Bernoulli Distribution

The random sample is from the probability density function:

is in the range:

is the success probability, with range:

Beta Distribution

The random sample is from the probability density function:

is in the range:

and are shape parameters, with range: and

Binomial Distribution

The random sample is from the probability density function:

is in the range:

is a success probability, with range:

specifies the number of independent trials, with range:

Cauchy Distribution

The random sample is from the probability density function:

is in the range:

Chi-Square Distribution

The random sample is from the probability density function:

is in the range:

is degrees of freedom, with range:

Erlang Distribution

The random sample is from the probability density function:

is in the range:

is an integer shape parameter, with range:

Exponential Distribution

The random sample is from the probability density function:

is in the range:

F Distribution ()

The random sample is from the probability density function:

is in the range:

and are degrees of freedom, with range: and

Gamma Distribution

The random sample is from the probability density function:

is in the range:

is a shape parameter:

Geometric Distribution

The random sample is from the probability density function:

is in the range:

is the success probability, with range:

Hypergeometric Distribution

The random sample is from the probability density function:

is in the range:

is the population size, with range:

is the size of the category of interest, with range:

is the sample size, with range:

Lognormal Distribution

The random sample is from the probability density function:

is in the range:

Negative Binomial Distribution

The random sample is from the probability density function:

is in the range:

is the success probability with range:

is an integer number that counts the number of successes, with range:

Normal Distribution

The random sample is from the probability density function:

is in the range:

is the mean, with range: . This parameter is optional and defaults to 0.

is the standard deviation, with range: . This parameter is optional and defaults to 1.

Poisson Distribution

The random sample is from the probability density function:

is in the range:

is the mean, with range

T Distribution

The random sample is from the probability density function:

is in the range:

is the degrees of freedom, with the range:

Table Distribution

The random sample is from the probability density function:

where is a vector of probabilities, such that , and is the largest integer such that and

Triangle Distribution

The random sample is from the probability density function:

is in the range:

is the horizontal location of the peak of the triangle, with range:

Uniform Distribution

The random sample is from the probability density function:

is in the range:

Weibull Distribution

The random sample is from the probability density function:

is in the range:

and are shape parameters, with range and

The following table describes how parameters of the RANDGEN call correspond to the distribution parameters.

In practice, distname can be in lowercase or uppercase, and you only need to specify enough letters to distinguish one distribution from the others. For example,

   /* generate 10 samples from a Bernoulli distribution */
   r = j(10, 1, .);         /* allocate room for samples */
   call randgen(r,"ber",p);

Except for the normal distribution, you must specify the parameters listed for each of the preceding distributions. For the normal distribution, default values of and are used if none are supplied.

The following example illustrates the use of the RANDGEN call.

   call randseed(12345);

   /* get four random observations from each distribution */
   x = j(1, 4, .);
   /* each row of m comes from a different distribution */
   m = j(20, 4, .);
   call randgen(x, 'BERN', 0.75);
   m[1, ] = x;
   call randgen(x, 'BETA', 3, 0.1);
   m[2, ] = x;
   call randgen(x, 'BINOM', 10, 0.75);
   m[3, ] = x;
   call randgen(x, 'CAUCHY');
   m[4, ] = x;
   call randgen(x, 'CHISQ', 22);
   m[5, ] = x;
   call randgen(x, 'ERLANG',  7);
   m[6, ] = x;
   call randgen(x, 'EXPO');
   m[7, ] = x;
   call randgen(x, 'F', 12, 322);
   m[8, ] = x;
   call randgen(x, 'GAMMA', 7.25);
   m[9, ] = x;
   call randgen(x, 'GEOM', 0.02);
   m[10, ] = x;
   call randgen(x, 'HYPER', 10, 3, 5);
   m[11, ] = x;
   call randgen(x, 'LOGN');
   m[12, ] = x;
   call randgen(x, 'NEGB', 0.8, 5);
   m[13, ] = x;
   call randgen(x, 'NORMAL'); /* default parameters */
   m[14, ] = x;
   call randgen(x, 'POISSON', 6.1);
   m[15, ] = x;
   call randgen(x, 'T', 4);
   m[16, ] = x;
   p = {0.1 0.2 0.25 0.1 0.15 0.1 0.1};
   call randgen(x, 'TABLE', p);
   m[17, ] = x;
   call randgen(x, 'TRIANGLE', 0.7);
   m[18, ] = x;
   call randgen(x, 'UNIFORM');
   m[19, ] = x;
   call randgen(x, 'WEIB', 0.25, 2.1);
   m[20, ] = x;
   print m;

The output is as follows:

                       M

             1         0         1         0
             1 0.9999234 0.9842784 0.9997739
             7         8         5        10
     -1.209834 3.9732282 -0.048339 -1.337284
     30.300691 20.653151 27.301922 26.878221
     10.636299 4.6455449 7.5284821 2.5558646
     0.2449632 2.7656037 4.2254588 0.2866158
     0.7035829 1.2676112 0.9806787 1.4811389
      8.475216 8.8723256 8.2993617 8.0409742
           109         4        33        30
             1         1         2         1
     0.7784513 0.9792472 0.6018993 0.3643607
             3         2         0         2
     0.0053637 1.4026784 -0.271338 -0.416685
             5        11         8         4
     1.3237918 0.0505162 -0.660845 -0.634447
             2         3         2         3
     0.5270875 0.6909336 0.8607548 0.5450831
     0.4064393 0.7464901 0.3463207 0.2615394
     0.4183405 0.9981923 16.812803 0.0001131