There has been a spate of recent high-profile airline crashes (Malaysia Airlines, TransAsia Airways, Germanwings,...) so I was surprised when I saw a time series plot of the number of airline crashes by year, which indicates that the annual number of airline crashes has been decreasing since 1993. The data
There's "big," and then there is "factorial big." If you have k items, the number of permutations is "k factorial," which is written as k!. The factorial function gets big fast. For example, the value of k! for several values of k is shown in the following table. You can
The title of this article makes no sense. How can the number of elements (in fact, the number of anything!) not be a whole number? In fact, it can't. However, the title refers to the fact that you might compute a quantity that ought to be an integer, but is
Imagine that you have one million rows of numerical data and you want to determine if a particular "target" value occurs. How might you find where the value occurs? For univariate data, this is an easy problem. In the SAS DATA step you can use a WHERE clause or a
This article show how to run a SAS program in batch mode and send parameters into the program by specifying the parameters when you run SAS from a command line interface. This technique has many uses, one of which is to split a long-running SAS computation into a series of
Saturday, March 14, 2015, is Pi Day, and this year is a super-special Pi Day! This is your once-in-a-lifetime chance to celebrate the first 10 digits of pi (π) by doing something special on 3/14/15 at 9:26:53. Apologies to my European friends, but Pi Day requires that you represent dates
Sometimes I get contacted by SAS/IML programmers who discover that the SAS/IML language does not provide built-in support for multiplication of matrices that have missing values. (SAS/IML does support elementwise operations with missing values.) I usually respond by asking what they are trying to accomplish, because mathematically matrix multiplication with
I often blog about the usefulness of vectorization in the SAS/IML language. A one-sentence summary of vectorization is "execute a small number of statements that each analyze a lot of data." In general, for matrix languages (SAS/IML, MATLAB, R, ...) vectorization is more efficient than the alternative, which is to
In my previous post, I showed how to approximate a cumulative density function (CDF) by evaluating only the probability density function. The technique uses the trapezoidal rule of integration to approximate the CDF from the PDF. For common probability distributions, you can use the CDF function in Base SAS to
Evaluating a cumulative distribution function (CDF) can be an expensive operation. Each time you evaluate the CDF for a continuous probability distribution, the software has to perform a numerical integration. (Recall that the CDF at a point x is the integral under the probability density function (PDF) where x is
