help random-number functions
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Title
[D] functions -- Functions
Description
This is a quick reference on functions for generating pseudorandom
variates. For help on all functions, see [D] functions. See [R] set
seed for setting the random-number seed.
Random-number functions
runiform()
Range: 0 to nearly 1 (0 to 1 - 2^(-32))
Description: returns uniform random variates.
runiform() returns uniformly distributed random variates
on the interval [0,1). runiform() takes no arguments,
but the parentheses must be typed. runiform() can be
seeded with the set seed command. (See matrix functions
for the related matuniform() matrix function.)
To generate random variates over the interval [a,b), use
a+(b-a)*runiform().
To generate random integers over [a,b], use
a+int((b-a+1)*runiform()).
rbeta(a, b)
Domain a: 0.05 to 1e+5
Domain b: 0.15 to 1e+5
Range: 0 to 1 (exclusive)
Description: returns beta(a,b) random variates, where a and b are the
beta distribution shape parameters.
Besides the standard methodology for generating random
variates from a given distribution, rbeta() uses the
specialized algorithms of Johnk (Gentle 2003), Atkinson
and Wittaker (1970, 1976), Devroye (1986), and Schmeiser
and Babu (1980).
rbinomial(n, p)
Domain n: 1 to 1e+11
Domain p: 1e-8 to 1-1e-8
Range: 0 to n
Description: returns binomial(n,p) random variates, where n is the
number of trials and p is the success probability.
Besides the standard methodology for generating random
variates from a given distribution, rbinomial() uses the
specialized algorithms of Kachitvichyanukul (1982),
Kachitvichyanukul and Schmeiser (1988), and Kemp (1986).
rchi2(df)
Domain df: 2e-4 to 2e+8
Range: 0 to c(maxdouble)
Description: returns chi-squared, with df degrees of freedom, random
variates.
rgamma(a, b)
Domain a: 1e-4 to 1e+8
Domain b: c(smallestdouble) to c(maxdouble)
Range: 0 to c(maxdouble)
Description: returns gamma(a,b) random variates, where a is the gamma
shape parameter and b is the scale parameter.
Methods for generating gamma variates are taken from
Ahrens and Dieter (1974), Best (1983), and Schmeiser and
Lal (1980).
rhypergeometric(N, K, n)
Domain N: 2 to 1e+6
Domain K: 1 to N-1
Domain n: 1 to N-1
Range: max(0,n-N+K) to min(K,n)
Description: returns hypergeometric random variates. The
distribution parameters are integer valued, where N is
the population size, K is the number of elements in the
population that have the attribute of interest, and n is
the sample size.
Besides the standard methodology for generating random
variates from a given distribution, rhypergeometric()
uses the specialized algorithms of Kachitvichyanukul
(1982) and Kachitvichyanukul and Schmeiser (1985).
rnbinomial(n, p)
Domain n: 0.1 to 1e+5
Domain p: 1e-4 to 1-1e-4
Range: 0 to 2^53-1
Description: returns negative binomial random variates. If n is
integer valued, rnbinomial() returns the number of
failures before the nth success, where the probability
of success on a single trial is p. n can also be
nonintegral.
rnormal()
Range: c(mindouble) to c(maxdouble)
Description: returns standard normal (Gaussian) random variates,
i.e., variates from a normal distribution with a mean of
0 and a standard deviation of 1.
rnormal(m)
Domain m: c(mindouble) to c(maxdouble)
Range: c(mindouble) to c(maxdouble)
Description: returns normal(m,1) (Gaussian) random variates, where m
is the mean and the standard deviation is 1.
rnormal(m, s)
Domain m: c(mindouble) to c(maxdouble)
Domain s: c(smallestdouble) to c(maxdouble)
Range: c(mindouble) to c(maxdouble)
Description: returns normal(m,s) (Gaussian) random variates, where m
is the mean and s is the standard deviation.
The methods for generating normal (Gaussian) random
variates are taken from Knuth (1998, 122-128);
Marsaglia, MacLaren, and Bray (1964); and Walker (1977).
rpoisson(m)
Domain m: 1e-6 to 1e+11
Range: 0 to 2^53-1
Description: returns Poisson(m) random variates, where m is the
distribution mean.
Poisson variates are generated using the probability
integral transform methods of Kemp and Kemp (1990,
1991), as well as the method of Kachitvichyanukul
(1982).
rt(df)
Domain df: 1 to 2^53-1
Range: c(mindouble) to c(maxdouble)
Description: returns Student's t random variates, where df is the
degrees of freedom.
Student's t variates are generated using the method of
Kinderman and Monahan (1977, 1980).
References
Ahrens, J. H., and U. Dieter. 1974. Computer methods for sampling from
gamma, beta, Poisson, and binomial distributions. Computing 12:
223-246.
Atkinson, A. C., and J. Whittaker. 1976. A switching algorithm for the
generation of beta random variables with at least one parameter less
than 1. Journal of the Royal Statistical Society, Series A 139:
462-467.
------. 1970. Algorithm AS 134: The generation of beta random variables
with one parameter greater than and one parameter less than 1.
Applied Statistics 28: 90-93.
Best, D. J. 1983. A note on gamma variate generators with shape
parameters less than unity. Computing 30: 185-188.
Devroye, L. 1986. Non-uniform Random Variate Generation. New York:
Springer.
Gentle, J. E. 2003. Random Number Generation and Monte Carlo Methods.
2nd ed. New York: Springer.
Kachitvichyanukul, V. 1982. Computer Generation of Poisson, Binomial,
and Hypergeometric Random Variables. PhD thesis, Purdue University.
Kachitvichyanukul, V., and B. Schmeiser. 1985. Computer generation of
hypergeometric random variates. Journal of Statistical Computation
and Simulation 22: 127-145.
------. 1988. Binomial random variate generation. Communications of
the Association for Computing Machinery 31: 216-222.
Kemp, C. D. 1986. A modal method for generating binomial variates.
Communications in Statistics: Theory and Methods 15: 805-813.
Kemp, A. W., and C. D. Kemp. 1990. A composition-search algorithm for
low-parameter Poisson generation. Journal of Statistical Computation
and Simulation 35: 239-244.
Kemp, C. D., and A. W. Kemp. 1991. Poisson random variate generation.
Applied Statistics 40: 143-158.
Kinderman, A. J., and J. F. Monahan. 1977. Computer generation of
random variables using the ratio of uniform deviates. Association
for Computing Machinery Transactions on Mathematical Software 3:
257-260.
------. 1980. New methods for generating Student's t and gamma
variables. Computing 25: 369-377.
Knuth, D. 1998. The Art of Computer Programming, Volume 2:
Seminumerical Algorithms. 3rd ed. Reading, MA: Addison Wesley.
Marsaglia, G., M. D. MacLaren, and T. A. Bray. 1964. A fast procedure
for generating normal random variables. Communications of the ACM 7:
4-10.
Schmeiser, B. W., and A. J. G. Babu. 1980. Beta variate generation via
exponential majorizing functions. Operations Research 28: 917-926.
Schmeiser, B. W., and R. Lal. 1980. Squeeze methods for generating gamma
variates. Journal of the American Statistical Association 75:
679-682.
Walker, A. J. 1977. An efficient method for generating discrete random
variables with general distributions. ACM Transactions on
Mathematical Software 3: 253-256.
Also see
Manual: [D] functions
Help: [D] drawnorm,
[D] egen
