. Equalities and inequalities for ranks of matrices. Linear and Multilinear Algebra, 2(3):269–292, 1974. CODEN LNMLAZ. ISSN 0308-1087 (print), 1563-5139 (electronic).

Marsaglia:1974:RCG

[82] George Marsaglia and George P. H. Styan. Rank conditions for generalized inverses of partitioned matrices. Sankhyā (Indian Journal of Statistics), Series A. Methods and Techniques, 36(4):437–442, 10 1974. CODEN SANABS. ISSN 0036-4452.

Fillet:1975:IHI

[83] G. Fillet and G. Marsaglia. Idiopathic hemochromatosis (IH) — abnormality in RBC transport of iron by reticuloendothelial system (RES). Blood, 46(6):1007, ???? 1975. CODEN BLOOAW. ISSN 0006-4971 (print), 1528-0020 (electronic).

Marsaglia:1975:EAL

[84] G. Marsaglia. Extension and applications of Lukacs’ characterization of the gamma distribution. In Saleh [192], page 13. ISBN ???? ISSN 0318-6288. LCCN QA276.A1 S92 1974.

Marsaglia:1975:NLM

[85] George Marsaglia and Alberto Tubilla. A note on the “lack of memory” property of the exponential distribution. Annals of Probability, 3 (2):353–354, April 1975. CODEN APBYAE. ISSN 0091-1798 (print),

2168-894X (electronic). URL http://projecteuclid.org/euclid.aop/
1176996406.

Marsaglia:1976:IFM

[86] G. Marsaglia, K. Ananthanarayanan, and N. J. Paul. Improvements on fast methods for generating normal random variables. Information Processing Letters, 5(2):27–30, June 1976. CODEN IFPLAT. ISSN 0020-0190 (print), 1872-6119 (electronic).

Marsaglia:1976:RNG

[87] George Marsaglia. Random number generation. In Ralston and Meek [193], pages 1192–1197. ISBN 0-88405-321-0. LCCN QA76.15 .E55 1976.

Marsaglia:1977:SMG

[88] George Marsaglia. The squeeze method for generating gamma variates. Computers and Mathematics with Applications, 3(4):321–325, 1977. CO-DEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (electronic).

Skarberg:1978:PRK

[89] Karl Skarberg, Mary Eng, Helmut Huebers, George Marsaglia, and Clement Finch. Plasma radioiron kinetics in man: explanation for the effect of plasma iron concentration. Proceedings of the National Academy of Sciences of the United States of America, 75(3):1559–1561, March 1978. CODEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (elec-

tronic). URL http://www.pnas.org/content/75/3/1559.short;
http://www.pubmedcentral.gov/articlerender.fcgi?artid=411513.

Marsaglia:1980:CGN

[90] George Marsaglia and I. J. Good. C69. Generating a normal sample with given sample mean and variance. Journal of Statistical Computation and Simulation, 11(1):71–74, 1980. CODEN JSCSAJ. ISSN 0094-9655 (print), 1026-7778 (electronic), 1563-5163.

Marsaglia:1980:GRV

[91] George Marsaglia. Generating random variables with a t-distribution. Mathematics of Computation, 34(149):235–236, January 1980. CODEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

Marsaglia:1983:RNG

[92] George Marsaglia. Random number generation. In Ralston and Reilly, Jr. [194], pages 1260–1264. ISBN 0-442-24496-7. LCCN QA76.15 .E48 1983.

Marsaglia:1983:RVI

[93] George Marsaglia. Random variables with independent binary digits. Kibern. Sb., Nov. Ser., 20:216–224, 1983. CODEN ???? ISSN 0453-8382.

Marsaglia:1984:EAM

[94] George Marsaglia. The exact-approximation method for generating random variables in a computer. Journal of the American Statistical Association, 79(385):218–221, March 1984. CODEN JSTNAL. ISSN 0162-1459 (print), 1537-274X (electronic). URL http://www.jstor.org/stable/

2288360.

