# Goodness-of-fit test

From Encyclopedia of Mathematics

A statistical test for goodness of fit. The essence of such a test is the following. Let $X_1,\ldots,X_n$ be independent identically-distributed random variables whose distribution function $F$ is unknown. Then the problem of statistically testing the hypothesis $H_0$ that $F\equiv F_0$ for some given distribution function $F_0$ is called a problem of testing goodness of fit. For example, if $F_0$ is a continuous distribution function, then as a goodness-of-fit test for testing $H_0$ one can use the Kolmogorov test.

See also Non-parametric methods in statistics.

**How to Cite This Entry:**

Goodness-of-fit test.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Goodness-of-fit_test&oldid=31804

This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article