=========================================================================
Date: Fri, 21 Feb 2003 10:34:27 -0500
Reply-To: "Chakravarthy, Venky" <Venky.Chakravarthy@PFIZER.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: "Chakravarthy, Venky" <Venky.Chakravarthy@PFIZER.COM>
Subject: Re: RAND function (was: Using a macro to simulate data)
Content-Type: text/plain; charset="iso-8859-1"
For folks who do not have V9, but are interested in seeing the documentation
it is freely available at the SAS site (after making a one time
registration). If you have already registered the link to the RAND function
is:
http://v9doc.sas.com/cgi-bin/sasdoc/cgigdoc?file=../lrdict.hlp/a001466748.ht
m
__________________________
Venky Chakravarthy
E-mail: swovcc@hotmail.com
-----Original Message-----
From: Pete Lund [mailto:pete.lund@NWCSR.COM]
Sent: Friday, February 21, 2003 10:27 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: Re: RAND function (was: Using a macro to simulate data)
Howard (and Ian)-
The V9 documentation for RAND is relatively extensive. Here's a
cut-and-paste from the on-line help - please note that the formula for
each distribution is given in the documentation but most are in graphic
form and don't come through in the text-based paste here:
Functions and CALL Routines
RAND Function
------------------------------------------------------------------------
--------
Generates random numbers from a specified distribution
Category: Random Number
------------------------------------------------------------------------
--------
Syntax
Arguments
Details
Reproducing a Random Number Stream
Bernoulli Distribution
Beta Distribution
Binomial Distribution
Cauchy Distribution
Chi-Square Distribution
Erlang Distribution
Exponential Distribution
F Distribution
Gamma Distribution
Geometric Distribution
Hypergeometric Distribution
Lognormal Distribution
Negative Binomial Distribution
Normal Distribution
Poisson Distribution
T Distribution
Tabled Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution
Examples
See Also
References
------------------------------------------------------------------------
--------
Syntax
RAND ('dist', parm-1, ... ,parm-k)
Arguments
'dist'
is a character string that identifies the distribution. Valid
distributions are as follows:
Distribution Argument
Bernoulli 'BERNOULLI'
Beta 'BETA'
Binomial 'BINOMIAL'
Cauchy 'CAUCHY'
Chi-Square 'CHISQUARE'
Erlang 'ERLANG'
Exponential 'EXPONENTIAL'
F 'F'
Gamma 'GAMMA'
Geometric 'GEOMETRIC'
Hypergeometric 'HYPERGEOMETRIC'
Lognormal 'LOGNORMAL'
Negative binomial 'NEGBINOMIAL'
Normal 'NORMAL'|'GAUSSIAN'
Poisson 'POISSON'
T 'T'
Tabled 'TABLE'
Triangular 'TRIANGLE'
Uniform 'UNIFORM'
Weibull 'WEIBULL'
Note: Except for T and F, you can minimally identify any distribution
by its first four characters.
parm-1, . . . ,parm-k
are shape, location, or scale parameters appropriate for the specific
distribution. See: Details for complete information about these
parameters
------------------------------------------------------------------------
--------
Details
The RAND function generates random numbers from various continuous and
discrete distributions. Wherever possible, the simplest form of the
distribution is used.
Reproducing a Random Number Stream
If you want to create reproducible streams of random numbers, then use
the CALL STREAMINT routine to specify a seed value for random number
generation. Do this once per DATA step before any invocation of the RAND
function. If you omit the call to the STREAMINIT routine (or if you
specify a non-positive seed value in the CALL STREAMINIT routine), then
RAND uses a call to the system clock to seed itself. For more
information, see CALL STREAMINT, Creating a Reproducible Stream of
Random Numbers.
