A SAS customer asks: How do I use SAS to generate multiple samples of size N from a multivariate normal distribution? Suppose that you want to simulate k samples (each with N observations) from a multivariate normal distribution with a given mean vector and covariance matrix. Because all of the
I have previously written about how to use the "table" distribution to generate random values from a discrete probability distribution. For example, if there are 50 black marbles, 20 red marbles, and 30 white marbles in a box, the following SAS/IML program simulates random draws (with replacement) of 1,000 marbles:
I wanted to write a blog post about the "Table distribution" in SAS. The Table distribution, which is supported by the RAND and the RANDGEN function, enables you to specify the probability of selecting each of k items. Therefore you can use the Table distribution to sample, with replacement, from
A while ago I saw a blog post on how to simulate Bernoulli outcomes when the probability of generating a 1 (success) varies from observation to observation. I've done this often in SAS, both in the DATA step and in the SAS/IML language. For example, when simulating data that satisfied
Last week I wrote about using acceptance-rejection algorithms in vector languages to simulate data. The main point I made is that in a vector language it is efficient to generate many more variates than are needed, with the knowledge that a certain proportion will be rejected. In last week's article,
A few days ago on the SAS/IML Support Community, there was an interesting discussion about how to simulate data from a truncated Poisson distribution. The SAS/IML user wanted to generate values from a Poisson distribution, but discard any zeros that are generated. This kind of simulation is known as an
I recently encountered a SUGI30 paper by Chuck Kincaid entitled "Guidelines for Selecting the Covariance Structure in Mixed Model Analysis." I think Kincaid does a good job of describing some common covariance structures that are used in mixed models. One of the many uses for SAS/IML is as a language
There are a lot of useful probability distributions that are not featured in standard statistical textbooks. Some of them have distinctive names. In the past year I have had contact with SAS customers who use the Tweedie distribution, the slash distribution, and the PERT distribution. Often these distributions are used
It is easy to simulate data that is uniformly distributed in the unit cube for any dimension. However, it is less obvious how to generate data in the unit simplex. The simplex is the set of points (x1,x2,...,xd) such that Σi xi = 1 and 0 ≤ xi ≤ 1
I was recently flipping through Ross' Simulation (2006, 4th Edition) and saw the following exercise: Let N be the minimum number of draws from a uniform distribution [until the sum of the variates]exceeds 1. What is the expected value of N? Write a simulation to estimate the expected value. For
