Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

Robust williams trent test

To investigate the biological activities of a new compound or drug, experimenters usually compare a series of increasing doses to a control. Among other objectives, one may try to investigate any possible dose-response trend and to determine the minimum effective dose among all the experimental doses. Williams (1971, 1972) proposed a procedure to test the dose-response trend and also to identify the minimum effective dose based on the normally distributed data. In this paper, we propose a similar test procedure based on the robust estimate'of the average response to perform similar analysis. The proposed method is more resistant to the outliers and more powerful than the Williams procedure when the data distribution deviates from normality. We illustrate the use of this procedure with data arising from a recent study.     

Projectors and linear estimation in general linear models

The paper gives a self-contained account of minimum disper­sion linear unbiased estimation of the expectation vector in a linear model with the dispersion matrix belonging to some, rather arbitrary, set of nonnegative definite matrices. The approach to linear estimation in general linear models recommended here is a direct generalization of some ideas and results presented by Rao (1973, 19 74) for the case of a general Gauss-Markov model

A new insight into the nature of some estimation problems originaly arising in the context of a general Gauss-Markov model as well as the correspondence of results known in the literature to those obtained in the present paper for general linear models are also given. As preliminary results the theory of projectors defined by Rao (1973) is extended.     

A Note on Functional Forms of Order Statistics

Functional forms of order statistics, as the solution of a system of equations, are studied. The case of the smaller and the larger of two random variables is discussed in detail. Some applications for normal and binomial distributions are presented.     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.     

论我国城市贫困化与城市居民最低生活保障制度

最低生活保障制度作为城市社会保障体系的“最后一道安全网” ,是我国城市社会保障体系的重要一环 ,对促进经济的发展 ,维护社会的稳定起着举足轻重的作用。但是 ,我国建立城市居民最低生活保障制度的时间较晚 ,还有许多不足之处等待改进和完善     

Estimation of Distribution Functions Using Data from Different Environments

Suppose that when a unit operatesin a certain environment, its lifetime has distribution G,and when the unit operates in another environment, its lifetimehas a different distribution, say F. Moreover, supposethe unit is operated for a certain period of time in the firstenvironment and is then transferred to the second environment.Thus we observe a censored lifetime in the first environmentand a failure time of a ``used' unit in the second environment.We propose an EM algorithm approach for obtaining a self-consistentestimator of F. Moreover, suppose using observations from both environments.The case where failure times are subject to right censoring isconsidered as well. We also establish the maximum likelihoodestimator of F. Moreover, suppose when the unit is repairable. Applicationand simulation studies are presented to illustrate the methodsderived.     

Asymptotic properties of a generalized regression-type predictor of a finite population variance in probability sampling

A system of predictors for estimating a finite population variance is defined and shown to be asymptotically design-unbiased (ADU) and asymptotically design-consistent (ADC) under probability sampling. An asymptotic mean squared error (MSE) of a generalized regression-type predictor, generated from the system, is obtained. The suggested predictor attains the minimum expected variance of any design-unbiased estimator when the superpopulation model is correct. The generalized regression-type predictor and the predictor suggested by Mukhopadhyay (1990) are compared.     

On Approximability of Boolean Formula Minimization

For a Boolean function given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to , or -equivalent to , i.e., . In this paper we prove that if P NP then this problem can not be approximated with a good approximation ratio by a polynomial time algorithm.