Marsaglia:1984:FEI

[95] George Marsaglia and Wai Wan Tsang. A fast, easily implemented method for sampling from decreasing or symmetric unimodal density functions. SIAM Journal on Scientific and Statistical Computing, 5(2):349–359, June 1984. CODEN SIJCD4. ISSN 0196-5204.

Marsaglia:1984:GCM

[96] George Marsaglia and Ingram Olkin. Generating correlation matrices. SIAM Journal on Scientific and Statistical Computing, 5(2):470–475, 1984. CODEN SIJCD4. ISSN 0196-5204.

Marsaglia:1985:CVR

[97] George Marsaglia. A current view of random number generators. In Billard [195], pages 3–10. ISBN 0-444-87725-8. LCCN QA276.4

.S95 1984. URL http://stat.fsu.edu/pub/diehard/;   http://www.
evensen.org/marsaglia/keynote.ps.

Marsaglia:1985:MSR

[98] George Marsaglia and Liang-Huei Tsay. Matrices and the structure of random number sequences. Linear Algebra and its Applications, 67:147–156, 1985. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Marsaglia:1985:NPT

[99] George Marsaglia. Note on a proposed test for random number generators. IEEE Transactions on Computers, C-34(8):756–758, August 1985. CODEN ITCOB4. ISSN 0018-9340 (print), 1557-9956 (electronic).

URL http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=
1676623.

Marsaglia:1986:IFC

[100] George Marsaglia. The incomplete Γ function as a continuous Poisson distribution. Computers and Mathematics with Applications. Part B, 12 (5–6):1187–1190, September/December 1986. CODEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (electronic).

Tsang:1987:DTA

[101] Wai Wan Tsang and George Marsaglia. A decision tree algorithm for squaring histograms in random number generation. Ars Combinatoria. The Canadian Journal of Combinatorics, 23A:291–301, 1987. CODEN ???? ISSN 0381-7032.

Marsaglia:1989:CAA

[102] George Marsaglia, Arif Zaman, and Youlu Zheng. C309: An algorithm for the area of the union of a collection of convex sets. Journal of Statistical Computation and Simulation, 31(1):46–49, ???? 1989. CODEN JSCSAJ. ISSN 0094-9655 (print), 1563-5163 (electronic).

Marsaglia:1989:CGD

[103] George Marsaglia. The X + Y, X/Y characterization of the gamma distribution. In Gleser et al. [198], pages 91–98. ISBN 0-387-97076-2, 3-540-97076-2. LCCN QA273.18 .C683 1989.

Marsaglia:1989:NSS

[104] George Marsaglia, Arif Zaman, and John C. W. Marsaglia. Numerical solution of some classical differential-difference equations. Mathematics of Computation, 53(187):191–201, July 1989. CODEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

Marsaglia:1989:RVS

[105] George Marsaglia. Random variables for supercomputers. In Wegman

[197], page 103. URL http://www.dtic.mil/dtic/tr/fulltext/u2/

a205068.pdf. Abstract only.

Marsaglia:1990:DBR

[106] George Marsaglia, B. Narasimhan, and Arif Zaman. The distance between random points in rectangles. Communications in Statistics: Theory and Methods, 19(11):4199–4212, 1990. CODEN CSTMDC. ISSN 0361-0926 (print), 1532-415X (electronic).

Marsaglia:1990:NDS

[107] George Marsaglia and John C. W. Marsaglia. A new derivation of Stirling’s approximation to n!. American Mathematical Monthly, 97(9):826–829, November 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Marsaglia:1990:RNG

[108] George Marsaglia, B. Narasimhan, and Arif Zaman. A random number generator for PC’s. Computer Physics Communications, 60(3):345–349, October 1990. CODEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (electronic).

Marsaglia:1990:TUR

[109] George Marsaglia, Arif Zaman, and Wai Wan Tsang. Toward a universal random number generator. Statistics & Probability Letters, 9(1):35–39, January 1990. CODEN SPLTDC. ISSN 0167-7152 (print), 1879-2103 (electronic).

Zaman:1990:RSS

[110] Arif Zaman and George Marsaglia. Random selection of subsets with specified element probabilities. Communications in Statistics: Theory and Methods, 19(11):4419–4434, ???? 1990. CODEN CSTMDC. ISSN 0361-0926 (print), 1532-415x (electronic).

