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Discriminating between the Weibull and log‐normal distributions

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  • Debasis Kundu
  • Anubhav Manglick

Abstract

Log‐normal and Weibull distributions are the most popular distributions for modeling skewed data. In this paper, we consider the ratio of the maximized likelihood in choosing between the two distributions. The asymptotic distribution of the logarithm of the maximized likelihood ratio has been obtained. It is observed that the asymptotic distribution is independent of the unknown parameters. The asymptotic distribution has been used to determine the minimum sample size required to discriminate between two families of distributions for a user specified probability of correct selection. We perform some numerical experiments to observe how the asymptotic methods work for different sample sizes. It is observed that the asymptotic results work quite well even for small samples also. Two real data sets have been analyzed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Debasis Kundu & Anubhav Manglick, 2004. "Discriminating between the Weibull and log‐normal distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 893-905, September.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:6:p:893-905
    DOI: 10.1002/nav.20029
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    References listed on IDEAS

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    1. 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.
    2. White, Halbert, 1982. "Regularity conditions for cox's test of non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 301-318, August.
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    Cited by:

    1. Shovan Chowdhury, 2019. "Selection between Exponential and Lindley distributions," Working papers 316, Indian Institute of Management Kozhikode.

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