Estimation and comparison of lognormal parameters in the presence of censored data

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Abstract

It is assumed that k(k > 2) independent samples of sizes n i(i = 1, ..., k) are available from k lognormal distributions. Four hypothesis cases (H1-H4) are defined. Under H 1, all k median parameters as well as all k skewness parameters are equal; under H2, all k skewness parameters are equal but not all k median parameters are equal; under H3, all k median parameters are equal but not all k skewness parameters are equal; under H4, neither the k median parameters nor the k skewness parameters are equal. The Expectation Maximization (EM) algorithm is used to obtain the maximum likelihood (ML) estimates of the lognormal parameters in each of these four hypothesis cases. A (2k - 1) degree polynomial is solved at each step of the EM algorithm for the H3 case. A two-stage procedure for testing the equality of the medians either under skewness homogeneity or under skewness heterogeneity is also proposed and discussed. A simulation study was performed for the case k = 3.

Original languageEnglish
Pages (from-to)157-169
Number of pages13
JournalJournal of Statistical Computation and Simulation
Volume74
Issue number3
DOIs
Publication statusPublished - Mar 2004

Keywords

  • EM algorithm
  • Equality of medians
  • ML estimates
  • Skewness parameter

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