Testing the Equality of Two Exponential Distributions

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzman's overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.     

序言

编者按:由埃及著名学者侯赛因·卡米勒·巴哈丁著,朱威烈、丁俊译的<十字路口>一书已由上海外语教育出版社于2005年4月出版,特选录其中的"序言"、"译后记"及部分章节,以飨读者.     

A comparison of age difference reaction to computer interface

In this work, a simplified interface system for education of people with disabilities is presented. This platform allows the control of different tools (PC games, robot, and electric wheelchair) using different interfaces (mouse, joysticks, etc.). This interface system can be automatically reconfigured to match user’s ability, and it is operated locally or remotely through the internet. Saving of experimental progress data for later analysis can be done. Quantitative indicators are defined for evaluation purposes and to determine the needed assistance and adaptation. The system is tested on different age groups for people without physical disability. Results are presented and discussed.     

Bayes and Empirical Bayes Estimation of the Parameter n in a Binomial Distribution

The problem of estimating the total number of trials n in a binomial distribution is reconsidered in this article for both cases of known and unknown probability of success p from the Bayesian viewpoint. Bayes and empirical Bayes point estimates for n are proposed under the assumption of a left-truncated prior distribution for n and a beta prior distribution for p. Simulation studies are provided in this article in order to compare the proposed estimate with the most familiar n estimates.     

THE INVESTIGATION OF COST VARIANCES: A FUZZY SET THEORY APPROACH*

In a standard costing system, deviations (variances) of actual cost from standard cost should be investigated in order to help management identify the causes of the variances and who is responsible for them before corrective actions are taken. In reality, however, actual cost rarely equals standard cost and so many variances occur that it is impractical and uneconomical to investigate all of them. These two conflicting factors—the necessity of investigating cost variances and the impracticality of investigating all the variances—present management with the problem of deciding which variances to investigate. In this paper a model, based on fuzzy set theory, for the cost-variance investigation is proposed and applied to an actual investigation problem faced by a manufacturing company.     

Testing the similarity of two normal populations with application to the bioequivalence problem

The problem of testing the similarity of two normal populations is reconsidered, in this article, from a nonclassical point of view. We introduce a test statistic based on the maximum likelihood estimate of Weitzman's overlapping coefficient. Simulated critical points are provided for the proposed test for various sample sizes and significance levels. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing tests. Furthermore, Type-I error robustness of the proposed and the existing tests are studied via simulation studies when the underlying distributions are non-normal. Two data sets are analyzed for illustration purposes. Finally, the proposed test has been implemented to assess the bioequivalence of two drug formulations.     

Model selection in randomized response techniques for binary responses

Randomized response techniques (RRTs) have been proposed in survey sampling literature as a solution to the problem of social desirability bias (SDB) while dealing with sensitive questions. All RRTs reduce the SDB by introducing privacy protection for the respondents, but the variances of the estimates become larger compared with the ones obtained from direct questioning technique (DQT). The success of RRTs heavily depends on the assumption that the variable of interest is in fact sensitive for the population under study. There might be situations, however, where a presumably sensitive question is not considered to be sensitive in some populations, in which case using an RRT instead of the DQT would inflate the variance of the estimates unreasonably. In this study, we propose a two-stage sampling procedure for a binary response, which enables one to accurately estimate both the prevalence of the sensitive characteristic and the probability of cheating in a population. The proposed model allows one to choose between an RRT and the DQT. We support our theoretical results with numerous simulations.     

Admissible minimax estimators for the shape parameter of Topp–Leone distribution

Abstract

The shape parameter of Topp–Leone distribution is estimated in this article from the Bayesian viewpoint under the assumption of known scale parameter. Bayes and empirical Bayes estimates of the unknown parameter are proposed under non informative and suitable conjugate priors. These estimates are derived under the assumption of squared and linear-exponential error loss functions. The risk functions of the proposed estimates are derived in analytical forms. It is shown that the proposed estimates are minimax and admissible. The consistency of the proposed estimates under the squared error loss function is also proved. Numerical examples are provided.