This is my Pi Day post for 2021. Every year on March 14th (written 3/14 in the US), geeky mathematicians and their friends celebrate "all things pi-related" because 3.14 is the three-decimal approximation to pi. Most years I write about lower-case pi (π), which is the ratio of a circle's
Finite-precision computations can be tricky. You might know, mathematically, that a certain result must be non-negative or must be within a certain interval. However, when you actually compute that result on a computer that uses finite-precision, you might observe that the value is slightly negative or slightly outside of the
Finding the root (or zero) of a nonlinear function is an important computational task. In the case of a one-variable function, you can use the SOLVE function in PROC FCMP to find roots of nonlinear functions in the DATA step. This article shows how to use the SOLVE function to
If you have ever run a Kolmogorov-Smirnov test for normality, you have encountered the Kolmogorov D statistic. The Kolmogorov D statistic is used to assess whether a random sample was drawn from a specified distribution. Although it is frequently used to test for normality, the statistic is "distribution free" in
In a previous article, I discussed the definition of the Kullback-Leibler (K-L) divergence between two discrete probability distributions. For completeness, this article shows how to compute the Kullback-Leibler divergence between two continuous distributions. When f and g are discrete distributions, the K-L divergence is the sum of f(x)*log(f(x)/g(x)) over all
This article shows how to perform two-dimensional bilinear interpolation in SAS by using a SAS/IML function. It is assumed that you have observed the values of a response variable on a regular grid of locations. A previous article showed how to interpolate inside one rectangular cell. When you have a
I've previously written about linear interpolation in one dimension. Bilinear interpolation is a method for two-dimensional interpolation on a rectangle. If the value of a function is known at the four corners of a rectangle, an interpolation scheme gives you a way to estimate the function at any point in
This article shows how to find local maxima and maxima on a regression curve, which means finding points where the slope of the curve is zero. An example appears at the right, which shows locations where the loess smoother in a scatter plot has local minima and maxima. Except for
I recently showed how to use linear interpolation in SAS. Linear interpolation is a common way to interpolate between a set of planar points, but the interpolating function (the interpolant) is not smooth. If you want a smoother interpolant, you can use cubic spline interpolation. This article describes how to
SAS programmers sometimes ask about ways to perform one-dimensional linear interpolation in SAS. This article shows three ways to perform linear interpolation in SAS: PROC IML (in SAS/IML software), PROC EXPAND (in SAS/ETS software), and PROC TRANSREG (in SAS/STAT software). Of these, PROC IML Is the simplest to use and
