```.-
help for random number generators                update from STB-28: sg44
.-                                                    Hilbe/Linde-Zwirble

Current as of 15May2000
Random number generators
-------------------------

[noncentral] Student's t:   ^rndt^ obs df [delta]
Example: rndt 10000 10
rndt 10000 10 3

[noncentral] Chi-square:   ^rndchi^ obs df [lambda]
Example: rndchi 10000 4
rndchi 10000 4 3

[noncentral] F:   ^rndf^ obs df_numer df_denom [lambda]
Example: rndf 10000 4 15
rndf 10000 4 15 3

log normal:   ^rndlgn^ obs mean stddev
Example: rndlgn 10000 0 0.5

Poisson:   ^rndpoi^ obs mean
^rndpoix^ [ mu ]
Example: rndpoi 10000 4
rndpoix mu

Poisson:   ^rndpod^ obs mean dispersion
(ovedispersed)   ^rndpodx^ [mu], s(#)
Example: rndpod 10000 4 1.2
rndpodx mu, s(1.2)

binomial:   ^rndbin^ obs prob numb
^rndbinx^ [ prob ] den
Example: rndbin 10000 0.5 1
rndbinx mu den
Note: mu = variable with p values
den = case denominator (1=binary)

negative binomial:   ^rndnbx^ [mu] , k(#)
Example: rndnblx mu, k(0.5)

Gamma:   ^rndgam^ obs shape scale
^rndgamx^ [mu], s(#)
Example: rndgam 10000 4 2
rndgamx mu, s(1)
Note: s(1) specifies a shape parameter of 1;
the scale is calculated from mu*shape

inverse Gaussian:   ^rndivg^ obs mean sigma
^rndivgx^ [mu], s(#)
Example: rndivg 10000 10 0.05
rndivgx mu, s(0.05)
Note: mu = 1/sqrt(eta)
variance = sigma^2*mu*3

exponential:   ^rndexp^ obs shape
Example: rndexp 10000 3

Weibull:   ^rndwei^ obs shape scale
Example: rndwei 10000 3 2

Beta binomial:   ^rndbb^ obs denom prob k
Example: 10000 200 0.2 0.05
Note: prob= p = a1/(a1+a2)
k = dispersion = 1/(a1+a2+1)
This generator will return beta-binomial random
deviates within the following constraints. Although
k can take any value from 0 to 1, in this program
k is limited because of the volatility of the
distribution outside this range of k. k must be as
follows: k< the lessor of p' and (1-p')/2 where p'=p
if p<0.5, else p'=1-p. This should work well within
the physical representation of an overdispersed binomial.

Generalized logistic:   ^rndglog^ obs L A T
(3 parameter)     Example: rndglog 10000 3.0 0.7 4.5
Note: L = (long) right hand tail
A = (alpha) left hand tail
T = (time) position parameter
Based on Fit-Meister (W. Linde-Zwirble)

Description
------------

The programs listed above generate random numbers for a variety of important
distributions.  In the syntax diagrams, ^obs^ indicates the number of
observations to be generated.  The other parameters are self-explanatory.
Commands whose names end in ^x^ provide the capability to model a complete
synthetic data set.

Examples of Constructing a Data Set
------------------------------------

Constructed Poisson data set with parameters of:
_b[0] =   1
_b[1] =   0.5
_b[2] =  -0.25

. ^set obs 50000^                          [data set of size 50,000]
. ^generate x1 = abs(invnorm(uniform())^   [variable 1]
. ^generate x2 = abs(invnorm(uniform())^   [variable 2]
. ^generate lp = 1 + .5*x1 - .25*x2^       [linear predictor]
. ^generate mu = exp(lp)^                  [inverse link]
. ^rndpoix mu^

See STB28 (sg44) article for details and other examples.

Note: Noncentrality parameters have been added to the following RNG's"
^t^, ^f^, and ^chi2^. My thanks to Thomas Steichen for this addition.

Contact
--------
^Joseph Hilbe^
Arizona State University
jhilbe@@aol.com
or  hilbe@@asu.edu

```