Parameter Estimation in Reliability and Life Span Models

A. Clifford Cohen is Professor Emeritus of Statistics at the University of Georgia in Athens, where he has been affiliated since 1947. An editorial board member of the Journal of Quality Technology, Dr. Cohen has published more than 60 research papers and technical reports on the subjects of estimation from truncated and censored samples, and modified estimators. He is a Fellow and Founding Member of the American Society for Quality Control, Founding  Member of the Operations Research Society of America, Fellow of the American Statistical Association and American Association for the Advancement of Science, and member of the Institute of Mathematical Statistics, Mathematical Association of America, International Statistical Institute, and Sigma Xi. He is certified by the American Society for Quality Control as both a quality engineer and a reliability engineer. Dr. Cohen received the B.S. (1932) and M.S. (1933) degrees in electrical engineering from Auburn University in Alabama, and M.A. (1940) and Ph.D. (1941) degrees in mathematics from the University of Michigan in Ann Arbor. Betty Jones Whitten is Associate Professor in the Department of Management Sciences at the University of Georgia in Athens. She has coedited one book, and authored or coauthored more than 30 articles, proceedings papers and technical reports on her research interests in estimation procedures in life testing distributions, modified moment estimation for the three-parameter gamma, inverse Gaussian, lognormal and Weibull distributions, and other related topics. She is the recipient of the first Josiah Meigs Award for Excellence in Teaching and Pro Optime Perdocendo Honoratus Award from the University of Georgia. Dr. Whitten is treasurer of the Decision Sciences Institute (national office), president of the Southeastern  Region of the Decision Sciences Institute, and a member of the American Statistical Association, Sigma Xi, Phi Kappa Phi, and Beta Gamma Sigma. She received the B.S. (1962) and M.S. (1963) degrees in mathematics from the University of Illinois in Urbana, and Ph.D. (1972) degree in statistics from the University of Georgia.

• Contents Preface List of Illustrations List of Tables List of Programs 1.INTRODUCTION. Introductory Remarks. An Overview of Skewed Distributions. Parameter Estimation. Some Comparisons.2. CONCEPTS FOR THE ANALYSIS OF RELIABILITY AND LIFE DISTRIBUTION DATA. Life Distributions and Reliability Discrete Models. 3.THE WEIBULL, EXPONENTIAL, AND EXTREME VALUE DISTRIBUTIONS. Background. Characteristics of the Weibull Distribution. Maximum Likelihood Estimation. Moment Estimators. Modified Moment Estimators. Wycoff, Bain, Engelhardt, and Zanakis Estimators. Special Cases: Shape Parameter o Known. Errors of Estimates. The Exponential Distribution. The Extreme Value Distribution. Illustrative Examples. Reflections. 4. LOGNORMAL DISTRIBUTION Introduction. Some Fundamentals. Moment Estimators. Maximum Likelihood Estimators. Asymptotic Variances and Covariances. Modified Moment Estimators. Illustrative Examples. Reflections. 5. THE INVERSE GAUSSIAN DISTRIBUTION. Background. The Probability Density Function. Maximum Likelihood Estimation. Asymptotic Variances and Covariances. Moment Estimators. Modified Moment Estimators. Illustrative Examples. Reflections. 6. THE GAMMA DISTRIBUTION. Background. The Density Function and Its Characteristics.Moment Estimators. Maximum Likelihood Estimators. Asymptotic Variances and Covariances. Modified Moment Estimators. Illustrative Examples. Reflections. 7. CENSORED SAMPLING IN THE EXPONENTIAL AND WEIBULL DISTRIBUTIONS. Introduction. Progressively Censored Samples. Censored Samples from the Exponential Distribution. Censored Samples from the Weibull Distribution. The Hazard Plot. Estimate Variances and Covariances. An Illustrative Example. 8. CENSORED AND TRUNCATED SAMPLES FROM THENORMAL AND THE LOGNORMAL DISTRIBUTIONS. Introductory Remarks. Maximum Likelihood Estimation Modified Maximum Likelihood Estimators for Lognormal Parameters Based on Censored Samples. Maximum Likelihood Estimation in the Normal Distribution. An Illustrative Example from a Lognormal Distribution. CENSORED SAMPLING IN THE INVERSE GAUSSIAN AND GAMMA DISTRIBUTIONS. Introduction. Censored Sampling in the Inverse Gaussian Distribution. A Pseudocomplete Sample Technique. Censored Sampling in the Gamma Distribution. An Illustrative Example. 10. THE RAYLEIGH DISTRIBUTION. Introduction. Maximum Likelihood and Moment Estimation in the p-Dimensional Distribution. Special Cases. Complete Sample Estimators When p = 1, 2, and 3. Two-Parameter Rayleigh Distribution. Estimation in the Two-Parameter Rayleigh Distribution. Truncated Samples. Censored Samples. Reliability of Estimates. Illustrative Examples. Parameter Estimation in the Two-Parameter Rayleigh Distribution of Dimension 2, When Samples Are Censored. Some Concluding Remarks 11. THE PARETO DISTRIBUTION. Introduction. Some Fundamentals. Parameter Estimation from Complete Samples. Parameter Estimation from Truncated Censored Samples. Reliability of Estimates. An Illustrative Example 12. THE GENERALIZED GAMMA DISTRIBUTION. Introduction. Parameter Estimation in the Three-Parameter Distribution. The Four-Parameter Distribution. Estimate Variances and Covariances. Simplified Computational Procedures for the Modified Moment Estimators. Illustrative Examples Censored Samples. Asymptotic Variances and Covariances of Maximum Likelihood Estimators. An Illustrative Example Some Comments and Recommendations. APPENDIX A. SOME CONCLUDING REMARKS. FURTHER COMPARISONS. TABLES OF CUMULATIVE DISTRIBUTION FUNCTIONS. COMPUTER PROGRAMS. Glossary. Bibliography. Index