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Random number transform methods
  Compares random number transform methods (and makes a graph) for a Gaussian variable.
2024.Nov.25 04:42:33
ntrials × 106 No. of trials from distribution (→ ≤ 2 M). •
method Method of transformation. •
.repeat Repeatability (0 | 1: yes | no).
klasses, ymax No. of classes (points) for graph; and max. y (automatic iff 0). •
.L, U Lower and upper limits for probability verification.
Show values Show the values of the graph coordinates.
  Makes a histogram from a standard Gaussian variable for comparison of random number transform methods. These are: (0) inversion method; (1) acceptance-rejection method; (2) Box-Muller method; and (3) ditto, modified.
  For '(1)', the majorizing function is just a uniform in (−6, +6), which yields a large rejection rate, [6 − (−6)] ⁄ √(2 π) − 1 ~= 3.8.
  (The ymax = 0.45 is suggested so as to span 1 ⁄ √(2π) ~= 0.399 .)
References:

• Fishman, George S., 1978 (2004), "Principles of discrete event simulation", John Wiley & Sons, New York, NY (USA) (ISBN 0-471-04395-8; IST-B. Mat.-BC QA276/1.Fis.30389), Ch. 9, "Sampling on a computer", pp 392–433.

• Box, G. E. P. and M. E. Muller, 1958, "A note on the generation of random normal deviates", Ann. Math. Stat., 29, pp 610–612.

• Weisstein, Eric W., Box-Muller Transformation. From MathWorld--A Wolfram Web Resource [on 'Created' date].

• Random Number Bibliography, RandomNumber.org .

• Scott, David W., 1992, "Multivariate density estimation: theory, practice, and visualization", John Wiley, New York, NY (IST-B. Mat.-BC QA276.7-.8.SCO.47011)

• 1832-01-27: Dodgson, Charles Lutwidge (Lewis Carroll).

 
 
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Created: 2008-01-27 — Last modified: 2018-11-19