Marsaglia:1991:NCR

[111] George Marsaglia and Arif Zaman. A new class of random number generators. Annals of applied probability, 1(3):462–480, August 1991. CODEN

???? ISSN 1050-5164. URL http://projecteuclid.org/euclid.aoap/
1177005878.

Marsaglia:1991:NGR

[112] George Marsaglia. Normal (Gaussian) random variables for supercomputers. The Journal of Supercomputing, 5(1):49–55, June 1991. CODEN JOSUED. ISSN 0920-8542 (print), 1573-0484 (electronic).

Marsaglia:1992:MRN

[113] George Marsaglia. The mathematics of random number generators. In Burr [199], pages 73–90. ISBN 0-8218-5501-8. LCCN QA241 .U67 1992.

Marsaglia:1993:KG

[114] George Marsaglia and Arif Zaman. The KISS generator. Technical report ??, Department of Statistics, Florida State University, Tallahassee, FL, USA, ???? 1993. See report of cryptographic insecurity of KISS generator [183]. See also [174].

Marsaglia:1993:LHR

[115] George Marsaglia and Arif Zaman. Letter: How random is random enough? Science News (Washington, DC), 143(11):163, March 13, 1993. CODEN SCNEBK. ISSN 0036-8423 (print), 1943-0930 (elec-

tronic). URL http://www.jstor.org/stable/10.2307/3977245. Cau-

tionary comment on [169].

Marsaglia:1993:MTR

[116] George Marsaglia and Arif Zaman. Monkey tests for random number generators. Computers and Mathematics with Applications, 26(9):1–10, November 1993. CODEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (electronic). See also [170].

Marsaglia:1993:RNG

[117] George Marsaglia. Random number generation. In Ralston and Reilly, Jr. [201], pages 1145–1148. ISBN 0-442-27679-6. LCCN QA76.15 .E48 1993.

Marsaglia:1993:SIS

[118] G. Marsaglia and B. Narasimhan. Simulating interpolation search. Computers and Mathematics with Applications, 26(8):31–42, October 1993. CODEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (electronic).

Marsaglia:1993:TCR

[119] George Marsaglia. Technical correspondence: Remarks on choosing and implementing random number generators. Communications of the ACM, 36(7):105–108, July 1993. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:1994:MAR

[120] George Marsaglia. The mother of all random generators. Web document,

October 1994. URL ftp://ftp.taygeta.com/pub/c/mother.c.

Marsaglia:1994:REI

[121] George Marsaglia, Arif Zaman, and John C. W. Marsaglia. Rapid evaluation of the inverse of the normal distribution function. Statistics & Probability Letters, 19(4):259–266, March 15, 1994. CODEN SPLTDC. ISSN 0167-7152 (print), 1879-2103 (electronic). URL http:

//www.sciencedirect.com/science/article/pii/0167715294901740.

Marsaglia:1994:SPV

[122] George Marsaglia and Arif Zaman. Some portable very-long-period random number generators. Computers in physics, 8(1):117–121, January/ February 1994. CODEN CPHYE2. ISSN 0894-1866 (print), 1558-

4208 (electronic). URL https://aip.scitation.org/doi/10.1063/1.
168514.

Marsaglia:1994:YAR

[123] George Marsaglia. Yet another rug. Posted to the electronic billboard sci.stat.math., August 1, 1994.

Marsaglia:1995:MRN

[124] George Marsaglia. The Marsaglia random number CDROM including the Diehard Battery of Tests of randomness. Web site at the Department of Statistics, Florida State University, Tallahassee, FL, USA., 1995. URL

http://stat.fsu.edu/pub/diehard/.

Marsaglia:1995:RVI

[125] G. Marsaglia. Random variables with independent integer and fractional parts. Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research, 49(2):133–137, July 1995. CODEN ???? ISSN 0039-0402 (print), 1467-9574 (electronic).