Bernoulli Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('BERNOULLI',p)
where
x
is an observation from the distribution with the following probability
density function:
Range: x = 0, 1
p
is a numeric probability of success. Range: 0 p 1
Beta Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('BETA',a,b)
where
x
is an observation from the distribution with the following probability
density function:
Range: 0 < x < 1
a
is a numeric shape parameter. Range: a > 0
b
is a numeric shape parameter. Range: b > 0
Binomial Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('BINOMIAL',p,n)
where
x
is an integer observation from the distribution with the following
probability density function:
Range: x = 0, 1, ..., n
p
is a numeric probability of success. Range: 0 p 1
n
is an integer parameter that counts the number of independent Bernoulli
trials. Range: n = 1, 2, ...
Cauchy Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('CAUCHY')
where
x
is an observation from the distribution with the following probability
density function:
Range: - < x <
Chi-Square Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('CHISQUARE',df)
where
x
is an observation from the distribution with the following probability
density function:
Range: x > 0
df
is a numeric degrees of freedom parameter. Range: df > 0
Erlang Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('ERLANG',a)
where
x
is an observation from the distribution with the following probability
density function:
Range: x > 0
a
is an integer numeric shape parameter. Range: a = 1, 2, ...
Exponential Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('EXPONENTIAL')
where
x
is an observation from the distribution with the following probability
density function:
Range: x > 0
F Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('F',ndf, ddf)
where
x
is an observation from the distribution with the following probability
density function:
Range: x > 0
ndf
is a numeric numerator degrees of freedom parameter. Range: ndf > 0
ddf
is a numeric denominator degrees of freedom parameter. Range: ddf > 0
Gamma Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('GAMMA',a)
where
x
is an observation from the distribution with the following probability
density function:
Range: x > 0
a
is a numeric shape parameter. Range: a > 0
Geometric Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('GEOMETRIC',p)
where
x
is an integer observation from the distribution with the following
probability density function:
Range: x = 1, 2, ...
p
is a numeric probability of success. Range: 0 < p 1
Hypergeometric Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('HYPER',N,R,n)
where
x
is an integer observation from the distribution with the following
probability density function:
Range: x = max(0, (n - (N - R))), ..., min(n, R)
N
is an integer population size parameter. Range: N = 1, 2, ...
R
is an integer number of items in the category of interest. Range: R = 0,
1, ..., N
n
is an integer sample size parameter. Range: n = 1, 2, ..., N
The hypergeometric distribution is a mathematical formalization of an
experiment in which you draw n balls from an urn that contains N balls,
R of which are red. The hypergeometric distribution is the distribution
of the number of red balls in the sample of n.
Lognormal Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('LOGNORMAL')
where
x
is an observation from the distribution with the following probability
density function:
Range: x 0
Negative Binomial Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('NEGBINOMIAL',p,k)
where
x
is an integer observation from the distribution with the following
probability density function:
Range: x = 0, 1, ...
k
is an integer number parameter that counts the number of successes.
Range: k = 1, 2, ...
p
is a numeric probability of success. Range: 0 < p 1
The negative binomial distribution is the distribution of the number of
failures before k successes occur in sequential independent trials, all
with the same probability of success, p.
Normal Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('NORMAL',<, , >)
where
x
is an observation from the normal distribution with a mean of and a
standard deviation of , that has the following probability density
function:
Range: - < x <
is the mean parameter. Default: 0
is the standard deviation parameter. Default: 1
Range: > 0
Poisson Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('POISSON',m)
where
x
is an integer observation from the distribution with the following
probability density function:
Range: x = 0, 1, ...
m
is a numeric mean parameter. Range: m > 0
T Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('T',df)
where
x
is an observation from the distribution with the following probability
density function:
Range: - < x <
df
is a numeric degrees of freedom parameter. Range: df > 0
Tabled Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('TABLE',p1,p2, ...)
where
x
is an integer observation from one of the following distributions:
If , then x is an observation from this probability density function:
If for some index , then x is an observation from this probability
density function:
p1, p2, ...
are numeric probability values. Range: 0 p1, p2, ... 1
Restriction: The maximum number of probability parameters depends on
your operating environment, but the maximum number of parameters is at
least 32,767.
