Preface to the Paperback Edition. Preface. About the Author. 1. Overview and Background. 2. Basic Concepts and Distributions for Product Life. 3. Probability Plotting of Complete and Singly Censored Data. 4. Graphical Analysis of Multiply Censored Data. 5. Series Systems and Competing Risks. 6. Analysis of Complete Data. 7. Linear Methods for Singly Censored Data. 8. Maximum Likelihood Analysis of Multiply Censored Data. 9. Analyses of Inspection Data (Qualtal--Response and Interval Data). 10. Comparisons (Hypothesis Tests) For Complete Data. 11. Comparisons with Linear Estimators (Singly Censored and Complete Data). 12. Maximum Likelihood Comparisons (Multiply Censored and Other Data). 13. Survey of Other Topics. Appendix A. Tables. References. Index.

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Applied life data analysis

A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

Statistical Size Distributions in Economics and Actuarial Sciences

Properties of progressively censored order statistics and inferential procedures based on progressively censored samples have recently attracted considerable attention in the literature. In this paper, I provide an overview of various developments that have taken place in this direction and also suggest some potential problems of interest for further research.

Progressive censoring methodology: an appraisal

SUMMARY A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed method are described. In particular it is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist. Moreover it gives consistent, asymptotically efficient estimators in situations where ML fails. Examples are given including numerical ones showing the advantages of the method.

Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin

Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters (reliability, and hazard functions), as well as the parameters of the Burr-XII model, are derived. The Bayes estimators are obtained using both the symmetric (Squared Error, SE) loss function, and asymmetric (LINEX, and General Entropy, GE) loss functions. This was done with respect to the conjugate prior for the one shape parameter, and discrete prior for the other parameter of this model. Also the existence, uniqueness, and finiteness of the ML parameter estimates for this type of censoring are discussed. A practical example consisting of data from an accelerated test on insulating fluid reported by Nelson (1982) was used for illustration, and comparison. Finally, some numerical results using simulation study concerning different sample sizes, and progressive censoring schemes were reported.

Estimation of parameters of life from progressively censored data using Burr-XII model

The location, shape, and scale parameters of the Weibull distribution are estimated from Type I progressively censored samples by the method of maximum likelihood. Nonlinear logarithmic likelihood estimating equations are derived, and the approximate asymptotic variance-covariance matrix for the maximum likelihood parameter estimates is given. The iterative procedure to solve the likelihood equations is a stable and rapidly convergent constrained modified quasilinearization algorithm which is applicable to the general case in which all three parameters are unknown. The numerical results indicate that, in terms of the number of iterations required for convergence and in the accuracy of the solution, the proposed algorithm is a very effective technique for solving systems of logarithmic likelihood equations for which all iterative approximations to the solution vector must satisfy certain intrinsic constraints on the parameters. A FORTRAN IV program implementing the maximum likelihood estimation procedure is included.

Errata: Solution of the Three-Parameter Weibull Equations by Constrained Modified Quasilinearization (Progressively Censored Samples)

A method of centres algorithm for maximum likelihood estimation in the three-parameter lognormal model is presented and discussed, The algorithm is a member of the class of moving truncations algorithms for solving nonlinear programming problems and is able to move the numerical search out of the region of the infinite maximum of the conditional likelihood function, thereby permitting convergence to an interior relative maximum of this function. The algorithm also includes an optimality test to locate the primary relative maximum of the likelihood function.

Moving truncations barrier-function methos for estimation in three-parameter lognormal models

This paper treats the theoretical and computational problems of maximum likelihood parameter estimation in a Pareto distribution. Logarithmic likelihood estimating equations and the associated conditional log-likelihood function are derived, and expressions for the asymptotic variances and covariances of the parameters are given. Discussions pertinent to tests of hypotheses and the construction of simultaneous s-confidence contours are provided. The computations required for estimation are illustrated by an example in which the parameters are estimated by numerically maximizing the conditional log-likelihood function and by using an algorithm for global optimization which exploits the mathematical structure of this function. The parameter estimates obtained in this way are guaranteed to be those at which the likelihood function is globally maximum over the space of permissible parameter values. A Fortran program exists for performing these calculations.

Dallas R. Wingo

Papers

Errata: Solution of the Three-Parameter Weibull Equations by Constrained Modified Quasilinearization (Progressively Censored Samples)

Moving truncations barrier-function methos for estimation in three-parameter lognormal models

Estimation in a Pareto Distribution: Theory & Computation