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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]

Negative hypergeometric distribution arises as a waiting time distribution when we sample without replacement from a finite population. It has applications in many areas such as inspection sampling and estimation of wildlife populations. However, as is well known, the negative hypergeometric distribution is over-dispersed in the sense that its variance is greater than the mean. To make it more flexible and versatile, we propose a modified version of negative hypergeometric distribution called COM-Negative Hypergeometric distribution (COM-NH) by introducing a shape parameter as in the COM-Poisson and COMP-Binomial distributions. It is shown that under some limiting conditions, COM-NH approaches to a distribution that we call the COM-Negative binomial (COMP-NB), which in turn, approaches to the COM Poisson distribution. For the proposed model, we investigate the dispersion characteristics and shape of the probability mass function for different combinations of parameters. We also develop statistical inference for this model including parameter estimation and hypothesis tests. In particular, we investigate some properties such as bias, MSE, and coverage probabilities of the maximum likelihood estimators for its parameters by Monte Carlo simulation and likelihood ratio test to assess shape parameter of the underlying model. We present illustrative data to provide discussion. [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]

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]

Using multivariate statistical models, no significant relationship was found between the rate of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) elimination and the occurrence or time to onset of diabetes in 343 veterans of Operation Ranch Hand, the unit responsible for the aerial spraying of Agent Orange and other TCDD-contaminated herbicides during the Vietnam War. Without adjustment for age, body mass index, family history of diabetes, and smoking history, the time to onset of diabetes decreased and the risk of diabetes increased with a diminished elimination rate. However, after adjustment, diabetes time to onset and occurrence were not significantly associated with TCDD elimination. Analyses of covariance found no significant difference between the average elimination rates of diabetic and nondiabetic veterans, without or with adjustment for risk factors. To our knowledge, this is the only study to date to examine TCDD elimination and diabetes. [ABSTRACT FROM AUTHOR]

A combined analysis of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) elimination in Seveso adults and Ranch Hand veterans found a period of fast elimination within the first 0.27 years after exposure in Seveso, followed by a period of slower elimination between 3 and 16.35 years from exposure. The mean TCDD elimination rate within the first 0.27 years after exposure among six adult males in the Seveso cohort was 2.0646 year[sup -1] (half-life = 0.34 years). The mean rate from 3 to 16.35 years was 0.1011 year[sup -1] (half-life = 6.9 years). The mean Ranch Hand elimination rate, 00924 year[sup -1] (half-life = 6.9 years), measured between 9 and 33 years after exposure, was significantly less than the Seveso mean in the first 0.27 years after exposure, but not significantly different from the Seveso mean between 3 and 16.35 years after exposure. The fast elimination within the first 0.27 years followed by a slower rate after 3 years is consistent with the expected pattern in a two-compartment open model, with a distribution phase of rapid elimination followed by a slower elimination phase. [ABSTRACT FROM AUTHOR]

Using multiple measurements from serum collected over 15 yr (in 1982, 1987, 1992, and 1997), the half-life of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in 97 veterans of Operation Ranch Hand, the Air Force unit responsible for the aerial spraying of Agent Orange in Vietnam, was estimated. The potential influences of age, percent body fat, and changes in percent body fat on the half-life estimate were also examined. The elimination rate of TCDD for these veterans was 0.0915 per year with 95% confidence interval 0.0844 to 0.0986 per year; the corresponding half-life estimate was 7.6 yr with 95% confidence interval 7.0 to 8.2 yr. The elimination rate decreased significantly with increasing body fat, but not with age or relative changes in percent body fat. [ABSTRACT FROM AUTHOR]

The authors present algorithms to compute the confidence interval for a Poisson parameter (λ) and the p value for testing the hypothesis that λ is equal to a constant, which can be used to make inferences about the standardized mortality ratio and the standardized incidence ratio. The p value and confidence interval always agree, despite the discrete nature of the Poisson distribution. The authors also give simple equations to compute numeric approximations of the confidence limits that do not require the use of any probability distributions. An example based on data arising from a study of cancer incidence is given. [ABSTRACT FROM PUBLISHER]

Using multiple m easurem ents from serum collected over 10 yr (1982, 1987, and 1992), we estimated the half-life of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in 213 veterans of Operation Ranch Hand, the Air Force unit responsible for the aerial spraying of Agent Orange in Vietnam. The potential influences of age, percent body fat, and changes in percent body fat on the half-life estimate were also examined. The mean decay rate of TCDD for these veterans is 0.0797 per year with 95% confidence interval 0.0727 to 0.0868 per year; the corresponding half-life estimate is 8.7 yr with 95% confidence interval 8.0-9.5 yr. Half-life increased significantly with increasing body fat, but not with age or relative changes in percent body fat. [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]

This article investigates the effect of misclassification and measurement error in the basic data on the asymptotic bias and efficiency of the logistic regression (LR) and normal discrimination (ND) classification procedures. The effect of misclassification in a single binary independent variable on the bias and efficiency of both procedures is also presented. Typically, asymptotic bias increases and efficiency decreases as misclassification and measurement error increase. The performance of LR relative to ND is shown to be better in the presence of error than without error. [ABSTRACT FROM AUTHOR]

Presents a simple approximation for unbiased estimation of the standard deviation. Adjustments of the sample standard deviation; Multiplication of the sample standard deviation with a corrective constant; Modification of the degrees of freedom in the denominator of the estimator.