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351.
The generalized Waring distribution is a discrete distribution with a wide spectrum of applications in areas such as accident statistics, income analysis, environmental statistics, etc. It has been used as a model that better describes such practical situations as opposed to the Poisson distribution or the negative binomial distribution. Associated to both the Poisson and negative binomial distributions are the well-known Poisson and Pólya processes. In this article, the generalized Waring process is defined. Two models have been shown to lead to the generalized Waring process. One is related to a Cox process, while the other is a compound Poisson process. The defined generalized Waring process is shown to be a stationary, but non homogenous Markov process. Several properties are studied and the intensity, individual intensity, and Chapman–Kolmogorov differential equations of it are obtained. Moreover, the Poisson and Pólya processes are shown to arise as special cases of the generalized Waring process. Using this fact, some known results and some properties of them are obtained. 相似文献
352.
Comparative lifetime experiments are important when the object of a study is to determine the relative merits of two competing duration of life products. This study considers the interval estimation for two Weibull populations when joint Type-II progressive censoring is implemented. We obtain the conditional maximum likelihood estimators of the two Weibull parameters under this scheme. Moreover, simultaneous approximate confidence region based on the asymptotic normality of the maximum likelihood estimators are also discussed and compared with two Bootstrap confidence regions. We consider the behavior of probability of failure structure with different schemes. A simulation study is performed and an illustrative example is also given. 相似文献
353.
In this paper, Anbar's (1983) approach for estimating a difference between two binomial proportions is discussed with respect to a hypothesis testing problem. Such an approach results in two possible testing strategies. While the results of the tests are expected to agree for a large sample size when two proportions are equal, the tests are shown to perform quite differently in terms of their probabilities of a Type I error for selected sample sizes. Moreover, the tests can lead to different conclusions, which is illustrated via a simple example; and the probability of such cases can be relatively large. In an attempt to improve the tests while preserving their relative simplicity feature, a modified test is proposed. The performance of this test and a conventional test based on normal approximation is assessed. It is shown that the modified Anbar's test better controls the probability of a Type I error for moderate sample sizes. 相似文献
354.
Debanjan Bhattacharjee 《统计学通讯:理论与方法》2013,42(6):1046-1053
Walsh (1995) introduced a heuristic approach to motivate Stirling's formula by equating a Poisson probability to an analogous value from a normal density function. We explore similar heuristics to derive approximations for various binomial, negative binomial, and multinomial coefficients. Also, using heuristics markedly different from those of Walsh, we develop an approximation of (nk)! for positive integers n (large) and k. These heuristics are then used to validate Stirling's formula for Γ(nα) where α is a positive real number. To derive each of our approximations we use a different probability distribution, and hence each section may serve as pedagogical module. 相似文献
355.
356.
Aleksandar S. Nastić 《统计学通讯:理论与方法》2013,42(23):4285-4301
Two types of shifted geometric integer valued autoregressive models of order one (SGINAR(1)) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR(1) models. 相似文献
357.
Two generalized hypergeometric distributions are identified as mixed binomial distributions by conditional specification. Both distributions show profiles that are not possible in other mixed binomial distributions such as the beta-binomial distribution. A simulation study illustrates that beta-binomial distribution is more precise to fit data with usual profiles but the two distributions presented can improve the capability of fitting data in other less common scenes. 相似文献
358.
ABSTRACTA bivariate integer-valued autoregressive time series model is presented. The model structure is based on binomial thinning. The unconditional and conditional first and second moments are considered. Correlation structure of marginal processes is shown to be analogous to the ARMA(2, 1) model. Some estimation methods such as the Yule–Walker and conditional least squares are considered and the asymptotic distributions of the obtained estimators are derived. Comparison between bivariate model with binomial thinning and bivariate model with negative binomial thinning is given. 相似文献
359.
Bayes estimation of the binomial parameter n based on a general prior distribution for n is studied. As special cases improper prior and Poisson prior (which is a natural choice) are considered, and formulae for the marginal and posterior distributions are obtained. It is shown that the assumption of improper priors in both p and n leads to implausible results. 相似文献
360.
Two Bayes-type procedures for estimating a multinomial cell probabilities vector, P, in the presence of linear constraints on the parameters are proposed and illustrated by examples from contingency table analysis. Estimation under log-linear constraints is also considered. 相似文献