The tabled distribution takes on the values 1, 2, ..., n with specified
probabilities.
Note: By using the FORMAT statement, you can map the set {1, 2, ...,
n} to any set of n or fewer elements.
Triangular Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('TRIANGLE',h)
where
x
is an observation from the distribution with the following probability
density function:
where 0 h 1. Range: 0 x 1
Note: The distribution can be easily shifted and scaled.
h
is the horizontal location of the peak of the triangle. Range: 0 h 1
Uniform Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('UNIFORM')
where
x
is an observation from the distribution with the following probability
density function:
Range: 0 < x < 1
The uniform random number generator that the RAND function uses is the
Mersenne-Twister (Matsumoto and Nishimura 1998). This generator has a
period of and 623-dimensional equidistribution up to 32-bit accuracy.
This algorithm underlies the generators for the other available
distributions in the RAND function.
Weibull Distribution
------------------------------------------------------------------------
--------
Syntax
x = RAND('WEIBULL',a,b)
where
x
is an observation from the distribution with the following probability
density function:
Range: x 0
a
is a numeric shape parameter. Range: a > 0
b
is a numeric scale parameter. Range: b > 0
------------------------------------------------------------------------
--------
Examples
SAS Statements Results
x=rand('BERN',.75);
0
x=rand('BETA',3,0.1);
.99920
x=rand('BINOM',10,0.75);
10
x=rand('CAUCHY');
-1.41525
x=rand('CHISQ',22);
25.8526
x=rand('ERLANG', 7);
7.67039
x=rand('EXPO');
1.48847
x=rand('F',12,322);
1.99647
x=rand('GAMMA',7.25);
6.59588
x=rand('GEOM',0.02);
43
x=rand('HYPER',10,3,5);
1
x=rand('LOGN');
0.66522
x=rand('NEGB',5,0.8);
33
x=rand('NORMAL');
1.03507
x=rand('POISSON',6.1);
6
x=rand('T',4);
2.44646
x=rand('TABLE',.2,.5);
2
x=rand('TRIANGLE',0.7);
.63811
x=rand('UNIFORM');
.96234
x=rand('WEIB',0.25,2.1);
6.55778
------------------------------------------------------------------------
--------
See Also
CALL Routine: CALL STREAMINIT Routine
------------------------------------------------------------------------
--------
References
Fishman, G. S. 1996. Monte Carlo: Concepts, Algorithms, and
Applications.New York: Springer-Verlag.
Fushimi, M., and S. Tezuka. 1983. "The k-Distribution of Generalized
Feedback Shift Register Pseudorandom Numbers." Communications of the ACM
26: 516-523.
Gentle, J. E. 1998. Random Number Generation and Monte Carlo Methods.
New York: Springer-Verlag.
Lewis, T. G., and W. H. Payne. 1973. "Generalized Feedback Shift
Register Pseudorandom Number Algorithm." Journal of the ACM 20: 456-468.
Matsumoto, M., and Y. Kurita. 1992. "Twisted GFSR Generators." ACM
Transactions on Modeling and Computer Simulation 2: 179-194.
Matsumoto, M., and Y. Kurita. 1994. "Twisted GFSR Generators II." ACM
Transactions on Modeling and Computer Simulation 4: 254-266.
Matsumoto, M., and T. Nishimura. 1998. "Mersenne Twister: A
623-Dimensionally Equidistributed Uniform Pseudo-Random Number
Generator." ACM Transactions on Modeling and Computer Simulation 8:
3-30.
Ripley, B. D. 1987. Stochastic Simulation. New York: Wiley.
Robert, C. P., and G. Casella. 1999. Monte Carlo Statistical Methods.
New York: Springer-Verlag.
Ross, S. M. 1997. Simulation. San Diego: Academic Press.
