Abstract
Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based on this idea. Our results show that although these two tests are asymptotically equivalent under the null hypothesis and are equally efficient, one test is always more efficient than the other one for small and medium sample sizes.
Highlights
The Poisson distribution is the standard model for counting data, for example, the number of telephone calls within a specific time period [1]
The Zero-inflated Poisson (ZIP) distribution [2] and the negative binomial distribution [3,4] have been proposed to catch this overdispersion in practical data
El-Shaarawi [6] compares the properties of the likelihood ratio test, the Cochran test [13], and the Rao test [17]
Summary
The Poisson distribution is the standard model for counting data, for example, the number of telephone calls within a specific time period [1]. In the definition of ZIP distribution, the parameter p in the Bernoulli distribution is required to be in 0,1 , formula (1) always define a valid probability distribution as long as p. This means that p can be greater than 1. When 0.1 , p 10.1, formula (1) still defines a valid probability distribution. In this paper we construct two nonparametric test statistics and compare the efficiency, the empirical size, and power of two closely related tests, especially for the cases of small and medium sample sizes
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