There are several ways to simulate multinomial data in SAS. In the SAS/IML matrix language, you can use the RANDMULTINOMIAL function to generate samples from the multinomial distribution. If you don't have a SAS/IML license, I have previously written about how to use the SAS DATA step or PROC SURVEYSELECT
Today is March 14th, which is annually celebrated as Pi Day. Today's date, written as 3/14/16, represents the best five-digit approximation of pi. On Pi Day, many people blog about how to approximate pi. This article uses a Monte Carlo simulation to estimate pi, in spite of the fact that
Many simulation and resampling tasks use one of four sampling methods. When you draw a random sample from a population, you can sample with or without replacement. At the same time, all individuals in the population might have equal probability of being selected, or some individuals might be more likely
How do you sample with replacement in SAS when the probability of choosing each observation varies? I was asked this question recently. The programmer thought he could use PROC SURVEYSELECT to generate the samples, but he wasn't sure which sampling technique he should use to sample with unequal probability. This
The FREQ procedure in SAS supports computing exact p-values for many statistical tests. For small and mid-sized problems, the procedure runs very quickly. However, even though PROC FREQ uses efficient methods to avoid unnecessary computations, the computational time required by exact tests might be prohibitively expensive for certain tables. If
How do you simulate a contingency table that has a specified row and column sum? Last week I showed how to simulate a random 2 x 2 contingency table when the marginal frequencies are specified. This article generalizes to random r x c frequency tables (also called cross-tabulations) that have the same marginal row
When modeling and simulating data, it is important to be able to articulate the real-life statistical process that generates the data. Suppose a friend says to you, "I want to simulate two random correlated variables, X and Y." Usually this means that he wants data generated from a multivariate distribution,
You can use SAS to generate random integers between 1–10 or in the range 1–100. This article shows how to generate random integers as easily as Excel does. I was recently talking with some SAS customers and I was asked "Why can't SAS create an easy way to generate random
In a previous post I described how to simulate random samples from an urn that contains colored balls. The previous article described the case where the balls can be either of two colors. In that csae, all the distributions are univariate. In this article I examine the case where the
If not for probability theory, urns would appear only in funeral homes and anthologies of British poetry. But in probability and statistics, urns are ever present and contain colored balls. The removal and inspection of colored balls from an urn is a classic way to demonstrate probability, sampling, variation, and
