A set of continuous univariate pseudo-random number generation routines for use in computer simulation

Hall, D.E. 1992. A set of continuous univariate pseudo-random number generation routines for use in computer simulation. M.S. thesis. Moscow, ID: University of Idaho. 98 p.

Keywords: random number generator, beta distribution, triangular distribution, lognormal distribution

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Abstract: Many existing pseudo-random number generators in commercial software and textbooks are bad. I studied the literature to compare methods used in generators of various distribution types, and compiled a set of "good" functions which return pseudo-random independent sequences of numbers fitting the standard uniform, triangular, general normal, lognormal, exponential and beta distributions. They have a consistent calling convention, are intended to be portable across hardware and software, are coded in a high-level language, produce theoretically defensible results and allow easy splitting of the sequences into disjoint subsequences.

I have described the computational model and given algorithms in BASIC for each distribution type. Discussion of each distribution type also includes a review of other generation methods. A test result is given in the comments of the code for each generator to help the user ensure that the routines have been implemented correctly on his or her system.

Plots of running values of mean and variance from returned sequences of 2 to 600 values for each generator show visually the sensitivity of the generators to number of samples. These plots for the uniform generator for different seed values also show its sensitivity to seed value.

The pseudo-random uniform generator routine is also coded in APL, C, and FORTRAN.

Moscow FSL publication no. 1992b