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Assessing the fit of finite mixture distributions

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Abstract
Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.
Keywords
goodness of fit, score tests, smooth tests, MAXIMUM-LIKELIHOOD, GENE-EXPRESSION, EM ALGORITHM

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MLA
Suesse, Thomas, John CW Rayner, and Olivier Thas. “Assessing the Fit of Finite Mixture Distributions.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 59.4 (2017): 463–483. Print.
APA
Suesse, T., Rayner, J. C., & Thas, O. (2017). Assessing the fit of finite mixture distributions. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 59(4), 463–483.
Chicago author-date
Suesse, Thomas, John CW Rayner, and Olivier Thas. 2017. “Assessing the Fit of Finite Mixture Distributions.” Australian & New Zealand Journal of Statistics 59 (4): 463–483.
Chicago author-date (all authors)
Suesse, Thomas, John CW Rayner, and Olivier Thas. 2017. “Assessing the Fit of Finite Mixture Distributions.” Australian & New Zealand Journal of Statistics 59 (4): 463–483.
Vancouver
1.
Suesse T, Rayner JC, Thas O. Assessing the fit of finite mixture distributions. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS. 2017;59(4):463–83.
IEEE
[1]
T. Suesse, J. C. Rayner, and O. Thas, “Assessing the fit of finite mixture distributions,” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, vol. 59, no. 4, pp. 463–483, 2017.
@article{8551037,
  abstract     = {Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.},
  author       = {Suesse, Thomas and Rayner, John CW and Thas, Olivier},
  issn         = {1369-1473},
  journal      = {AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS},
  keywords     = {goodness of fit,score tests,smooth tests,MAXIMUM-LIKELIHOOD,GENE-EXPRESSION,EM ALGORITHM},
  language     = {eng},
  number       = {4},
  pages        = {463--483},
  title        = {Assessing the fit of finite mixture distributions},
  url          = {http://dx.doi.org/10.1111/anzs.12213},
  volume       = {59},
  year         = {2017},
}

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