Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data

In this paper, we establish the existence and uniqueness of the maximum-likelihood estimates of the parameters of a general class of inverse exponentiated distributions based on complete as well as progressively Type-I and Type-II censored data.     

澜湄命运共同体建设的意义、动因和路径选择

构建澜湄国家命运共同体是中国周边外交和亚洲命运共同体构想的具体实践，将助力东盟共同体建设，促进次区域稳定和繁荣。本文通过对澜湄命运共同体建设的意义、动因和影响因素分析，提出了澜湄命运共同体建设的路径选择。     

The exponential–Weibull lifetime distribution

In this paper, we propose a new three-parameter model called the exponential–Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for the incomplete moments based on infinite sums of Meijer's G functions. We also obtain explicit expressions for the generating function and mean deviations. We estimate the model parameters by maximum likelihood and determine the observed information matrix. Some simulations are run to assess the performance of the maximum likelihood estimators. The flexibility of the new distribution is illustrated by means of an application to real data.     

农村劳动力转移就业的多元路径选择

长期以来，我国农村劳动力转移就业基本上是以流向东部沿海经济发达地区为主的单一模式。近年来，受东部沿海地区产业向中西部地区转移进程加快和内地经济快速发展的影响，区域间的比较优势逐渐弱化，农村劳动力远距离就业的选择空间越来越大，当地政府必须通过调整农业经济结构、鼓励农民自主创业、加大招商引资力度和开辟国外劳务市场等途径探索多元转移就业路径，实现农村劳动力合理转移就业。     

Testing for a change point in a sequence of exponential random variables with repeated values

Two test statistics are proposed for the change-point problem with repeated values when the data follow an exponential distribution. The properties of these two statistics have been studied and their asymptotic distributions under the alternative have been derived. The powers of the two test statistics are compared. Real-data examples are presented to illustrate the application of these tests.     

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G.M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883–898], proposed a new generalized distribution (denoted here with the prefix ‘Kw-G’ (Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-G density function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155–161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279–285] and Kw-Flexible Weibull [M. Bebbington, C.D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719–726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Rényi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.     

Empirical Bayes estimation in continuous one-parameter exponential families under associated samples

In this paper, we study the empirical Bayes (EB) estimation in continuous one-parameter exponential families under negatively associated (NA) samples and positively associated (PA) samples. Under certain regularity conditions, it is shown that the convergence rates of proposed EB estimators under NA or PA samples are the same as those of EB estimators under independent observations, which significantly improve the existing results in EB estimation under associated samples.     

Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.     

The competing risks analysis for parallel and series systems using Type-II progressive censoring

Abstract

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach.     

The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.