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Comparison of k independent,zero‐heavy lognormal distributions
Authors:Marwan Zidan  Jung‐Chao Wang  Magdalena Niewiadomska‐bugaj
Institution:1. Wayne State University, Detroit, MI, USA;2. Western Michigan University, Kalamazoo, MI, USA
Abstract:Lachenbruch ( 1976 , 2001 ) introduced two‐part tests for comparison of two means in zero‐inflated continuous data. We are extending this approach and compare k independent distributions (by comparing their means, either overall or the departure from equal proportion of zeros and equal means of nonzero values) by introducing two tests: a two‐part Wald test and a two‐part likelihood ratio test. If the continuous part of the distributions is lognormal then the proposed two test statistics have asymptotically chi‐square distribution with $2(k-1)$equation image degrees of freedom. A simulation study was conducted to compare the performance of the proposed tests with several well‐known tests such as ANOVA, Welch ( 1951 ), Brown & Forsythe ( 1974 ), Kruskal–Wallis, and one‐part Wald test proposed by Tu & Zhou ( 1999 ). Results indicate that the proposed tests keep the nominal type I error and have consistently best power among all tests being compared. An application to rainfall data is provided as an example. The Canadian Journal of Statistics 39: 690–702; 2011. © 2011 Statistical Society of Canada
Keywords:Delta distributions  data with excess of zeros  two‐part‐tests  MSC 2010: Primary 62F03
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