Finding the root (or zero) of a function is an important computational task because it enables you to solve nonlinear equations. I have previously blogged about using Newton's method to find a root for a function of several variables. I have also blogged about how to use the bisection method
While sorting through an old pile of papers, I discovered notes from a 2012 SAS conference that I had attended. Next to the abstract for one presentation, I had scrawled a note to myself that read "BLOG about the incomplete beta function!" Okay, Rick, whatever you say! In statistics, the
This is the last post in my recent series of articles on computing contours in SAS. Last month a SAS customer asked how to compute the contours of the bivariate normal cumulative distribution function (CDF). Answering that question in a single blog post would have resulted in a long article,
I'm spoiled by the internet. I've grown so accustomed to being able to instantly find an answer to any query—no matter how obscure—that I am surprised when I don't find what I am looking for. The other day I was trying to find a mathematical result: a formula for the
Like many other computer packages, SAS can produce a contour plot that shows the level sets of a function of two variables. For example, I've previously written blogs that use contour plots to visualize the bivariate normal density function and to visualize the cumulative normal distribution function. However, sometimes you
In a previous post, I showed how to solve differential equations in SAS by using the ODE subroutine in the SAS/IML language, which solves initial value problems. This article describes how to draw phase portraits for two classic differential equations: the equations of motion for the simple harmonic oscillator and
Differential equations arise in the modeling of many physical processes, including mechanical and chemical systems. You can solve systems of first-order ordinary differential equations (ODEs) by using the ODE subroutine in the SAS/IML language, which solves initial value problems. This article uses the equations of motion for the classic simple
Finding the maximum value of a function is an important task in statistics. There are three approaches to finding a maxima: When the function is available as an analytic expression, you can use an optimization algorithm to find the maxima. For example, in the SAS/IML language, you can use any
The truncated normal distribution TN(μ, σ, a, b) is the distribution of a normal random variable with mean μ and standard deviation σ that is truncated on the interval [a, b]. I previously blogged about how to implement the truncated normal distribution in SAS. A friend wanted to simulate data
As I wrote in my previous post, a SAS customer noticed that he was getting some duplicate values when he used the RAND function to generate a large number of random uniform values on the interval [0,1]. He wanted to know if this result indicates a bug in the RAND
