The first P1 is the seed (x0) and determines the sequence of
numbers generated, whereas the P2, N and the subsequent P1 values
determine the characteristics of the PRNGs. The “mod N” signifies
that the preceding portion of the equation is divided by N and the
remainder calculated to produce the first random number. The first
random number becomes the P1 value for the second iteration of
the equation to produce the second random number, and so on.
Other computational methods to generate PRNGs use probability
functions. For example, SAS can use the standard normal distribu-
tion with a seed. The program and output are shown in Figure 3.
For sampling from multivariate distributions, functions such as
randnormal, randmvt and randmultinomial can be used to generate samples from multivariate normal, multivariate Student’s t and
multinomial distributions, respectively.
Random sampling from a finite data set is used to determine
conformance to specifications. A program and output using Proc
Figure 5: A setup to generate 500 runs using a response y with 2
factors x1 and x2 and random noise from a normal distribution for
each factor and random noise in the response.
Figure 4: Using Proc surveyselect in SAS