Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
Sometimes it is useful to know the extreme values in data. You might need to know the Top 5 or the Top 10 smallest data values. Or, the Top 5 or Top 10 largest data values. There are many ways to do this in SAS, but this article shows examples
How can you estimate percentiles in SAS Viya? This article shows how to call the percentile action from PROC CAS to estimate percentiles of variables in a CAS data table. Percentiles and quantiles are essentially the same (the pth quantile is the 100*pth percentile for p in [0, 1]), so
Here's a fun problem to think about: Suppose that you have two different valid ways to test a statistical hypothesis. For a given sample, will both tests reject or fail to reject the hypothesis? Or might one test reject it whereas the other does not? The answer is that two
Several probability distributions model the outcomes of various trials when the probabilities of certain events are given. For some distributions, the definitions make sense even when a probability is 0. For other distributions, the definitions do not make sense unless all probabilities are strictly positive. This article examines how zero
Some colors have names, such as "Red," "Magenta," and "Dark Olive Green." But the most common way to specify a color is to use a hexadecimal value such as CX556B2F. It is not obvious that "Dark Olive Green" and CX556B2F represent the same color, but they do! I like to
On this blog, I write about a diverse set of topics that are relevant to statistical programming and data visualization. In a previous article, I presented some of the most popular blog posts from 2021. The most popular articles often deal with elementary or familiar topics that are useful to
You can use the Cholesky decomposition of a covariance matrix to simulate data from a correlated multivariate normal distribution. This method is encapsulated in the RANDNORMAL function in SAS/IML software, but you can also perform the computations manually by calling the ROOT function to get the Cholesky root and then
Last year, I wrote almost 100 posts for The DO Loop blog. My most popular articles were about data visualization, statistics and data analysis, and simulation and bootstrapping. If you missed any of these gems when they were first published, here are some of the most popular articles from 2021:
Suppose you are creating a craft project for the Christmas holidays, and you want to choose a palette of Christmas colors to give it a cheery holiday appearance. You could use one of the many online collections of color palettes to choose a Christmas-themed palette. However, I didn't want to
In a previous article, I visualized seven Christmas-themed palettes of colors, as shown to the right. You can see that the palettes include many red, green, and golden colors. Clearly, the colors in the Christmas palettes are not a random sample from the space of RGB colors. Rather, they represent
In data visualization, colors can represent the values of a variable in a choropleth map, a heatmap, or a scatter plot. But how do you visualize a palette of colors from the RGB or hexadecimal values of the colors? One way is to use the HEATMAPDISC subroutine in SAS/IML, which
While discussing how to compute convex hulls in SAS with a colleague, we wondered how the size of the convex hull compares to the size of the sample. For most distributions of points, I claimed that the size of the convex hull is much less than the size of the
Did you know that the loess regression algorithm is not well-defined when you have repeated values among the explanatory variables, and you request a very small smoothing parameter? This is because loess regression at the point x0 is based on using the k nearest neighbors to x0. If x0 has
When SAS 9 programmers transition to SAS Viya, there are inevitably questions about how new concepts in Cloud Analytic Services (CAS) relate to similar concepts in SAS. This article discusses the question, "What is the difference between a libref and a caslib?" Both are used to access data, but they
I attended a seminar last week whose purpose was to inform SAS 9 programmers about SAS Viya. I could tell from the programmer's questions that some programmers were confused about three basic topics: What are the computing environments in Viya, and how should a programmer think about them? What procedures
In a previous article, I showed how to use theCVEXHULL function in SAS/IML to compute the convex hull of a finite set of planar points. The convex hull is a convex polygon, which is defined by its vertices. To visualize the polygon, you need to know the vertices in sequential
Given a cloud of points in the plane, it can be useful to identify the convex hull of the points. The convex hull is the smallest convex set that contains the observations. For a finite set of points, it is a convex polygon that has some of the points as
I was recently asked how to create a frequency polygon in SAS. A frequency polygon is an alternative to a histogram that shows similar information about the distribution of univariate data. It is the piecewise linear curve formed by connecting the midpoints of the tops of the bins. The graph
Recall that the binomial distribution is the distribution of the number of successes in a set of independent Bernoulli trials, each having the same probability of success. Most introductory statistics textbooks discuss the approximation of the binomial distribution by the normal distribution. The graph to the right shows that the
A SAS programmer asked whether it is possible to add reference lines to the categorical axis of a bar chart. The answer is yes. You can use the VBAR statement, but I prefer to use the VBARBASIC (or VBARPARM) statement, which enables you to overlay a wide variety of graphs
A previous article discusses how to use SAS regression procedures to fit a two-parameter Weibull distribution in SAS. The article shows how to convert the regression output into the more familiar scale and shape parameters for the Weibull probability distribution, which are fit by using PROC UNIVARIATE. Although PROC UNIVARIATE
It can be frustrating when the same probability distribution has two different parameterizations, but such is the life of a statistical programmer. I previously wrote an article about the gamma distribution, which has two common parameterizations: one that uses a scale parameter (β) and another that uses a rate parameter
A genetic algorithm (GA) is a heuristic optimization technique. The method tries to mimic natural selection and evolution by starting with a population of random candidates. Candidates are evaluated for "fitness" by plugging them into the objective function. The characteristics of the better candidates are combined to create a new
This article uses an example to introduce to genetic algorithms (GAs) for optimization. It discusses two operators (mutation and crossover) that are important in implementing a genetic algorithm. It discusses choices that you must make when you implement these operations. Some programmers love using genetic algorithms. Genetic algorithms are heuristic
Sometimes we can learn as much from our mistakes as we do from our successes. Recently, I needed to solve an optimization problem for which the solution vector was a binary vector subject to a constraint. I was in a hurry. Without thinking much about what I was doing, I
Many optimization problems in statistics and machine learning involve continuous parameters. For example, maximum likelihood estimation involves optimizing a log-likelihood function over a continuous domain, possibly with constraints. Recently, however, I had to solve an optimization problem for which the solution vector was a 0/1 binary variable. To solve the
In a matrix-vector language such as SAS/IML, it is useful to always remember that the fundamental objects are matrices and that all operations are designed to work on matrices. (And vectors, which are matrices that have only one row or one column.) By using matrix operations, you can often eliminate
A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific
Graphing data is almost always more informative than displaying a table of summary statistics. In a recent article about "dynamite plots," I briefly mentioned that graphs such as box plots and strip plots are better at showing data than graphs that merely show the mean and standard deviation. This article
The field of probability and statistics is full of asymptotic results. The Law of Large Numbers and the Central Limit Theorem are two famous examples. An asymptotic result can be both a blessing and a curse. For example, consider a result that says that the distribution of some statistic converges
