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.     

二元Block～Basu型指数分布的特征及其应用

导出了二元Block~Basu型指数分布的一个特征,利用该特征,获得了二元Block~Basu型指数分布参数的最大似然估计及矩估计,给出了强度服从二元Block~Basu型分布时并联结构系统可靠度的估计,并给出了二元Block~Basu型指数分布的一个随机模拟.     

二元Freund型指数分布的特征及参数估计

利用分布密度分拆的思想,导出了二元Freund型指数分布的一个特征,利用该特征,获得了二元Freund型指数分布参数的最大似然估计及矩估计,还给出了强度服从二元Freund型指数分布时并联结构系统的可靠度估计及模拟.     

二元Marshall~Olkin型指数分布的独立性和不相关性

若(X,Y)服从二元Marshall^Olkin型指数分布,则X,Y相互独立与不相关是等价的.     

二元Marshall-Olkin型指数分布的独立性和不相关性

若（X,Y）服从二元Marshall-Olkin型指数分布,则X,Y相互独立与不相关是等价的．     

二元Block-Basu型指数分布的独立性与不相关性

若（X,Y）服从二元Block-Basu型指数分布,则X,Y相互独立与不相关是等价的．还给出了X,Y的相关系数和尾部相关系数．     

二元一般指数分布的识别性及其参数估计

讨论了一般二元指数分布的识别性问题及参数估计问题.本文证明了两个结论:其一、当只有最大值随机变量的分布已知时,仅一个参数可识别;其二、当可识别最大值的分布已知时,所有参数皆可识别.进一步根据上述结论得到了所有参数的最大似然估计.     

一类多维指数分布的参数估计

考虑生存函数为(F)(x1,x2,…,xn)=P{X1＞x1,…,Xn＞xn}=exp{-[n∑i=1(xi/θi)1/δ]δ}(0＜xi＜∞,0＜δ≤ 1,0＜θi＜∞,i=(1,n))的一类多维指数分布,给出了它的密度函数的表示式,并讨论了它的性质.提出了相关参数δ的估计(^δ),证明了(^δ)有相合性和渐近正态性,得到了(^δ)的渐近方差σ2δ.最后还给出了若干随机模拟的结果.     

连续指数分布族中多维参数的改进估计

本文给出了Ｂｅｒｇｅｒ微分不等式的两类新解，并运用这些新解得到了连续指数分布族吕几种特殊分布族－正态分布族、Ｇａｍｍａ分布族等的改进估计表，推广了Ｂｅｒｇｅｒ、Ｇｈｏｓｈ的结果。     

二元Weinman型指数分布随机变量之和、差、积、商及比率的分布

出于水文科学应用的需要,本文导出了二元Weinman型指数分布随机变量之和、差、及比率的精确分布;计算了二元Weinman型指数分布随机变量之积、及商的精确分布,所得结果可应用于水文科学的教学和研究之中.     

On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation

In this paper, we consider two main families of bivariate distributions with exponential marginals for a couple of random variables $(X_1,X_2)$. More specifically, we derive closed-form expressions for the distribution of the sum $S=X_1+X_2$, the TVaR of $S$ and the contributions of each risk under the TVaR-based allocation rule. The first family considered is a subset of the class of bivariate combinations of exponentials, more precisely, bivariate combinations of exponentials with exponential marginals. We show that several well-known bivariate exponential distributions are special cases of this family. The second family we investigate is a subset of the class of bivariate mixed Erlang distributions, namely bivariate mixed Erlang distributions with exponential marginals. For this second class of distributions, we propose a method based on the compound geometric representation of the exponential distribution to construct bivariate mixed Erlang distributions with exponential marginals. Notably, we show that this method not only leads to Moran–Downton’s bivariate exponential distribution, but also to a generalization of this bivariate distribution. Moreover, we also propose a method to construct bivariate mixed Erlang distributions with exponential marginals from any absolutely continuous bivariate distributions with exponential marginals. Inspired from Lee and Lin (2012), we show that the resulting bivariate distribution approximates the initial bivariate distribution and we highlight the advantages of such an approximation.     

On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhy Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.     

Representation of Downton’s bivariate exponential random vector and its applications

Downton’s bivariate exponential distribution is one of the most important bivariate distributions in reliability theory. In this paper a simple representation for Downton’s bivariate exponential random vector is given. As an application of this representation, we consider a reliability model where an item is subject to shocks and obtain an explicit expression for the long-run cost rate.     

Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.     

On a class of bivariate exponential distributions

A class of absolutely continuous bivariate exponential distributions is constructed using the product form of a first order autoregressive model. Inference methods are proposed for parameter estimation and diagnosis. Data analysis is carried out to illustrate the applications.     

Statistical inference for a bivariate exponential distribution based on grouped data

Consider the bivarate exponential distribution due to Marshall and Olkin [2], whose survival function is F(x,y)=exp[-λ1x-λ2y-λ12 max(x,y)] (x≥0,y≥0)with unknown pexameters λ1＞0,λ2＞0 andλ12≥0. Based on grouped data, a new estimstor for ,λ1, ,λ2 and ,λ12 is derlved and its asymptotic perties are discussed.Bealdes, some test procedures of equalmarginals and independence are gven. A simulation result is given, too.     

Testing for symmetry and independence in a bivariate exponential distribution

Several bivariate exponential distributions have been proposed in the literature. A common problem for independent exponentials is to test the quality of the two distributions. The analogous problem for bivariate exponentials is to test for symmetry. For the bivariate exponential model of Freund (1961, Journal of the American Statistical Association 56, 971–977), tests of symmetry and independence are derived and the small sample distributions of the test statistics are found. The power function of the tests are calculated. The efficiency of the tests is found to be high on both an asymptotic and small sample basis.     

A note on the Sarmanov bivariate distributions

We investigate the maximum correlation for Sarmanov bivariate distributions with fixed marginals and strengthen the existing results in the literature. The improvement in the maximum correlation is significant. A characterization of the Sarmanov distribution via chi-square divergence is also given. This extends Nelsen [13] result about the Farlie-Gumbel-Morgenstern (FGM) distribution.