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 (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 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.
skewness parameter em algorithm equality of medians ml estimates