Happy Pi Day! Every year on March 14th (written 3/14 in the US), people in the mathematical sciences celebrate all things pi-related because 3.14 is the three-decimal approximation to π ≈ 3.14159265358979.... Pi is a mathematical constant defined as the ratio of a circle's circumference (C) to its diameter (D).
I recently wrote about the Number-Word Game, which is an iterative algorithm that generates a sequence of natural numbers by using the lengths of the words for the numbers. In English, the words are "one", "two", "three", and so on. You can play the Number-Word Game in any alphabetic language
Have you heard about the Number-Word Game? This is a simple game that has the following rules: Start with any positive integer. Write down the English word for the integer. Count the number of letters in the word. This gives a new positive integer. Go to (2). Repeat until a
I sometimes see analysts overuse colors in statistical graphics. My rule of thumb is that you do not need to use color to represent a variable that is already represented in a graph. For example, it is redundant to use a continuous color ramp to represent the lengths of bars
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
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
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
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
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
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
