## 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 (H_{1}-H_{4}) are defined. Under H _{1}, all k median parameters as well as all k skewness parameters are equal; under H_{2}, all k skewness parameters are equal but not all k median parameters are equal; under H_{3}, all k median parameters are equal but not all k skewness parameters are equal; under H_{4}, 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 H_{3} 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 language | English |
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Pages (from-to) | 157-169 |

Number of pages | 13 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 74 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2004 |

## Keywords

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