Generation of Continuous Multivariate Distributions for Statistical Applications

SYNOPTIC ABSTRACTTwo general and several specific schemes are described for generating variates from continuous multivariate distributions. Algorithms are provided for the multivariate normal, Johnson system, Cauchy, elliptically contoured (including Pearson Types II and VII), Morgenstern, Plackett, Ali, Gumbel, Burr (and related), Beta-Stacy and Khintchine distributions. Issues in designing multivariate Monte Carlo studies are discussed.

[1]  I. J. Schoenberg.  Metric spaces and completely monotone functions , 1938 .

[2]  Koiti Takahasi,et al.  Note on the multivariate burr’s distribution , 1965 .

[3]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[4]  N L JOHNSON,et al.  Bivariate distributions based on simple translation systems. , 1949, Biometrika.

[5]  Leon Jay Gleser.  A Canonical Representation for the Noncentral Wishart Distribution Useful for Simulation , 1976 .

[6]  P. Odell,et al.  A Numerical Procedure to Generate a Sample Covariance Matrix , 1966 .

[7]  Mir M. Ali,et al.  A class of bivariate distri-butions including the bivariate logistic , 1978 .

[8]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[9]  M. Chmielewski.  A re-appraisal of tests for normality , 1981 .

[10]  R. Plackett.  A Class of Bivariate Distributions , 1965 .

[11]  A. Afifi,et al.  On Tests for Multivariate Normality , 1973 .

[12]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[13]  D. Stoller,et al.  On the Generation of Normal Random Vectors , 1962 .

[14]  K. Mardia,et al.  Some contributions to contingency-type bivariate distributions. , 1967, Biometrika.

[15]  I. W. Burr.  Cumulative Frequency Functions , 1942 .

[16]  G. A. Mihram,et al.  A Bivariate Warning-Time/Failure-Time Distribution , 1967 .

[17]  Dallas Johnson,et al.  Procedures to generate random matrices with noncentral distributions , 1974 .

[18]  V. Klema.  LINPACK user's guide , 1980 .

[19]  Mervin E. Muller,et al.  A note on a method for generating points uniformly on n-dimensional spheres , 1959, CACM.

[20]  Yoshihiro Tashiro,et al.  On methods for generating uniform random points on the surface of a sphere , 1977 .

[21]  A. C. Atkinson,et al.  The handbook of random number generation and testing with Testrand computer code , 1981 .

[22]  M. E. Johnson,et al.  A Bivariate Distribution Family with Specified Marginals , 1981 .

[23]  J. G. Ramage,et al.  Computer methods for sampling from student's t distribution , 1977 .

[24]  M. E. Johnson,et al.  A Family of Distributions for Modelling Non‐Elliptically Symmetric Multivariate Data , 1981 .

[25]  Mark E. Johnson.  C137. Computer generation of the generalized eyraud distribution , 1982 .

[26]  Douglas M. Hawkins,et al.  A new test for multivariate normality and homoscedasticity , 1981 .

[27]  G. Simons,et al.  On the theory of elliptically contoured distributions , 1981 .

[28]  E. Gumbel.  Bivariate Exponential Distributions , 1960 .

[29]  T. A. Bray,et al.  A Convenient Method for Generating Normal Variables , 1964 .

[30]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[31]  J. Wahrendorf.  Inference in contingency tables with ordered categories using Plackett's coefficient of association for bivariate distributions , 1980 .

[32]  Mark E. Johnson,et al.  Constructing and simulating multivariate distributions using khintchine's theorem , 1982 .

[33]  M. E. Johnson,et al.  A Ranking Procedure for Partial Discriminant Analysis , 1981 .

[34]  M. A. Chmielewski,et al.  Elliptically Symmetric Distributions: A Review and Bibliography , 1981 .

[35]  Bruce W. Schmeiser,et al.  Bivariate Gamma Random Vectors , 1982, Oper. Res..

[36]  J. Ramberg,et al.  The johnson translation system in monte carlo studies , 1982 .

[37]  Stamatis Cambanis.  Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions , 1977 .

[38]  Mark E. Johnson,et al.  Complete guide to gamma variate generation , 1981 .