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A density power divergence measure to discriminate between generalized exponential and Weibull distributions

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  • Suparna Basu

    (M.M.V, Banaras Hindu University)

  • Hon Keung Tony Ng

    (Bentley University)

Abstract

Discriminating two similar candidate statistical models for a given data set based on the conventional ratio of maximized likelihood values has been studied extensively in the literature. The problem of model discrimination becomes more complicated when the candidate models resemble each other closely for a certain region in the parametric space, with only a handful of different characteristics that are difficult to extract or identify from a given data set. The conventional method may fail to provide conclusive discriminatory evidence toward either model for such cases. In this paper, a novel discrimination criterion based on the density power divergence is proposed for model discrimination between the generalized exponential distribution and the Weibull distribution. Along with the discriminating procedure, asymptotic properties of the associated discriminating statistic are discussed. A Monte Carlo simulation study is used to evaluate the performance of the proposed model discrimination method and compare it with the ratio of the maximized likelihood method under different scenarios with and without contamination. A numerical example is presented to illustrate the proposed model discrimination method developed here.

Suggested Citation

  • Suparna Basu & Hon Keung Tony Ng, 2025. "A density power divergence measure to discriminate between generalized exponential and Weibull distributions," Statistical Papers, Springer, vol. 66(1), pages 1-25, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01637-y
    DOI: 10.1007/s00362-024-01637-y
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    References listed on IDEAS

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    1. Mohammad Z. Raqab, 2013. "Discriminating between the generalized Rayleigh and Weibull distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1480-1493, July.
    2. Tommasi, C. & López-Fidalgo, J., 2010. "Bayesian optimum designs for discriminating between models with any distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 143-150, January.
    3. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    4. A. Basu & A. Mandal & N. Martin & L. Pardo, 2013. "Testing statistical hypotheses based on the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 319-348, April.
    5. Gupta, Rameshwar D. & Kundu, Debasis, 2003. "Discriminating between Weibull and generalized exponential distributions," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 179-196, June.
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