The Generalized Birnbaum–Saunders Distribution and Its Theory,Methodology, and Application

In this paper, we discuss the class of generalized Birnbaum–Saunders distributions, which is a very flexible family suitable for modeling lifetime data as it allows for different degrees of kurtosis and asymmetry and unimodality as well as bimodality. We describe the theoretical developments on this model including properties, transformations and related distributions, lifetime analysis, and shape analysis. We also discuss methods of inference based on uncensored and censored data, diagnostics methods, goodness-of-fit tests, and random number generation algorithms for the generalized Birnbaum–Saunders model. Finally, we present some illustrative examples and show that this distribution fits the data better than the classical Birnbaum–Saunders model.     

Statistical Inference for Damaged Poisson Distribution

Abstract

For non-negative integer-valued random variables, the concept of “damaged” observations was introduced, for the first time, by Rao and Rubin [Rao, C. R., Rubin, H. (1964). On a characterization of the Poisson distribution. Sankhya 26:295–298] in 1964 on a paper concerning the characterization of Poisson distribution. In 1965, Rao [Rao, C. R. (1965). On discrete distribution arising out of methods of ascertainment. Sankhya Ser. A. 27:311–324] discusses some results related with inferences for parameters of a Poisson Model when it has occurred partial destruction of observations. A random variable is said to be damaged if it is unobservable, due to a damage mechanism which randomly reduces its magnitude. In subsequent years, considerable attention has been given to characterizations of distributions of such random variables that satisfy the “Rao–Rubin” condition. This article presents some inference aspects of a damaged Poisson distribution, under reasonable assumption that, when an observation on the random variable is made, it is also possible to determine whether or not some damage has occurred. In other words, we do not know how many items are damaged, but we can identify the existence of damage. Particularly it is illustrated the situation in which it is possible to identify the occurrence of some damage although it is not possible to determine the amount of items damaged. Maximum likelihood estimators of the underlying parameters and their asymptotic covariance matrix are obtained. Convergence of the estimates of parameters to the asymptotic values are studied through Monte Carlo simulations.     

Least squares and generalized least squares in models with orthogonal block structure

Besides the basic model, Kronecker products of rotated models are used to isolate the variance components as parameters of a linear model. A characterization of BLUE given by Zmy?lony (1980) is applied to the different models. Generalized least squares are used to complete the estimation.     

俞敏先生训诂方法研究

俞敏先生将传统训诂方法和现代语言学理论方法融会贯通,形成了他独特的研究方法,从而为汉语古文献的研究提出了很多独到的见解。他的训诂研究方法可以归结为3个方面:将因声求义与因形求义相结合进行训诂研究;首次利用语流音变对古文献进行研究;率先运用汉藏比较进行训诂研究。     

A Parametric approach to the Estimation of Cointegration Vectors in Panel Data

In this article, a parametric framework for estimation and inference in cointegrated panel data models is considered that is based on a cointegrated VAR(p) model. A convenient two-step estimator is suggested where, in the first step, all individual specific parameters are estimated, and in the second step, the long-run parameters are estimated from a pooled least-squares regression. The two-step estimator and related test procedures can easily be modified to account for contemporaneously correlated errors, a feature that is often encountered in multi-country studies. Monte Carlo simulations suggest that the two-step estimator and related test procedures outperform semiparametric alternatives such as the fully modified OLS approach, especially if the number of time periods is small.     

Bayesian Computations for Random Environment Models

This paper deals with the analysis of reliability data from a Bayesian perspective for Random Environment (RE) models. We give an overview of current literature on RE models. We also study the computational problems associated with the implementations of RE models in a Bayesian setting. Then, we present the Markov Chain Monte Carlo technique to solve such problems. These problems arise in posterior and predictive analysis and their relevant quantities such as mean, variance, and median. The suggested methodology is incorporated with an illustration.     

纳什均衡策略的极大熵估计方法

给出了策略熵的定义,论证了最大策略熵是纳什均衡的充分必要条件,并探讨了运用熵极大化准则来估计博弈参与者的混合策略的方法,得到了与传统方法相同的纳什均衡解,这表明纳什均衡策略是既定的收益约束条件的最大熵,为纳什均衡提供了基于信息论的解释,同时也为求解纳什均衡提供了一种极大熵估计方法,算例验证了该方法的可行性和有效性。