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971.
N. Unnikrishnan Nair 《统计学通讯:理论与方法》2013,42(2):222-232
Quantile functions are equivalent alternatives to distribution functions in modeling and analysis of statistical data. The present article discusses the role of quantile functions in reliability studies. We present the hazard, mean residual, variance residual, and percentile residual quantile functions, their mutual relationships and expressions for the quantile functions in terms of these functions. Further, some theoretical results relating to the Hankin and Lee (2006) lambda distribution are discussed. 相似文献
972.
This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered. 相似文献
973.
Efthymios G. Tsionas 《统计学通讯:理论与方法》2013,42(9):1361-1370
In this article, it is shown that many intractable problems of Bayesian inference can be cast in a form called “artificial augmenting regression” in which application of Markov Chain Monte Carlo techniques, especially Gibbs sampling with data augmentation, is rather convenient. The new techniques are illustrated using several challenging statistical problems and numerical results are presented. 相似文献
974.
In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models. 相似文献
975.
The subtangent is the projection of the tangent upon the axis of abscissa. The usefulness of the reciprocal subtangent as a measure of the survival and density curves has earlier been reported in the literature for univariate distributions. This measure was generalized for bivariate and multivariate setups and related characterization problems were examined. The conditionally specified bivariate exponential distribution has been uniquely determined from the local constancy of the bivariate reciprocal subtangents. The case of global constancy and other related results have been studied. Conditionally specified bivariate Lomax distribution and normal distribution were also studied. Further, the conditionally specified multivariate exponential distribution was uniquely determined from the local constancy of the multivariate reciprocal subtangents. 相似文献
976.
In this article, we formulate a transfer theorem in terms of probability generating functions and discuss two approaches to limit distributions of random sums of Z +-valued random variables. We then develop Z +-valued N-ID and ?-ID laws. 相似文献
977.
In this article, we consider a new insurance risk model based on the entrance process proposed in Li et al. (2005), and investigate the finite time ruin probabilities of this model. It is showed that an exponential upper bound for the finite time ruin probability exists, when the distributions of the claim size are light tailed. Furthermore, when the distributions of the claim size are heavy tailed, an asymptotic formula for the finite time ruin probability is obtained. 相似文献
978.
In this article, we focus on some diagnostics for linear regression model with first-order autoregressive and symmetrical errors. The symmetrical class includes both light- and heavy-tailed univariate symmetrical distributions, which offers a more flexible framework for modeling. Maximum likelihood estimates are computed via the Fisher-score method. Score statistic and its adjustment are proposed for testing autocorrelation of the random errors. Local influence diagnostics are also derived for the model under some usual perturbation schemes. The performances of the test statistics are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our diagnostic methods. 相似文献
979.
The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Rao's score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the test's statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors. 相似文献
980.
Omar Abd Al-Rahman Ibrahim Kittaneh 《统计学通讯:理论与方法》2013,42(9):1797-1805
On the basis of Kullback-Leibler discrimination information, and of discrimination measures introduced by Ebrahimi and Kirmani (1996a) and by Di Crescenzo and Longobardi (2004), we propose a measure of discrepancy between double truncated distributions. Some properties of this measure are studied and some mistakes in the preceding literature are corrected. 相似文献