The chi-squared distribution is a continuous probability distribution defined as the distribution of a sum of the squares of a number of independent standard normal random variables, that number being the distribution's single parameter, known as its degrees of freedom. It was first derived by the German geodesist Friedrich Robert Helmert in the 1870s, but it owes its modern name and its central place in statistics to Karl Pearson, who introduced the Pearson chi-squared test in 1900 as a way of measuring how well observed categorical data fit an expected distribution. Because the sampling distribution of the variance of a normal population, and many related test statistics, follow a chi-squared distribution, it underlies goodness of fit tests, tests of independence in contingency tables, and the construction of confidence intervals for a variance, making it one of the most widely used distributions in applied statistics.
Facts
Partially Attested
Origin YearSource dates Helmert's derivation to papers of 1875 to 1876, not a single year; 1876 is used here as the representative year. Sources
1. Wikipedia: Probability distribution
IntroductionQuote, Introduction
Formally, it is a probability measure: a function that assigns probabilities to events in a way that satisfies the axioms of probability.
2. Wikipedia: Chi-squared distribution
History sectionQuote, History section
This distribution was first described by the German geodesist and statistician Friedrich Robert Helmert in papers of 1875-6, where he computed the sampling distribution of the sample variance of a normal population.
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