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Comparison of k independent, zero‐heavy lognormal distributions
Author(s) -
Zidan Marwan,
Wang JungChao,
Niewiadomskabugaj Magdalena
Publication year - 2011
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10127
Subject(s) - mathematics , statistics , log normal distribution , wald test , likelihood ratio test , type i and type ii errors , zero (linguistics) , statistical hypothesis testing , philosophy , linguistics
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 $2(k-1)$ 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