Distributional analysis of a generalization of the Polya process

A nonhomogeneous birth process generalizing the Polya process is analyzed, and the distribution of the transition probabilities is shown to be the convolution of a negative binomial distribution and a compound Poisson distribution, whose secondary distribution is a mixture of zero-truncated geometric distributions. A simplified form of the secondary distribution is obtained when the transition intensities have a particular structure, and may sometimes be expressed in terms of Stirling numbers and special functions such as the incomplete gamma function, the incomplete beta function, and the exponential integral. Conditions under which the compound Poisson form of the marginal distributions may be improved to a geometric mixture are also given.     

On the Bessel Distribution and Related Problems

This article investigates basic properties of the Bessel distribution, a power series distribution which has not been fully explored before. Links with some well-known distributions such as the von Mises-Fisher distribution are described. A simulation scheme is also proposed to generate random samples from the Bessel distribution. This scheme is useful in Bayesian inferences and Monte Carlo computation.     

Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments

The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments.     

Estimating stability in the problem of reconstructing the additive type of a distribution

A numerical estimate of stability is obtained in the problem of reconstructing the additive type of a distribution via the distribution of a maximal invariant.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im V. A. Steklova AN SSSR, Vol. 61, pp. 68–74, 1976.     

A new method to simulate the triangular distribution

A new method is developed to simulate the triangular distribution. The result is of interest from a practical as well as a theoretical viewpoint. The new method is surprisingly simple and is more efficient than the standard method of simulation by inversion of the cumulative distribution function. The method is also generalized to simulate the two-sided power distribution.     

Question of stability estimation in the problem of reconstructing the type of a distribution

A quantitative estimate is obtained for the stability in the problem of reconstructing the complete type of a distribution according to the distribution of a maximal invariant.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 87, pp. 7–17, 1979.     

Probability plots and order statistics of the standard extreme value distribution

A comparison between the ordinary least-squares estimator and the weighted least-squares estimator when the data set arises from the standard extreme value distribution is provided. Probability plot of the extreme value distribution is applied. A goodness-of-fit test of the standard extreme value distribution is introduced. The percentage points of the test statistic are investigated. The results of power study for the test statistic under various alternatives show that in most situations the proposed test statistic serves as well as do competing alternatives.     

无失效数据情形失效率的估计及其应用

该文对指数分布的无失效数据,在失效率　的先验密度的核为　ａ－１时,给出了失效率　的Ｂａｙｅｓ估计和多层Ｂａｙｅｓ估计．并对某液压电动机,在寿命眼从指数分布时,给出了该液压电动机无失效数据情形可靠度的估计．     

Percentile estimation based on the power-normal distribution

The authors propose several estimation methods for the confidence interval of the percentile of the power-normal distribution, which specifies the distribution of the observed values before Box–Cox transformation and assumes that transformed distribution is the truncated normal distribution. Their approaches are based on the delta method and the inverse transformation method. Then the finite sample performance of each estimation method is compared through a simulation, and it is shown that the performance of the inverse transformation method is superior to the delta method. A reparametrization method of the power-normal distribution, which is useful parameter setting tool in simulations, is suggested. The authors also investigate the asymptotic behavior of the coverage probability of the confidence interval of the percentile of the power-normal distribution in the case wherein the variance inflation of the MLE associated with the estimation of the transformation parameter of the power-normal distribution is ignored.     

Reconstruction of the error distribution in the linear regression scheme

Under a certain condition, the characterization of the additive type of an error distribution by the distribution of a maximal invariant is proved in the linear regression scheme. With an added condition on the design matrix, the possibility of reconstructing the error distribution itself is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 87, pp. 36–40, 1979.The author is grateful to L. B. Klebanov for his interest in this article.     

Estimation of the Scale Matrix and its Eigenvalues in the Wishart and the Multivariate F Distributions

In this paper, the problem of estimating the scale matrix and their eigenvalues in a Wishart distribution and in a multivariate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean are proposed. It is shown that the new estimator which dominates the usual unbiased estimator under the squared error loss function. A simulation study was carried out to study the performance of these estimators.     

LAPLACE TRANSFORM OF THE SURVIVAL PROBABILITY UNDER SPARRE ANDERSEN MODEL

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.     

二元Weinman型指数分布的特征及其应用

导出了Weinman型二元指数分布的一个特征,由此获得了参数θj(j=0,1)的最大似然估计及矩估计,给出了二元Weinman型指数分布的二种模拟,还得到了强度为二元Weinman分布时并联结构系统可靠度的估计.     

On the Inverse Source Problem for the Newtonian Potential

The paper deals with the inverse source problems for the Newtonian potential in the sense of distribution (generalized functions). The inverse source problem is defined as follows: A domain G is given. To find is a distribution creating the potential which is known outside of the closed domain G. New results can be applied to electronical fields, because the electrical charge is distributed only on the surface of conductor.     

A preliminary test procedure for the scale parameter of exponential distribution when the selection parameter is unknown

Summary A preliminary test estimator is considered for the scale parameter of the two-parameter exponential distribution with unknown selection parameter, where the distribution does not satisfy the regularity condition of Wilks' theorem—the density is not differentiable. A method of specifying the level of significance of the preliminary test based on is proposed AIC. This work was partly supported by Scientific Research Fund No. 58450058 from the Ministry of Education of Japan. The Institute of Statistical Mathematics     

On the compounded bivariate Poisson distribution: A unified treatment

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the conditional distribution is simplified. Four cases are presented in detail.     

震后初期应急物资短缺情景下的定位-路径问题研究

基于公平视角研究震后初期灾区应急物资短缺情景下的定位-路径问题(location-routing problem,LRP),综合考虑灾害级别、灾区应急路网不同程度损毁、需求点易损性与车辆随机行驶时间等因素,以单个需求点的最大损失最小作为应急物资分配的公平性衡量指标、以总配送时间最短作为应急物资配送的效率性衡量指标,在此基础上构建双目标LRP模型,并基于分层序列法思想设计一种二阶段混合启发式求解算法。最后,采用汶川地震之后的帐篷配送数据验证本文方法公平性与效率性兼顾。     

Reducing bias of the maximum likelihood estimator of shape parameter for the gamma Distribution

The gamma distribution is an important probability distribution in statistics. The maximum likelihood estimator (MLE) of its shape parameter is well known to be considerably biased, so that it has some modified versions. A new modified MLE of the shape for the gamma distribution is proposed in this paper, which is consistent, asymptotically normal and efficient. For finite-sample behavior, the new estimator improves the traditional MLE not only for reducing bias but also for gaining estimation efficiency significantly. In terms of estimation efficiency, it dominates other existing modified estimators.     

Distribution of k-th record values in the discrete case

A result is found for discrete random variables, which lets one express the distribution of k-th record values in terms of the distribution of sums of independent summands.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 133–137, 1987.