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