Marsaglia:1996:DBT

[126] George Marsaglia. DIEHARD: A battery of tests of randomness. Technical report ??, Florida State University, Tallahassee, FL, USA, 1996.

URL http://euler.bd.psu.edu/~naras/diehard/snapshots.html;
http://stat.fsu.edu/~geo/.

Marsaglia:1997:RNG

[127] George Marsaglia. A random number generator for C. Posted to the sci.math.num-analysis news group, September 29, 1997. URL

http://mathforum.org/kb/thread.jspa?messageID=1607565. From

the posting: “Keep the following six lines of code somewhere in your files. #define znew ((z=36969*(z&65535)+(z¿¿16))¡¡16) #define wnew ((w=18000*(w&65535)+(w¿¿16))&65535) #define IUNI (znew+wnew) #define UNI (znew+wnew)*4.656613e-10 static unsigned long z=362436069, w=521288629; void setseed(unsigned long i1,unsigned long i2)z=i1; w=i2; Whenever you need random integers or random reals in your C program, just insert those six lines at (near?) the beginning of the program. In every expression where you want a random real in [0,1) use UNI, or use IUNI for a random 32-bit integer. No need to mess with ranf() or ranf(lastI), etc, with their requisite overheads. Choices for replacing the two multipliers 36969 and 18000 are given below. Thus you can tailor your own in-line multiply-with-carry random number generator.”.

Marsaglia:1998:MPMa

[128] George Marsaglia and Wai Wan Tsang. The Monty Python method for generating gamma variables. Journal of Statistical Software, 3 (3):1–8, 1998. CODEN JSSOBK. ISSN 1548-7660. URL http:

//www.jstatsoft.org/v03/i03;   http://www.jstatsoft.org/v03/
i03/GERMGAM.PDF;   http://www.jstatsoft.org/v03/i03/GERMGAM.
PS;   http://www.jstatsoft.org/v03/i03/updates.

Marsaglia:1998:MPMb

[129] George Marsaglia and Wai Wan Tsang. The Monty Python method for generating random variables. ACM Transactions on Mathematical Software, 24(3):341–350, September 1998. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL http://www.acm.org:

80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/.

Marsaglia:1999:RNC

[130] George Marsaglia. Random numbers for C: The END? Message-ID

36A5FC62.17C9CC33@stat.fsu.edu. Posting to the sci.crypt.random-numbers,

sci.math, and sci.stat.math news groups., January 20, 1999.

URL http://groups.google.com/group/sci.crypt/browse_thread/
thread/ca8682a4658a124d/.

Marsaglia:19xx:TNP

[131] George Marsaglia. Tables of the normal probability measure of an offset circle. Report ??, Boeing Scientific Research Laboratories, Seattle, WA, USA, ???? 19xx.

Marsaglia:2000:ADS

[132] J. C. Marsaglia and G. Marsaglia. The Anderson–Darling–Savage goddessof-fit test. Unpublished. See [156, 157]., 2000.

Marsaglia:2000:MRN

[133] George Marsaglia. The monster, a random number generator with period over 10^{2857} times as long as the previously touted longest-period one. Technical report ????, Florida State University, Tallahassee, FL, USA, ???? 2000.

Marsaglia:2000:SMG

[134] George Marsaglia and Wai Wan Tsang. A simple method for generating gamma variables. ACM Transactions on Mathematical Software, 26(3): 363–372, September 2000. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Marsaglia:2000:ZMG

[135] George Marsaglia and Wai Wan Tsang. The ziggurat method for generating random variables. Journal of Statistical Software, 5(8):1–7, 2000. CO-

DEN JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.org/v05/
i08;   http://www.jstatsoft.org/v05/i08/rnorrexp.c;   http:/
/www.jstatsoft.org/v05/i08/updates;   http://www.jstatsoft.org/
v05/i08/ziggurat.pdf. See [178, ?].

Marsaglia:2001:MOF

[136] George Marsaglia. Memoranda to Office of Florida State Courts Administrator. February 5, 2001 and May 29, 2001, with recommendations on jury selection., 2001.

