Comparison of k independent, zero-heavy lognormal distributions

作者：Zidan Marwan^*; Wang Jung Chao; Niewiadomska Bugaj Magdalena

来源：Canadian Journal of Statistics, 2011, 39(4): 690-702.

DOI：10.1002/cjs.10127

• Delta distributions
• data with excess of zeros
• two-part-tests
• MSC 2010: Primary 62F03

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), KruskalWallis, 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: 690702; 2011.

• 出版日期2011-12