On some mixture models based on the Birnbaum-Saunders distribution and associated inference

N. Balakrishnan, Ramesh C. Gupta, Debasis Kundu, VICTOR ELISEO LEIVA SANCHEZ, Antonio Sanhueza

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31 Scopus citations

Abstract

In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) distribution, viz., (1) mixture of two different BS distributions, (2) mixture of a BS distribution and a length-biased version of another BS distribution, and (3) mixture of a BS distribution and its length-biased version. For all these models, we study their characteristics including the shape of their density and hazard rate functions. For the maximum likelihood estimation of the model parameters, we use the EM algorithm. For the purpose of illustration, we analyze two data sets related to enzyme and depressive condition problems. In the case of the enzyme data, it is shown that Model 1 provides the best fit, while for the depressive condition data, it is shown all three models fit well with Model 3 providing the best fit.

Original languageEnglish
Pages (from-to)2175-2190
Number of pages16
JournalJournal of Statistical Planning and Inference
Volume141
Issue number7
DOIs
StatePublished - 1 Jul 2011

Keywords

  • EM algorithm
  • Fisher information
  • Goodness-of-fit
  • Hazard rate function
  • Inverse Gaussian distribution
  • Length-biased distributions
  • Maximum likelihood methods

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