Marsaglia:2001:PUC

[137] George Marsaglia. Problems with the use of computers for selecting jury panels. Jurimetrics, 41(??):425–427, Summer 2001. CODEN JURIFF.

ISSN 0897-1277. URL http://heinonline.org/HOL/Page?handle=
hein.journals/juraba41&div=38&g_sent=1&collection=journals.

Marsaglia:2002:RGB

[138] George Marsaglia. Re: *good* 64-bit random-number generator. Posting to the sci.crypt.random-numbers news group, September 3, 2002.

URL http://groups.google.ws/group/comp.sys.sun.admin/browse_
thread/thread/683ff52120e5b4d/b53ccad5aa5d6017.

Marsaglia:2002:SDP

[139] George Marsaglia and Wai Wan Tsang. Some difficult-to-pass tests of randomness. Journal of Statistical Software, 7(3):1–8, 2002. CODEN

JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.org/v07/
i03;   http://www.jstatsoft.org/v07/i03/tuftests.c;   http:/
/www.jstatsoft.org/v07/i03/tuftests.pdf;   http://www.jstatsoft.
org/v07/i03/updates.

Marsaglia:2003:EKD

[140] George Marsaglia, Wai Wan Tsang, and Jingbo Wang. Evaluating Kolmogorov’s distribution. Journal of Statistical Software, 8(18):1–4, 2003. CODEN JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.org/

v08/i18;   http://www.jstatsoft.org/v08/i18/k.pdf.

Marsaglia:2003:MCM

[141] George Marsaglia. Monte Carlo method. In Ralston et al. [202],

pages 1192–1193.  ISBN 0-470-86412-5.  LCCN QA76.15 .E48

2003. URL http://www.e-streams.com/es0707/es0707\_3357.htm;
http://www.loc.gov/catdir/bios/wiley046/2003283283.htm;   http:
//www.loc.gov/catdir/description/wiley041/2003283283.htm;   http:
//www.loc.gov/catdir/toc/wiley041/2003283283.htm.

Marsaglia:2003:RNG

[142] George Marsaglia. Random number generators. Journal of Modern Applied Statistical Methods, 2(1):2–13, May 2003. CODEN ???? ISSN 1538-

9472. URL http://stat.fsu.edu/pub/diehard/;   http://tbf.coe.
wayne.edu/jmasm/; http://www.csis.hku.hk/~diehard/.

Marsaglia:2003:TOS

[143] George Marsaglia. Technical opinion: Seeds for random number generators: Techniques for choosing seeds for social and scientific applications of random number generators. Communications of the ACM, 46(5):90– 93, May 2003. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Marsaglia:2003:XR

[144] George Marsaglia. Xorshift RNGs. Journal of Statistical Software, 8 (14):1–6, 2003. CODEN JSSOBK. ISSN 1548-7660. URL http:

//www.jstatsoft.org/v08/i14;   http://www.jstatsoft.org/v08/

i14/xorshift.pdf. See [145] for corrections and the equivalence of xorshift generators and the well-understood linear feedback shift register generators. See also [184, 185, 186] for the failure of Marsaglia’s xorwow() generator from this paper. See [179, 187] for detailed analysis.

Brent:2004:NMX

[145] Richard P. Brent. Note on Marsaglia’s xorshift random number generators. Journal of Statistical Software, 11(5):1–5, 2004. CODEN JSSOBK.

ISSN 1548-7660. URL http://www.jstatsoft.org/counter.php?id=
101&url=v11/i05/v11i05.pdf&ct=1. See [144, 179, 187]. This article

shows the equivalence of xorshift generators and the well-understood linear feedback shift register generators.

Marsaglia:2004:BURa

[146] George Marsaglia and Wai Wan Tsang. The 64-bit universal RNG. Statistics & Probability Letters, 66(2):183–187, 2004. CODEN SPLTDC. ISSN 0167-7152 (print), 1879-2103 (electronic). URL http://www.doornik.

com/research/randomdouble.pdf.

