Undergraduate textbooks on probability and statistics typically prove theorems that show how the variance of a sum of random variables is related to the variance of the original variables and the covariance between them. For example, the Wikipedia article on Variance contains an equation for the sum of two random
A SAS programmer wanted to compute the distribution of X-Y, where X and Y are two beta-distributed random variables. Pham-Gia and Turkkan (1993) derive a formula for the PDF of this distribution. Unfortunately, the PDF involves evaluating a two-dimensional generalized hypergeometric function, which is not available in all programming languages.
In applied mathematics, there is a large collection of "special functions." These function appera in certain applications, often as the solution to a differential equation, but also in the definition of probability distributions. For example, I have written about Bessel functions, the complete and incomplete gamma function, and the complete
The metalog family of distributions (Keelin, Decision Analysis, 2016) is a flexible family that can model a wide range of continuous univariate data distributions when the data-generating mechanism is unknown. This article provides an overview of the metalog distributions. A subsequent article shows how to download and use a library
A SAS programmer asked for help to simulate data from a distribution that has certain properties. The distribution must be supported on the interval [a, b] and have a specified mean, μ, where a < μ < b. It turns out that there are infinitely many distributions that satisfy these
You can use a Markov transition matrix to model the transition of an entity between a set of discrete states. A transition matrix is also called a stochastic matrix. A previous article describes how to use transition matrices for stochastic modeling. You can estimate a Markov transition matrix by using
SAS programmers love to make special graphs for Valentine's Day. In fact, there is a long history of heart-shaped graphs and love-inspired programs written in SAS! Last year, I added to the collection by showing how a ball bounces on a heart-shaped billiards table. This year, I create a similar
This article is about how to use Git to share SAS programs, specifically how to share libraries of SAS IML functions. Some IML programmers might remember an earlier way to share libraries of functions: SAS/IML released "packages" in SAS 9.4m3 (2015), which enable you to create, document, share, and use
SAS supports the ColorBrewer system of color palettes from the ColorBrewer website (Brewer and Harrower, 2002). The ColorBrewer color ramps are available in SAS by using the PALETTE function in SAS IML software. The PALETTE function supports all ColorBrewer palettes, but some palettes are not interpretable by people with color
Did you know that about 8% of the world's men are colorblind? (More correctly, 8% of men are "color vision deficient," since they see colors, but not all colors.) Because of the "birthday paradox," in a room that contains eight men, the probability is 50% that at least one is
