Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
A convolution is a mathematical operation on two discrete sequences (or continuous functions) that produces a new sequence (or function). In probability and statistics, a convolution is closely associated with the concept of a "moving window," which time series analysts often call a "filter." If you have ever smoothed a
While researching a topic in probability, I encountered a special mathematical function that I had not previously known about. The function is called Owen's T function (Owen, 1956, Ann. Math. Stat.). It is useful for computing multivariate probabilities, for defining the skew-normal distribution, and for computing probabilities associated with certain
I write a lot of Monte Carlo simulations. This article discusses how to assess whether two independent Monte Carlo estimates are close to each other. This result can be used to test the correctness of a Monte Carlo simulation. It can also be used to compare different Monte Carlo algorithms