Marsaglia:2004:EAD

[147] George Marsaglia and John Marsaglia. Evaluating the Anderson–Darling distribution. Journal of Statistical Software, 9(2):1–5, February 25, 2004. CODEN JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.org/

v09/i02/ad.pdf;   http://www.jstatsoft.org/v09/i02/ADinf.c;
http://www.jstatsoft.org/v09/i02/AnDarl.c.

Marsaglia:2004:END

[148] George Marsaglia. Evaluating the normal distribution. Journal of Statistical Software, 11(4):1–7, ???? 2004. CODEN JSSOBK. ISSN 1548-7660.

URL http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/
cphi.pdf&ct=1.

Marsaglia:2004:FGD

[149] George Marsaglia, Wai Wan Tsang, and Jingbo Wang. Fast generation of discrete random variables. Journal of Statistical Software, 11(3):1–8, ???? 2004. CODEN JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.

org/counter.php?id=99&url=v11/i03/discrete.pdf&ct=1.

Marsaglia:2005:MGF

[150] George Marsaglia. Monkeying with the goodness-of-fit test. Journal of Statistical Software, 14(13):1–4, September 20, 2005. CO-DEN JSSOBK. ISSN 1548-7660. URL http://www.jstatsoft.org/

counter.php?id=138&url=v14/i13&ct=2;   http://www.jstatsoft.
org/counter.php?id=138&url=v14/i13/v14i13.pdf&ct=1.

Marsaglia:2005:RPO

[151] George Marsaglia. On the randomness of pi and other decimal expansions. InterStat: statistics on the Internet, page 17, October 2005. CODEN ????

ISSN 1941-689X. URL http://interstat.statjournals.net/INDEX/
Oct05.html;   http://interstat.statjournals.net/YEAR/2005/articles/
0510005.pdf.

Marsaglia:2006:RCS

[152] George Marsaglia. Refutation of claims such as “Pi is less random than we thought”. InterStat: statistics on the Internet, January 23, 2006. CODEN

???? ISSN 1941-689X. URL http://interstat.statjournals.net/
YEAR/2006/articles/0601001.pdf.

Marsaglia:2006:RNV

[153] George Marsaglia. Ratios of normal variables. Journal of Statistical Software, 16(4):1–10, May 2006. CODEN JSSOBK. ISSN 1548-7660. URL

http://www.jstatsoft.org/v16/i04.

Marsaglia:2010:SKR

[154] George Marsaglia. SUPER KISS random-number generator. Web posting,

November 3, 2010. URL http://www.velocityreviews.com/forums/
t704080-re-rngs-a-super-kiss.html.

Marsaglia:2011:RPE

[155] George Marsaglia. RNGs with periods exceeding 1040 million. Message-ID

<603ebe15-a32f-4fbb-ba44-6c73f7919a33@t35g2000yqj.googlegroups.com>

in newsgroups sci.math, comp.lang.c and sci.crypt., January 16, 2011.

Anderson:1952:ATC

[156] T. W. Anderson and D. A. Darling. Asymptotic theory of certain ‘goodness of fit’ criteria based on stochastic processes. Annals of mathematical statistics, 23(2):193–212, June 1952. CODEN AASTAD. ISSN 0003-4851 (print), 2168-8990 (electronic). URL http://www.jstor.org/stable/

2236446.

Savage:1957:ITR

[157] Richard Savage. On the independence of tests of randomness and other hypotheses. Journal of the American Statistical Association, 52(277):53– 57, March 1957. CODEN JSTNAL. ISSN 0162-1459 (print), 1537-274X

(electronic). URL http://www.jstor.org/stable/2281400.

Coveyou:1967:FAU

[158] R. R. Coveyou and R. D. MacPherson. Fourier analysis of uniform random number generators. Journal of the ACM, 14(1):100–119, January 1967. CODEN JACOAH. ISSN 0004-5411 (print), 1557-735X (electronic).

VanGelder:1967:SNR

[159] A. Van Gelder. Some new results in pseudo-random number generation. Journal of the ACM, 14(4):785–792, October 1967. CODEN JACOAH. ISSN 0004-5411 (print), 1557-735X (electronic).

