The DO Loop

Programming Tips

Strengthen your programming skills with tips and techniques from the experts

Graphical comparison of two methods for estimating confidence intervals of eigenvalues of a correlation matrix

Rick WicklinOctober 26, 2020 3

Confidence intervals for eigenvalues of a correlation matrix

A fundamental principle of data analysis is that a statistic is an estimate of a parameter for the population. A statistic is calculated from a random sample. This leads to uncertainty in the estimate: a different random sample would have produced a different statistic. To quantify the uncertainty, SAS procedures

English

Data Visualization | Programming Tips

Decomposition of a convex polygon into triangles

Rick WicklinOctober 21, 2020 0

Generate random points in a polygon

The triangulation theorem for polygons says that every simple polygon can be triangulated. In fact, if the polygon has V vertices, you can decompose it into V-2 non-overlapping triangles. In this article, a "polygon" always means a simple polygon. Also, a "random point" means one that is drawn at random

English

Analytics | Programming Tips

Rick WicklinOctober 19, 2020 5

Generate random points in a triangle

How can you efficiently generate N random uniform points in a triangular region of the plane? There is a very cool algorithm (which I call the reflection method) that makes the process easy. I no longer remember where I saw this algorithm, but it is different from the "weighted average"

English

Analytics | Programming Tips

Rick WicklinOctober 7, 2020 0

The Poisson-binomial distribution for hundreds of parameters

A previous article shows how to use a recursive formula to compute exact probabilities for the Poisson-binomial distribution. The recursive formula is an O(N2) computation, where N is the number of parameters for the Poisson-binomial (PB) distribution. If you have a distribution that has hundreds (or even thousands) of parameters,

English

Programming Tips

Rick WicklinOctober 5, 2020 0

Trap and map: Trapping invalid values

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

English

Programming Tips

PDF of the Poisson-binomial distribution

Rick WicklinSeptember 30, 2020 0

Density, CDF, and quantiles for the Poisson-binomial distribution

When working with a probability distribution, it is useful to know how to compute four essential quantities: a random sample, the density function, the cumulative distribution function (CDF), and quantiles. I recently discussed the Poisson-binomial distribution and showed how to generate a random sample. This article shows how to compute

English

Analytics | Programming Tips

Rick WicklinSeptember 28, 2020 0

The Poisson-binomial distribution

The Poisson-binomial distribution is a generalization of the binomial distribution. For the binomial distribution, you carry out N independent and identical Bernoulli trials. Each trial has a probability, p, of success. The total number of successes, which can be between 0 and N, is a binomial random variable. The distribution

English

Learn SAS | Programming Tips

Rick WicklinSeptember 23, 2020 3

Working with recurrence relations in SAS

Many textbooks and research papers present formulas that involve recurrence relations. Familiar examples include: The factorial function: Set Fact(0)=1 and define Fact(n) = n*Fact(n-1) for n > 0. The Fibonacci numbers: Set Fib(0)=1 and Fib(1)=1 and define Fib(n) = Fib(n-1) + Fib(n-2) for n > 1. The binomial coefficients (combinations

English

Analytics | Programming Tips

Rick WicklinSeptember 16, 2020 1

Restricted least squares regression in SAS

A data analyst recently asked a question about restricted least square regression in SAS. Recall that a restricted regression puts linear constraints on the coefficients in the model. Examples include forcing a coefficient to be 1 or forcing two coefficients to equal each other. Each of these problems can be

English

Analytics | Programming Tips

Rick WicklinSeptember 10, 2020 0

Iterative proportional fitting in SAS

I previously wrote about the RAS algorithm, which is a simple algorithm that performs matrix balancing. Matrix balancing refers to adjusting the cells of a frequency table to match known values of the row and column sums. Ideally, the balanced matrix will reflect the structural relationships in the original matrix.

English

Blogs

Blogs

Programming Tips