The kernel density estimate (KDE) is a powerful tool for estimating the density of univariate data. The KDE is a flexible model. For example, it can fit data distributions that are multimodal or have long tails. It is nonparametric, which means that you do not need to assume any form
When you have a data matrix, the rows represent observations and the columns represent variables. If you sort the matrix by one or more columns, the sorting occurs in a way that preserves the elements within rows. Although the rows of the sorted matrix are permuted by the sort, the
A previous article discusses regression splines and how to use the EFFECT statement in SAS regression procedures to specify the location of knots for a regressor variable, X. Knots are breakpoints that partition the range of X into subintervals. The splines are defined on a set of adjacent subintervals. The
Did you know that, for skewed distributions, the sample median is a biased estimator of the population median? You can show this in two ways. For any distribution, you can run a Monte Carlo simulation that reveals the bias. And, for some distributions (such as the exponential distribution), you can
In a previous article, I presented some of the most popular blog posts from The DO Loop in 2025. In general, popular articles deal with elementary topics that have broad appeal. However, I also write technical articles about advanced topics, which typically do not make it onto a Top 10
In 2025, I wrote about 60 articles for The DO Loop blog. My most popular articles were about SAS programming, data visualization, and statistics. This blog post lists some of the most popular articles from 2025. Read on for the Reader's Choice Awards in various categories! SAS Programming The following
Recently, a colleague struggled to find the source of a run-time error happening somewhere within a very large library of SAS IML function modules. Since the error happens at run time, I told my colleague about how to find the location of a run time error by reading the traceback
While many applications of Monte Carlo techniques use pseudorandom numbers, some applications that involve integrals are more accurate when you use quasirandom numbers, which, despite their names, are not random but are deterministic sequences of numbers. Many of these sequences are constructed by representing base-10 numbers in a different base.
The new school year had barely started when I got a call from a friend who is an elementary school principal. She told me that every morning she announces the names of students who are celebrating a birthday. "One student noticed that we've already had two days on which no
In probability and statistics, special numbers are used to compute probabilities by counting the number of ways certain events can occur. The most famous are combinations and permutations. Both are used to count the ways to arrange or select items from a set. If a set contains n elements: A
