Estimating Average Worth of the Selected Subset from Two-Parameter Exponential Populations

ABSTRACT

Suppose independent random samples are available from k(k ≥ 2) exponential populations ∏₁,…,∏ _k with a common location θ and scale parameters σ₁,…,σ _k , respectively. Let X _i and Y _i denote the minimum and the mean, respectively, of the ith sample, and further let X = min{X ₁,…, X _k } and T _i  = Y _i  ? X; i = 1,…, k. For selecting a nonempty subset of {∏₁,…,∏ _k } containing the best population (the one associated with max{σ₁,…,σ _k }), we use the decision rule which selects ∏ _i if T _i  ≥ c max{T ₁,…,T _k }, i = 1,…, k. Here 0 < c ≤ 1 is chosen so that the probability of including the best population in the selected subset is at least P* (1/k ≤ P* < 1), a pre-assigned level. The problem is to estimate the average worth W of the selected subset, the arithmetic average of means of selected populations. In this article, we derive the uniformly minimum variance unbiased estimator (UMVUE) of W. The bias and risk function of the UMVUE are compared numerically with those of analogs of the best affine equivariant estimator (BAEE) and the maximum likelihood estimator (MLE).     

Bayesian Estimation of the Size of a Closed Population Using Photo-ID Data with Part of the Population Uncatchable

Abstract

We develop a Bayesian statistical model for estimating bowhead whale population size from photo-identification data when most of the population is uncatchable. The proposed conditional likelihood function is a product of Darroch's model, formulated as a function of the number of good photos, and a binomial distribution of captured whales given the total number of good photos at each occasion. The full Bayesian model is implemented via adaptive rejection sampling for log concave densities. We apply the model to data from 1985 and 1986 bowhead whale photographic studies and the results compare favorably with the ones obtained in the literature. Also, a comparison with the maximum likelihood procedure with bootstrap simulation is considered using different vague priors for the capture probabilities.     

Blinded sample size re-estimation in clinical trials comparing several treatments

An important question that arises in clinical trials is how many additional observations, if any, are required beyond those originally planned. This has satisfactorily been answered in the case of two-treatment double-blind clinical experiments. However, one may be interested in comparing a new treatment with its competitors, which may be more than one. This problem is addressed in this investigation involving responses from arbitrary distributions, in which the mean and the variance are not functionally related. First, a solution in determining the initial sample size for specified level of significance and power at a specified alternative is obtained. Then it is shown that when the initial sample size is large, the nominal level of significance and the power at the pre-specified alternative are fairly robust for the proposed sample size re-estimation procedure. An application of the results is made to the blood coagulation functionality problem considered by Kropf et al. [Multiple comparisons of treatments with stable multivariate tests in a two-stage adaptive design, including a test for non-inferiority, Biom. J. 42(8) (2000), pp. 951–965].     

Testing Variability in the Two-Sample Case

A number of robust methods for testing variability have been reported in previous literature. An examination of these procedures for a wide variety of populations confirms their general robustness. Shoemaker's improvement of the F test extends that test use to a realistic variety of population shapes. However, a combination of the Brown–Forsythe and O'Brien methods based on testing kurtosis is shown to be conservative for a wide range of sample sizes and population distributions. The composite test is also shown to be more powerful in most conditions than other conservative procedures.     

Suburban ethnicities: Home as the site of interethnic conviviality and racism

This article explores the ways in which the white working-class residents of a suburban English town reflect on their relationships with their British Asian Pakistani Muslim neighbors. Its focus is on how everyday constructions of home become sites for the intermingling of discourses of intercultural conviviality and racism. My contention is that the idea of home has not yet been given the detailed critical attention that it deserves in the sociological literature on everyday manifestations of multiculturalism, conviviality, and racism. My supposition is that a special focus on the idea of home as the site of conviviality offers a productive avenue to analyze how intercultural relationships are formed and how the norms of neighborliness are thought to break down, opening a space for commonplace racialized and racist stereotypes to take hold. The idea of home is central to the rhythm and landscape of the English suburbs. It conjures up the idea of a uniform and aspirational white space. Drawing on this imaginary of home, I shall trace how “white working class” “English,” “Scottish,” and “Anglo-Italian” residents’ everyday constructions of home become embroiled with their relationships with their British Asian Pakistani Muslim neighbors.     

‘When and where does being Welsh matter to me?’ The influence of cross-border mobilities on constructions of sub-national belonging in the lives of Welsh Muslims*

This article will discuss how Welsh Muslims construct what a sense of place means to them through their cross-border mobility between England and Wales, and how this contributes to the ongoing re-construction of a plural understanding of nationhood in an era of diversity. To understand when and where being Welsh matters to Welsh Muslims, it will explore how mobility rather than being the antithesis of belonging, can be used as an essential tool in highlighting how perceptions of the nation, sub-state nation, home and place are influenced and understood.     

美国的全日制伊斯兰学校

美国全日制伊斯兰学校是美国穆斯林团体或宗教组织自主创办和管理的学校,目的旨在培养子女继承伊斯兰传统文化和宗教信仰.本文运用文本资料和实地考察相结合的方法,首先对这些学校的现状进行了介绍,其次对其存在的问题进行了比较客观的分析,这些问题主要是办学宗旨或教学内容调整的问题、师资招募及其水平提高的问题、教材编写的问题、资金不...     

The simultaneous confidence intervals for all distances from the extreme populations for two-parameter exponential populations based on the multiply type II censored samples

Among k independent two-parameter exponential distributions which have the common scale parameter, the lower extreme population (LEP) is the one with the smallest location parameter and the upper extreme population (UEP) is the one with the largest location parameter. Given a multiply type II censored sample from each of these k independent two-parameter exponential distributions, 14 estimators for the unknown location parameters and the common unknown scale parameter are considered. Fourteen simultaneous confidence intervals (SCIs) for all distances from the extreme populations (UEP and LEP) and from the UEP from these k independent exponential distributions under the multiply type II censoring are proposed. The critical values are obtained by the Monte Carlo method. The optimal SCIs among 14 methods are identified based on the criteria of minimum confidence length for various censoring schemes. The subset selection procedures of extreme populations are also proposed and two numerical examples are given for illustration.     

西北穆斯林妇女参政现状及其制约因素——基于甘肃省广河县的田野调查

甘肃省广河县穆斯林人口占全县97%以上。近年来,该县妇女参政状况有了一定改善,但其参政比例仍然偏低,这其中有经济、文化、教育方面的因素,也与其薄弱的参政意识、社会分工与社会角色、社会认同与自我认同等密切相关。