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Rick WicklinOctober 6, 2025 0

The inverse power method for eigenvalues

The power method is a well-known iterative scheme to approximate the largest eigenvalue (in absolute value) of a symmetric matrix. It is useful in practice when you need only the largest eigenvalue and eigenvector of a large matrix. The method requires only matrix-vector multiplication and vector scaling. There is a

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Analytics | Programming Tips

Rick WicklinSeptember 29, 2025 1

Visualize Rayleigh quotients and eigenvectors

When I encounter a new function, I usually graph it to gain intuition about how the function transforms its inputs. Recently, I needed to use the Rayleigh quotient function, which is connected to the estimation of eigenvalues and eigenvectors for symmetric matrices. It has been several years since I last

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Analytics | Programming Tips

Rick WicklinSeptember 22, 2025 2

Birthdays and the coupon collector's problem

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

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Analytics | Programming Tips

Rick WicklinSeptember 15, 2025 0

Stirling numbers in SAS

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

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Analytics | Learn SAS | Programming Tips

Rick WicklinAugust 25, 2025 1

Implement the generalized extreme value distribution in SAS

SAS supports more than 25 common probability distributions for the PDF, CDF, QUANTILE, and RAND functions. If you need a less-common distribution, you can implement new distributions by using Base SAS (specifically, PROC FCMP) or the SAS/IML language. On the SAS Support Communities, a SAS programmer asked how to implement

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Analytics | Learn SAS | Programming Tips

Rick WicklinAugust 18, 2025 0

Confidence intervals for Cohen's d statistic in SAS

A previous article discusses Cohen's d statistic and how to compute it in SAS. For a two-sample independent design, Cohen's d estimates the standardized mean difference (SMD). Because Cohen's d is a biased statistic, the previous article also computes Hedges' g, which is an unbiased estimate of the SMD. Lastly,

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Analytics | Learn SAS | Programming Tips

Rick WicklinAugust 6, 2025 0

3 ways to estimate parameters when fitting a distribution to data

SAS provides procedures to fit common probability distributions to sample data. You can use PROC UNIVARIATE in Base SAS or PROC SEVERITY in SAS/ETS software to estimate the distribution parameters for approximately 20 common distributions, including normal, lognormal, beta, gamma, and Weibull. Since there are infinitely many distributions, you may

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Analytics | Learn SAS

Rick WicklinJuly 7, 2025 3

Noncentrality parameters and confidence intervals

While researching a topic on effect sizes, I learned about a SAS function that is related to noncentrality parameters. I previously wrote an article about the noncentral t distribution, which is one of several well-known distributions that contains an optional noncentrality parameter. I mentioned that the PDF, CDF, and QUANTILE

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Analytics | Data Visualization | Learn SAS | Programming Tips

Rick WicklinJune 16, 2025 0

Find the orthant that contains a point

This article shows how to classify a set of high-dimensional data into orthants. An orthant is the d-dimensional generalization of a quadrant. For 2-D Euclidean space, there are four quadrants, often labeled by Roman numerals I-IV. The quadrants are open sets that are defined by the signs of each coordinate

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Analytics | Data Visualization | Programming Tips

Rick WicklinMay 27, 2025 0

Visualize the Gini-Simpson diversity index

A previous article discusses the Gini-Simpson diversity index and how to compute it in SAS. Suppose you have a sample that contains R classes. (Classes are also called groups or categories.) Intuitively, the sample exhibits "high diversity" if the class sizes are approximately equal. The sample shows "low diversity" if

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