The book is concerned with the parametric estimation associated with the following distributions: Weibull, extreme value, lognormal, inverse Gaussian, Gamma, Rayleigh, Pareto and generalized Gamma. The common denomination of all these distributions is that they are usually skewed to the right. In the most general case a location shift parameter is added to the parametrization, on top of the usual scale and shape parameters.
In almost all the cases the following estimation methods are employed: maximum likelihood estimators (MLE), moment estimators (ME) and modified moment estimators (MME). In some cases also some modified maximum likelihood estimators (MMLE) and local maximum likelihood estimators (LMLE) are described and compared. The “modified” MME and MMLE are obtained by replacing one of the classical equations by a new equation which involves the smallest observation, that is, the first order statistic. The authors claim that this is a reasonable procedure when there is a shift parameter \(\gamma\) because the first-order statistic contains a lot of information about \(\gamma\).
The sets of data that the authors consider are the complete and also several variations of censored and truncated sets of data. In fact, the authors introduce a censoring procedure, called progressive censoring, which generalizes many commonly used censoring procedures. For such progressively censored data they describe the MLE, ME, MME, MMLE and LMLE.
The book is organized as follows. After two introducing chapters there are several chapters, each of which describes the estimators for a specific distribution based on complete samples. The rest of the monograph consists of chapters, each of which describes the estimators for specific distributions based on progressively censored samples. Most of the chapters include numerical tables and graphs which facilitate the numerical computation of the estimates. Also, almost every chapter contains one or more numerical illustrative examples which show in detail how to compute the estimates. In many cases the MLE, ME and MME are compared in a tabular fashion. Also, in most cases the asymptotic variance-covariance matrix is described. The appendices include additional numerical tables and some FORTRAN computer programs. The Glossary and the Index are very helpful.
The monograph can be of great use to any statistician who needs to estimate the parameters of these skewed distributions every once in a while. It is well written and is almost free of mistypes. In the future, it could be used as a yardstick as to how a monograph about specific parametric estimation should be written.