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The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality control, and the number of initial faults present in software coding. Recently, Borges et al. considered a COM type generalization of the binomial distribution, called COM–Poisson–Binomial (CMPB) and investigated many of its characteristics and some interesting applications. In the same spirit, we develop here a generalization of the hypergeometric distribution, called the COM–hypergeometric distribution. We discuss many of its characteristics such as the limiting forms, the over- and underdispersion, and the behavior of its failure rate. We write its probability-generating function (pgf) in the form of Kemp's family of distributions when the newly introduced shape parameter is a positive integer. In this form, closed-form expressions are derived for its mean and variance. Finally, we develop statistical inference procedures for the model parameters and illustrate the results by extensive Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The Wilcoxon rank-sum test is a well-known nonparametric test for the equality of two distributions. In this article, we study a two-stage nonparametric procedure by first testing symmetry for the two underlying distributions and then using the Wilcoxon-type precedence test based on right-censored samples. Specifically, in the first stage, we use a test of symmetry for the two underlying distributions. Then, in the second stage, the minimal Wilcoxon rank-sum precedence test based on a partial sample is used for testing the equality of the two distributions against the stochastically ordered alternative, in which the size of the partial sample is determined by the outcome in the first stage. A simulation study reveals that the proposed two-stage procedure maintains the nominal level of significance and performs better than the classical Wilcoxon rank-sum test in terms of power in many situations. Finally, a numerical example is presented to illustrate the nonparametric procedures developed here. [ABSTRACT FROM PUBLISHER]

Abstract: In reliability and survival analysis, comparison of two or more populations is an important problem. For example, while comparing a treatment group with a control group, one may be interested in determining whether the observations in the treatment group have a longer lifetime than those from the control group, that is, whether the treatment is effective or not. In such a study, it would be extremely valuable to make a decision based on early failures. In this paper, we consider independent progressively Type-II censored random samples from two populations with cumulative distribution function''s (cdf) and respectively, and discuss a precedence test for testing the equality of the two distributions based on placements. For this purpose, we derive the joint distribution of the first l placement statistics from the progressively censored sample from . We then derive the exact null distribution of the precedence test statistic which is simply the sum of the placements. We provide the rejection regions for fixed levels of significance and various sample sizes and different progressive censoring schemes. [Copyright &y& Elsevier]

In certain applications involving count data, it is sometimes found that zeros are observed with a frequency significantly higher (lower) than predicted by the assumed model. Examples of such applications are cited in the literature from engineering, manufacturing, economics, public health, epidemiology, psychology, sociology, political science, agriculture, road safety, species abundance, use of recreational facilities, horticulture and criminology. In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such an adjustment is necessary. Examples, with and without covariates, are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

A modification of the quadratic form involved in a generalized minimum chi-squared procedure yields the same asymptotic null distribution of the test statistic for testing fit by an assumed model, but a different form of nonnull distribution emerges. This result is applied to testing fit of the negative binomial and Neyman Type A distributions, and tables of asymptotic power are presented that show the increase of power obtained. A numerical example is presented to illustrate the technique. [ABSTRACT FROM AUTHOR]