.-
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   
     
