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Difference between revisions of "Goodness-of-fit test"

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A statistical test for goodness of fit. The essence of such a test is the following. Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446001.png" /> be independent identically-distributed random variables whose distribution function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446002.png" /> is unknown. Then the problem of statistically testing the hypothesis <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446003.png" /> that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446004.png" /> for some given distribution function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446005.png" /> is called a problem of testing goodness of fit. For example, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446006.png" /> is a continuous distribution function, then as a goodness-of-fit test for testing <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044600/g0446007.png" /> one can use the [[Kolmogorov test|Kolmogorov test]].
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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|Kolmogorov test]].
  
 
See also [[Non-parametric methods in statistics|Non-parametric methods in statistics]].
 
See also [[Non-parametric methods in statistics|Non-parametric methods in statistics]].

Latest revision as of 19:24, 16 April 2014

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
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