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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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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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The linear distribution on an interval

In a recent Monte Carlo project, I needed to simulate numbers on an interval by using a continuous linear probability density function (PDF). An example is shown to the right. In this example, the linear density function is decreasing on the interval, but the function could also be constant or

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The elliptical heart

Some hearts are famous. For example, there is the "Heart of Gold" (Neil Young), the "Heart of Glass" (Blondie), and the Heart of Darkness (Joseph Conrad). But have you heard of the "Heart of Ellipses"? No? Well, in 2023, Ted Conway published an amusingly titled article, "Total Ellipse of the

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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