Statistical Goodness-of-Fit Measure

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A Statistical Goodness-of-Fit Measure is a statistic function that quantifies how well a posited theoretical distribution function fits an empirical distribution function (on observed data).



References

2016

  • (Encyclopedia of Mathematics, 2016) ⇒ https://www.encyclopediaofmath.org/index.php/Goodness-of-fit_test
    • QUOTE: A statistical test for goodness of fit. The essence of such a test is the following. Let [math]\displaystyle{ X_1,\cdots,X_n }[/math] be independent identically-distributed random variables whose distribution function F is unknown. Then the problem of statistically testing the hypothesis [math]\displaystyle{ H0 }[/math] that [math]\displaystyle{ F≡F_0 }[/math] for some given distribution function [math]\displaystyle{ F0 }[/math] is called a problem of testing goodness of fit. For example, if [math]\displaystyle{ F0 }[/math] is a continuous distribution function, then as a goodness-of-fit test for testing [math]\displaystyle{ H_0 }[/math] one can use the Kolmogorov test.

2015

2012

2008

2004

1989

1976

  • TURNBULBL., W. and WEISSL, . (1976). A likelihood ratio statistic for testing goodness of fit with randomly censored data. Technical Report No. 307, School of Operations Research, Cornell University.,

1900

  • (Pearson, 1900) ⇒ Karl Pearson. (1900). “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.” In: Philosophical Magazine Series 5. 50 (302): 157–175. doi:10.1080/14786440009463897.