Statistical comparison of the goodness of fit delivered by five families of distributions used in distribution fitting

Haim Shore; Fatina A'Wad

doi:10.1080/03610920902887707

Statistical comparison of the goodness of fit delivered by five families of distributions used in distribution fitting

Haim Shore, Fatina A'Wad

Department of Industrial Engineering and Management

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L₂ norm and four-moment matching. Values of L₂ norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.

Original language	English
Pages (from-to)	1707-1728
Number of pages	22
Journal	Communications in Statistics - Theory and Methods
Volume	39
Issue number	10
DOIs	https://doi.org/10.1080/03610920902887707
State	Published - 1 Jun 2010

Keywords

ANOVA for single grouped repeated measures
Burr
Distributional distance indicators
GLD
Kullback-Leibler divergence
L norm
Moment-matching
Pearson
Response modeling methodology
Transformation

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610920902887707

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abstract = "A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L2 norm and four-moment matching. Values of L2 norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.",

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AB - A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L2 norm and four-moment matching. Values of L2 norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.

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Statistical comparison of the goodness of fit delivered by five families of distributions used in distribution fitting

Abstract

Keywords

ASJC Scopus subject areas

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