Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.

Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables, known as Generalized Order Statistics has been introduced relatively recently by Kamps (1995).

The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be useful o applied statisticians as well statisticians interrested to work in the area of extremen value distributions.vmonograph presents the central ideas and results of extreme value distributions.The monograph gives self-contained of theory and applications of extreme value distributions.

A lot of statisticians, actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists. Business and sport analysts deal with records which play important roles in various fields of statistics and its application. This book enables a reader to check his/her level of understanding of the theory of record values. We give basic formulae which are more important in the theory and present a lot of examples which illustrate the theoretical statements. For a beginner in record statistics, as well as for graduate students the study of our book needs the basic knowledge of the subject. A more advanced reader can use our book to polish his/her knowledge. An upgraded list of bibliography which will help a reader to enrich his/her theoretical knowledge and widen the experience of dealing with ordered observations, is also given in the book.

This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.

This book contains entirely new results, not to be found elsewhere. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions such as Weibull distributions, exponentiated Burr type XII distributions and exponentiated exponential distributions and their properties are demonstrated. Analysis of real as well as well-simulated data are analyzed. A number of inferences based on a finite mixture of distributions are also presented.

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.

Contents: Nonparametric Perspectives in Regression Analysis; Record Values of Univariate Distribution; A Transfer Theorem for Multitype Processes & Applications; The Generalized Order Statistics; Some Inference Aspects of a Social Network; Estimation of Mean Based on an Unbalanced Ranked Set Sample; Lower Bound to Mean Square Error of Estimator in Unequal Probability Sampling; Asymptomic Shrinkage Estimation: The Regression Case; Estimation of Parameters Using Modified Ranked Set Sampling; Certain Families of Distributions.

In this book, Mohammad Ahsanullah provides a detailed description of the general theory and applications of record values. Professor Ahsanullah thoroughly discusses the most useful distributions and inferences based on record values, resulting in conclusions that are not available in previously published works. The book, written on an intermediate level that requires the basic knowledge of calculus, probability theory, and mathematical statistics, can be used as a text for advanced undergraduate or graduate level courses.

Computers have taken a permanent place in almost every human endeavour in the last 20 years. This infiltration requires a learning process on the part of the people utilising them and realising where and how they can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and many others where the statistical studies are essential before the next step can be taken. This book gathers together the latest research in this dynamic and link field.

Exponential distribution is one of the most-used distributions in the theory and practice of statistics. It has several important properties like being memoryless and having a constant hazard rate. The field of characterization is developed in different branches of statistics and applied probability. Ordered random variables are common in various applications in practice. In this book, characterizations of exponential distribution using ordered random variables are presented. Most of the known results as well as many new results are given in this book. The aim of the book is to present various characterizations of exponential distribution based on ordered random variables. The book is written on a lower technical level and requires basic knowledge of mathematics and statistics. Chapter 1 gives some basic properties of exponential distribution. Chapters 2, 3, and 4 give the characterization of exponential distribution based on order statistics, record values, and generalized order statistics.

This book makes a significant contribution to the advancement of statistical science. It contains research in many statistical designs, compares many statistical models, and includes a theory that is oriented to real life problems.

Computers have taken a permanent place in almost every human endeavour in the last 20 years. This infiltration requires a learning process on the part of the people utilising them and realising where and how they can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and many others where the statistical studies are essential before the next step can be taken. This book gathers together the latest research in this dynamic and link field.

Ahsanullah (Rider University) presents recent work in applied statistics from around the world. Some specific topics covered are product integration and characterization on probability laws, bivariate Lukacs-type regression characterization, and characterizations of distributions by conditional expectations of generalized order statistics. Other subjects explored include characterization of distributions by regressional properties of records, moments of residual life, characterizing distributions by conditional expectations of functions of non-adjacent record values, and characterizations of univariate continuous distributions based on hazard function.

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 memory-less property. This book presents various properties of the exponential distribution and inferences about them.

This book concerns itself with record values and branching processes as rich research areas of applied probability and statistics. Over the last few decades, numerous interesting articles on these topics appeared, dealing with theoretical problems as well as a number of new applications. The authors have co-ordinated publishing works contributed by eminent researchers from all over the world. This book presents a selection of presentations of new developments and survey papers on the subjects of record values and branching processes. It is written at intermediate level which requires knowledge of probability theory and mathematical statistics.

Computers have taken a permanent place in almost every human endeavour in the last 20 years. This infiltration requires a learning process on the part of the people utilising them and realising where and how computers can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and numerous others where the statistical studies are essential before the next step can be taken. This book presents the latest research in the field from around the world.

Computers have taken a permanent place in almost every human endeavor in the last 20 years. This infiltration requires a learning process on the part of the people utilizing them and realizing where and how computers can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and numerous others where the statistical studies are essential before the next step can be taken. This new book presents the latest research in the field from around the globe.

The ordered random variables play important roles in the theory and practice of statistics. They possess significant statistical properties. Over the last few decades, many articles on various topics of ordered statistical data have appeared. Our handbook comprises twenty one chapters discussing various topics on theory and applications. The editors of this book worked together several articles on order and record statistics, which covered the subjects of distributional properties, characterisations and statistical inferences. It was a special interest to co-ordinate and edit an interesting research problem based on material contributed by several prominent researchers from all over the world. This book presents new developments in the subject of ordered random variables. These aspects involve theory of ordered random variables, reliability theory, stochastic ordering, bounds, characterisations, and estimation and prediction techniques.

This book is written for people who are interested to know the basics of probability theory. The basic knowledge of high school math will be enough to know the probability theory covered in the book. It covers basic theories of probability, statistical distributions, order statistics and record values, The use of characterization methods are described to identify various probability distributions. The book will be useful for undergraduate, graduate students and applied statisticians.

This book makes a significant contribution to the advancement of statistical science. It contains research in many statistical designs, compares many statistical models, and includes theories that are oriented to real life problems.