As mentioned in my article about Monte Carlo estimate of (one-dimensional) integrals, one of the advantages of Monte Carlo integration is that you can perform multivariate integrals on complicated regions. This article demonstrates how to use SAS to obtain a Monte Carlo estimate of a double integral over rectangular and

## Tag: **Simulation**

A previous article shows how to use Monte Carlo simulation to estimate a one-dimensional integral on a finite interval. A larger random sample will (on average) result in an estimate that is closer to the true value of the integral than a smaller sample. This article shows how you can

Numerical integration is important in many areas of applied mathematics and statistics. For one-dimensional integrals on the interval (a, b), SAS software provides two important tools for numerical integration: For common univariate probability distributions, you can use the CDF function to integrate the density, thus obtaining the probability that a

In a previous article, I showed how to generate random points uniformly inside a d-dimensional sphere. In that article, I stated the following fact: If Y is drawn from the uncorrelated multivariate normal distribution, then S = Y / ||Y|| has the uniform distribution on the unit sphere. I was

Imagine an animal that is searching for food in a vast environment where food is scarce. If no prey is nearby, the animal's senses (such as smell and sight) are useless. In that case, a reasonable search strategy is a random walk. The animal can choose a random direction, walk/swim/fly

Do you know that you can create a vector that has a specific correlation with another vector? That is, given a vector, x, and a correlation coefficient, ρ, you can find a vector, y, such that corr(x, y) = ρ. The vectors x and y can have an arbitrary number

When there are two equivalent ways to do something, I advocate choosing the one that is simpler and more efficient. Sometimes, I encounter a SAS program that simulates random numbers in a way that is neither simple nor efficient. This article demonstrates two improvements that you can make to your

The skewness of a distribution indicates whether a distribution is symmetric or not. The Wikipedia article about skewness discusses two common definitions for the sample skewness, including the definition used by SAS. In the middle of the article, you will discover the following sentence: In general, the [estimators]are both biased

The triangulation theorem for polygons says that every simple polygon can be triangulated. In fact, if the polygon has V vertices, you can decompose it into V-2 non-overlapping triangles. In this article, a "polygon" always means a simple polygon. Also, a "random point" means one that is drawn at random

How can you efficiently generate N random uniform points in a triangular region of the plane? There is a very cool algorithm (which I call the reflection method) that makes the process easy. I no longer remember where I saw this algorithm, but it is different from the "weighted average"