Month: November 2023

Steven Sanderson tests a distribution fit:

There are two main ways to fit a gamma distribution to a dataset in R:

1. Maximum likelihood estimation (MLE): This method estimates the parameters of the gamma distribution that are most likely to have produced the observed data.
2. Method of moments: This method estimates the parameters of the gamma distribution by equating the sample mean and variance to the theoretical mean and variance of the gamma distribution.

Click through to see which technique Steven uses and an example of how it all works.

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Bryan Shalloway explains how odds and probabilities intertwine:

However human understanding of odds predates our formal understanding of probability. You can find references to odds dating back to Shakespeare:

Knew that we ventured on such dangerous seas
That if we wrought out life ’twas ten to one;
– Shakespeare’s Henry IV, Part II, 1597

Yet, in most common settings, modern society has largely supplanted odds for probabilities. You can imagine if Shakespeare were writing today the line might end “’twas ten out of eleven.”

Read the whole thing.

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Steven Sanderson unleashes the power of the triangle:

The Triangular Distribution is a continuous probability distribution with a triangular shape, hence the name. It is defined by three parameters: min, max, and mode. These parameters determine the range of values the distribution can take and the most likely value within that range. In mathematical terms, the probability density function (PDF) of the Triangular Distribution is given by:

Read on to see the definition, as well as how you can use the four functions around the Triangular Distribution.

By the way, the best-known case of the Triangular Distribution is combining the results of two fair dice, which gives us a peak at the number 7 (1/6 of the time) for a pair of fair, six-sided dice and moving symmetrically down from there, so p(6) = p(8), p(5) = p(9), and so on.

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