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Rick WicklinApril 22, 2024 0

Use the moment-ratio diagram to visualize the sampling distribution of skewness and kurtosis

The moment-ratio diagram is a tool that is useful when choosing a distribution that models a sample of univariate data. As I show in my book (Simulating Data with SAS, Wicklin, 2013), you first plot the skewness and kurtosis of the sample on the moment-ratio diagram to see what common

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Analytics | Learn SAS | Programming Tips

Rick WicklinApril 15, 2024 1

Distributions with specified skewness and kurtosis

A SAS programmer wanted to simulate samples from a family of Beta(a,b) distributions for a simulation study. (Recall that a Beta random variable is bounded with values in the range [0,1].) She wanted to choose the parameters such that the skewness and kurtosis of the distributions varied over range of

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Analytics | Learn SAS | Programming Tips

Rick WicklinApril 8, 2024 1

Improve the Federal Reserve's dot plot

A dot plot is a standard statistical graphic that displays a statistic (often a mean) and the uncertainty of the statistic for one or more groups. Statisticians and data scientists use it in the analysis of group data. In late 2023, I started noticing headlines about "dot plots" in the

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Analytics | Learn SAS

Rick WicklinMarch 27, 2024 3

The likelihood ratio test for linear regression in SAS

A recent article describes how to estimate coefficients in a simple linear regression model by using maximum likelihood estimation (MLE). One of the nice properties of an MLE formulation is that you can compare a large model with a nested submodel in a natural way. For example, if you can

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Analytics | Learn SAS | Programming Tips

Rick WicklinMarch 20, 2024 1

Maximum likelihood estimates for linear regression

A statistical analyst used the GENMOD procedure in SAS to fit a linear regression model. He noticed that the table of parameter estimates has an extra row (labeled "Scale") that is not a regression coefficient. The "scale parameter" is not part of the parameter estimates table produced by PROC REG

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Analytics | Learn SAS

Rick WicklinFebruary 26, 2024 0

On using flexible distributions to fit data

With four parameters I can fit an elephant. With five I can make his trunk wiggle. — John von Neumann Ever since the dawn of statistics, researchers have searched for the Holy Grail of statistical modeling. Namely, a flexible distribution that can model any continuous univariate data. As the quote

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Analytics | Learn SAS | Programming Tips

Rick WicklinFebruary 21, 2024 0

On using the range to estimate the variability of small samples

In statistical quality control, practitioners often estimate the variability of products that are being produced in a manufacturing plant. It is important to estimate the variability as soon as possible, which means trying to obtain an estimate from a small sample. Samples of size five or less are not uncommon

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Analytics | Learn SAS | Programming Tips

Rick WicklinFebruary 12, 2024 0

An exact formula for the sampling distribution of the correlation coefficient

I read a journal article in which a researcher used a formula for the probability density function (PDF) of the sample correlation coefficient. The formula was rather complicated, and presented with no citation, so I was curious to learn more. I found the distribution for the correlation coefficient in the

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Analytics | Learn SAS

Rick WicklinFebruary 5, 2024 2

Peeling a convex hull

This article looks at a geometric method for estimating the center of a multivariate point cloud. The method is known as convex-hull peeling. In two-dimensions, you can perform convex-hull peeling in SAS 9 by using the CVEXHULL function in SAS IML software. For higher dimensions, you can use the CONVEXHULL

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Analytics

Rick WicklinJanuary 29, 2024 0

The geometry of Jacobi's method

A colleague remarked that my recent article about using Jacobi's iterative method for solving a linear system of equations "seems like magic." Specifically, it seems like magic that you can solve a certain class of linear systems by using only matrix multiplication. For any initial guess, the iteration converges to

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