Westlake:1967:URN

[160] W. J. Westlake. A uniform random number generator based on the combination of two congruential generators. Journal of the ACM, 14(2):337–340, April 1967. CODEN JACOAH. ISSN 0004-5411 (print), 1557-735X (electronic).

Whittlesey:1969:LEM

[161] John R. B. Whittlesey. Letter to the Editor: On the multidimensional uniformity of pseudorandom generators. Communications of the ACM, 12 (5):247, May 1969. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic). See [65].

Pokhodzei:1983:OMM

[162] B. B. Pokhodzeĭ. Optimality of the Marsaglia method for simulating discrete distributions. Vestnik Leningrad. Univ. Mat. Mekh. Astronom., 4:105–107, 1983. CODEN VMMAA3. ISSN 0024-0850.

Retter:1984:CMM

[163] C. Retter. Cryptanalysis of a Maclaren–Marsaglia system. Cryptologia, 8 (2):97–108, April 1984. CODEN CRYPE6. ISSN 0161-1194 (print), 1558-1586 (electronic). See also letters and responses, Cryptologia 8, 1984, pp. 374–378.

Retter:1985:KSA

[164] C. Retter. Key-search attack on Maclaren–Marsaglia systems. Cryptologia, 9(2):114–130, April 1985. CODEN CRYPE6. ISSN 0161-1194 (print), 1558-1586 (electronic).

Eichenauer:1988:MLTb

[165] Jürgen Eichenauer and Harald Niederreiter. On Marsaglia’s lattice test for pseudorandom numbers. Manuscripta Mathematica, 62(2):245–248, 1988. CODEN MSMHB2. ISSN 0025-2611 (print), 1432-1785 (electronic).

Eichenauer:1988:MLTc

[166] Jürgen Eichenauer, Holger Grothe, and Jürgen Lehn. Marsaglia’s lattice test and non-linear congruential pseudo-random number generators. Metrika. International Journal for Theoretical and Applied Statistics., 35 (3/4):241–250, 1988. CODEN MTRKA8. ISSN 0026-1335 (print), 1435-926X (electronic).

Harmon:1988:AIM

[167] Marion G. Harmon and Ted P. Baker. An Ada implementation of Marsaglia’s “universal” random number generator. ACM SIGADA Ada Letters, 8(2):110–112, March/April 1988. CODEN AALEE5. ISSN 1094-3641 (print), 1557-9476 (electronic).

Ferrenberg:1992:MCS

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/prl.aps.org/abstract/PRL/v69/i23/p3382_1. See also [200].

Peterson:1992:MCP

[169] I. Peterson. Monte Carlo physics: A cautionary lesson. Science News (Washington, DC), 142(25–26):422, December 19, 1992. CODEN SC-NEBK. ISSN 0036-8423 (print), 1943-0930 (electronic). URL http:// www.jstor.org/stable/4018020. Comment on negative experience with the Marsaglia–Zaman generator reported in [168]. See response [115].

Percus:1995:TAM

[170] Ora E. Percus and Paula A. Whitlock. Theory and application of Marsaglia’s monkey test for pseudorandom number generators. ACM Transactions on Modeling and Computer Simulation, 5(2):87–100, April 1995. CODEN ATMCEZ. ISSN 1049-3301 (print), 1558-1195 (electronic). See [116].

Dyadkin:1997:FEL

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URL http://www.cpc.cs.qub.ac.uk/cpc/;   http://www.cpc.cs.
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Dyadkin:1997:SBM

[172] Iosif G. Dyadkin and Kenneth G. Hamilton. A study of 64-bit multipliers for Lehmer pseudorandom number generators. Computer Physics Communications, 103(2–3):103–130, July 1997. CODEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (electronic).

Bach:1998:EPM

[173] Eric Bach. Efficient prediction of Marsaglia–Zaman random number generators. IEEE Transactions on Information Theory, 44(3):1253–1257, 1998. CODEN IETTAW. ISSN 0018-9448 (print), 1557-9654 (electronic).

Robert:1999:MCS

[174] Christian P. Robert and George Casella. Monte Carlo statistical methods. Springer texts in statistics. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1999. ISBN 0-387-98707-X. xxi + 507 pp. LCCN QA276 .R575 1999.

