CONNECTICUT UNIV STORRS DEPT OF STATISTICSOverview
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CONNECTICUT UNIV STORRS DEPT OF STATISTICS
Robustness of realiability predictions for a series system of identical components
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1 edition published in 1967 in English and held by 1 WorldCat member library worldwide The present research investigates the robustness of reliability prediction procedures based on the assumption of an exponential failure distribution. A system of n independent identical components in series is considered and a maximal region of robustness, in terms of the shape parameter of the Weibull failure distribution (having mean identical to that of the assumed exponential distribution), is determined. This region of robustness has the property that within this region the use of the exponential assumption will produce a prediction error no larger than the specified level of robustness for the region. Regions are obtained for an unrestricted time period and a restricted time period in which the individual components have a minimum reliability rho (rho = .95, .99). (Author)
Sampling Based Approach to Computing Nonparametric Bayesian Estimators with Doubly Censored Data
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1 edition published in 1992 in English and held by 1 WorldCat member library worldwide Nonparametric Bayesian estimators with Dirichlet process priors for doubly censored data can be derived from mixtures of Dirichlet distributions. To circumvent the computational difficulties in evaluating these mixtures, this paper describes the Gibbs sampling approach to approximating them. The Gibbs samplers augment the censored data by the number of observations falling into each interval. An example taken from Turnbull (1974) is given to illustrate the roach. Gibbs sampling; Stochastic substitution; Dirichlet process priors; Doubly censored data
Feasibility study on the determination of regions of robustness in the pearson system by monte carlo techniques
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1 edition published in 1966 in English and held by 1 WorldCat member library worldwide The feasibility of determining 'regions of robustness' of the ttest (with respect to deviations from normality within the Pearson system) by Monte Carlo techniques is investigated. A computer program for this purpose has been written and run using a highspeed digital computer. This study evaluates the quantity of computer time required to perform a large scale Monte Carlo study for both the singlesample and twosample ttest problems. A detailed description of the evaluation is presented and estimates of the pertinent computer times are given. (Author)
Bibliography on statistical robustness and related topics
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1 edition published in 1966 in English and held by 1 WorldCat member library worldwide This bibliography consists of 252 references in the area of statistical robustness. It is an attempt to provide an uptodate comprehensive collection of references in this general statistical area. (Author)
The generalized discriminant function and nuisance parameters in classification procedures
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1 edition published in 1969 in English and held by 1 WorldCat member library worldwide Extensions of the Fisher discriminant function have been given by several authors and S.N. Roy has generalized Fisher's approach to provide a generalized discriminant function applicable to the general multivariate linear mode. The paper considers the use of this discriminant function for classifying an individual into two or more populations when the populations are identified by only a subset of the parameters of the model. The generalized discriminant function is used to define a generalized discriminant statistic and an observation with an unknown treatment effect is classified according to the value of this statistic. Properties of this statistic are presented and these results are used to define classes of sample and asymptotic decision rules. Various criteria for selecting a decision rule from these classes are investigated. In particular, with respect to the probability of misclassification, the best asymptotic decision rule using the generalized discriminant statistic is identified and it is shown that if the populations are collinear then this decision rule is optimal. A numerical study provides an asymptotic evaluation of the proposed decision rule when the populations are not collinear
Robustness of the studentprocedure: a survey
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1 edition published in 1966 in English and held by 1 WorldCat member library worldwide The paper surveys the approaches and results of various investigations of the effects of deviations from assumptions when the Studentprocedure is used to test hypotheses on means (i.e., ttests). It is an attempt to provide a complete summary of the literature including both theoretical and empirical studies. At the same time, it also provides a study of the general techniques used to investigate the robustness of other statistical procedures since these techniques are similar to those used for the Studentprocedure. (Author)
A QUANTITATIVE APPROACH TO ROBUSTNESS
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1 edition published in 1969 in English and held by 1 WorldCat member library worldwide The reported research is an attempt to rigorize and quantify the concept of statistical robustness. A brief review of the literature is included and the concept of 'regions of robustness' is presented. Such regions are regions in the space of assumption alternatives within which the user of a statistical procedure is assured that he will make an error in his 'criterion function' of a magnitude no more than a prespecified level. Certain concepts associated with 'regions of robustness' are discussed and various properties of such regions are developed. Finally, four investigations of statistical procedures for testing or estimating population means are presented. Tables are given with each of these investigations which enable the reader to identify regions of robustness of various appropriate levels for any of these procedures. (Author)
Fourier series and chebyshev polynomials in statistical distribution theory
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1 edition published in 1968 in English and held by 1 WorldCat member library worldwide After the elementary functions, the Fourier series are the most important functions in applied mathematics. Nevertheless, they have been somewhat neglected in statistical distribution theory. In this paper, the reasons for this omission are investigated and certain modifications of the Fourier series proposed. These results are presented in the form of representation theorems. In addition to the basic theorems, computational algorithms and procedures are developed. As an illustration, a useful representation of the incomplete beta function ratio is developed. Although the representation theorems have been developed for those random variables whose range is contained in the intervals (0.1) and ( 1,1), methods of using the theorems for other intervals are discussed. In addition, multivariate analogues of the theorems are presented. The usefulness of the representation theorems extends beyond the evaluation of a distribution function. In particular, they are useful in investigating the accuracy of an approximation to a distribution function and can be used to improve the accuracy of such an approximation. As a final application of the procedures, three important distribution problems are discussed. These are the likelihood ratio tests, products of independent beta variables, and quadratic forms. (Author)
Fixed Sample and Sequential Problems with Applications in Reliability
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1 edition published in 1990 in English and held by 1 WorldCat member library worldwide The principal focus of this grant period had been on fixedsample problems for the estimation of parameters and reliability functions from different parametric families of distributions. Professor Dey and his PH. D. student (Ms. PeiSan Liu) first considered the estimation problems from generalized life distributions. They considered a decision theoretic route to obtain improved estimators of parameters and parametric functions. Professor Dey also considered the estimation of parameters from mixture distributions. Next, Professor Dey and his colleagues considered some related problems one for the estimation of the Poisson parameter under an asymmetric loss and the other is the determination of the class of minimax estimators of the scale parameter of the uniform distribution. Both these problems also have important applications in reliability. Professor Dey and his student (Mr. Y. Chung) then considered the estimation problems from the mixture of discrete exponential distributions. Through a mixing process, several complicated discrete multivariate distributions were created which included compound Poisson and negative binomial distributions. Improved estimators were then obtained under several plausible loss functions. In a related problem (in the mixture distribution scenario) Professor Dey and his colleagues considered the problem of estimation of parameters and reliability from a multivariate survival distribution generated by WeilbullInverse Gaussian mixture
Supplement to 'bibliography on statistical robustness and related topics'
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1 edition published in 1969 in English and held by 1 WorldCat member library worldwide In a previous bibliography, 252 references in the general area of statistical robustness were provided. The present paper is a supplement to this bibliography consisting of 100 additional references. (Author) Audience Level

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