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Records arise naturally in many fields of study such as climatology, sports, science, engineering, medicine, traffic, and industry, among others. An observation is called a record if its value is greater than (or analogously, less than) all the preceding observations. The exponential and Rayleigh distribution play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of lifetime data. In this handbook, various properties of record values of univariate exponential and Rayleigh distributions, including most of the recent works, are reviewed. Some new results on mean residual life based on records and the minimum variance linear unbiased estimators of past records from univariate exponential distribution are presented.

This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.

First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.

The exponential distribution is often used to model the failure time of manufactured items in production. If X denotes the time to failure of a light bulb of a particular make, with exponential distribution, then P(X>x) represent the survival of the light bulb. The larger the average rate of failure, the bigger will be the failure time. One of the most important properties of the exponential distribution is the memoryless property. This book presents various properties of the exponential distribution and inferences about them.

Exponential families of stochastic processes are parametric stochastic p- cess models for which the likelihood function exists at all?nite times and has an exponential representation where the dimension of the canonical statistic is?nite and independent of time. This de?nition not only covers manypracticallyimportantstochasticprocessmodels,italsogivesrisetoa rather rich theory. This book aims at showing both aspects of exponential families of stochastic processes. Exponential families of stochastic processes are tractable from an a- lytical as well as a probabilistic point of view. Therefore, and because the theory covers many important models, they form a good starting point for an investigation of the statistics of stochastic processes and cast interesting light on basic inference problems for stochastic processes. Exponential models play a central role in classical statistical theory for independent observations, where it has often turned out to be informative and advantageous to view statistical problems from the general perspective of exponential families rather than studying individually speci?c expon- tial families of probability distributions. The same is true of stochastic process models. Thus several published results on the statistics of parti- lar process models can be presented in a uni?ed way within the framework of exponential families of stochastic processes.

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon