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Euclidean and L1 distances between observations and a target value for standardized data

Rick WicklinMarch 28, 2018 3

Find the distances between observations and a target value

Suppose you want to find observations in multivariate data that are closest to a numerical target value. For example, for the students in the Sashelp.Class data set, you might want to find the students whose (Age, Height, Weight) values are closest to the triplet (13, 62, 100). The way to

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Analytics | Data Visualization

Rick WicklinMarch 26, 2018 3

A zipper plot for visualizing coverage probability in simulation studies

Simulation studies are used for many purposes, one of which is to examine how distributional assumptions affect the coverage probability of a confidence interval. This article describes the "zipper plot," which enables you to compare the coverage probability of a confidence interval when the data do or do not follow

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Analytics | Learn SAS

Rick WicklinMarch 21, 2018 2

The conjugate gradient method

I often claim that the "natural syntax" of the SAS/IML language makes it easy to implement an algorithm or statistical formula as it appears in a textbook or journal. The other day I had an opportunity to test the truth of that statement. A SAS programmer wanted to implement the

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Analytics

Rick WicklinMarch 12, 2018 1

Pi, special functions, and distributions

Welcome to my annual Pi Day post. Every year on March 14th (written 3/14 in the US), geeky mathematicians and their friends celebrate "all things pi-related" because 3.14 is the three-decimal approximation to pi. Pi is a mathematical constant that never changes. Pi is the same value today as it

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Analytics | Programming Tips

Rick WicklinMarch 7, 2018 11

Fit a distribution from quantiles

Data analysts often fit a probability distribution to data. When you have access to the data, a common technique is to use maximum likelihood estimation (MLE) to compute the parameters of a distribution that are "most likely" to have produced the observed data. However, how can you fit a distribution

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Analytics | Programming Tips

Rick WicklinMarch 5, 2018 6

The probability of a saddle point in a matrix

Many people know that a surface can contain a saddle point, but did you know that you can define the saddle point of a matrix? Saddle points in matrices are somewhat rare, which means that if you choose a random matrix you are unlikely to choose one that has a

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Analytics | Programming Tips

Solve nonlinear system of equations in SAS

Rick WicklinFebruary 28, 2018 3

Solve a system of nonlinear equations with SAS

This article shows how to use SAS to solve a system of nonlinear equations. When there are n unknowns and n equations, this problem is equivalent to finding a multivariate root of a vector-valued function F(x) = 0 because you can always write the system as f1(x1, x2, ..., xn)

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Analytics | Programming Tips

Quantiles are the solutions to the equation CDF(x)-p=0, where p is a probability

Rick WicklinFebruary 19, 2018 3

Compute the quantiles of any distribution

Your statistical software probably provides a function that computes quantiles of common probability distributions such as the normal, exponential, and beta distributions. Because there are infinitely many probability distributions, you might encounter a distribution for which a built-in quantile function is not implemented. No problem! This article shows how to

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Analytics | Learn SAS

Rick WicklinFebruary 14, 2018 13

The difference between CLASS statements and BY statements in SAS

When I first learned to program in SAS, I remember being confused about the difference between CLASS statements and BY statements. A novice SAS programmer recently asked when to use one instead of the other, so this article explains the difference between the CLASS statement and BY variables in SAS

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Analytics | Data Visualization

Rick WicklinFebruary 7, 2018 0

The distribution of shared birthdays in the Birthday Problem

If N random people are in a room, the classical birthday problem provides the probability that at least two people share a birthday. The birthday problem does not consider how many birthdays are in common. However, a generalization (sometimes called the Multiple-Birthday Problem) examines the distribution of the number of

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