Dyadkin:2000:SBM

[175] Iosif G. Dyadkin and Kenneth G. Hamilton. A study of 128-bit multipliers for congruential pseudorandom number generators. Computer Physics Communications, 125(1–3):239–258, March 2000. CODEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (electronic). URL http://cpc.cs.

qub.ac.uk/summaries/ADLK;   http://www.elsevier.com/gej-ng//
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[176] Cleve B. Moler. Cleve’s corner: Normal behavior: Ziggurat algorithm generates normally distributed random numbers. Technical note, The Math-Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA, Spring

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Robert:2004:MCS

[177] Christian P. Robert and George Casella. Monte Carlo statistical methods. Springer texts in statistics. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., second edition, 2004. ISBN 0-387-21239-6. xxx + 645 pp. LCCN QA276

.R575 2004. URL http://www.loc.gov/catdir/enhancements/fy0818/
2004049157-d.html;   http://www.loc.gov/catdir/enhancements/
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Leong:2005:CIZ

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URL http://www.jstatsoft.org/counter.php?id=114&url=v12/i07&
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Panneton:2005:XRN

[179] François Panneton and Pierre L’Ecuyer. On the xorshift random number generators. ACM Transactions on Modeling and Computer Simulation, 15 (4):346–361, October 2005. CODEN ATMCEZ. ISSN 1049-3301 (print), 1558-1195 (electronic). See [144, 145, 187].

Tu:2005:SRD

[180] Shu-Ju Tu and Ephraim Fischbach. A study on the randomness of the digits of π. International Journal of Modern Physics C [Physics and Computers], 16(2):281–294, February 2005. CODEN IJMPEO. ISSN 0129-1831 (print), 1793-6586 (electronic). URL http://www.worldscinet.

com/ijmpc/16/1602/S01291831051602.html. The statistical analysis in

this work is flawed; see [151, 152].

Agapie:2010:RPH

[181] Stefan C. Agapie and Paula A. Whitlock. Random packing of hyperspheres and Marsaglia’s parking lot test. Monte Carlo Methods and Applications, 16(3–4):197–209, December 2010. CODEN MCMAC6. ISSN 0929-9629 (print), 1569-3961 (electronic). URL http://www.degruyter.com/view/

j/mcma.2010.16.issue-3-4/mcma.2010.019/mcma.2010.019.xml.

Anonymous:2011:OGM

[182] Anonymous. Obituary: George Marsaglia (1924–2011). Tallahassee Democrat, page ??, February 22, 2011. ISSN 0738-5153.

URL http://www.legacy.com/obituaries/tallahassee/obituary.
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[183] Greg Rose. KISS: A bit too simple. Report ??, Qualcomm Inc., ????,

April 18, 2011. URL http://eprint.iacr.org/2011/007.pdf.

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Saito:2012:DCS

[185] Mutsuo Saito and Makoto Matsumoto. A deviation of CURAND: Standard pseudorandom number generator in CUDA for GPGPU. Slides presented at the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, February 2012. URL http:

//www.mcqmc2012.unsw.edu.au/slides/MCQMC2012_Matsumoto.pdf.

Steele:2014:FSP

[186] Guy L. Steele, Jr., Doug Lea, and Christine H. Flood. Fast splittable pseudorandom number generators. ACM SIGPLAN Notices, 49(10):453– 472, October 2014. CODEN SINODQ. ISSN 0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic).

Vigna:2016:EEM

[187] Sebastiano Vigna. An experimental exploration of Marsaglia’s xorshift generators, scrambled. ACM Transactions on Mathematical Software, 42 (4):30:1–30:23, July 2016. CODEN ACMSCU. ISSN 0098-3500 (print),

1557-7295 (electronic). URL http://dl.acm.org/citation.cfm?id=
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[200] Peter Grassberger. On correlations in “good” random number generators. Physics Letters A, 181(1):43–46, September 27, 1993. CODEN PYLAAG. ISSN 0375-9601 (print), 1873-2429 (electronic). URL http:

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See [168].

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