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

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.