Mohammad Ahsanullah – författare

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.

This book offers a comprehensive exploration of popular continuous distribution families, including Exponentiated, Beta, Kumaraswamy, T-X, and Transmuted. It details methods for developing new distribution families, their properties, and inference. Practical applications of the members of families are enhanced by R code for maximum likelihood estimation.This resource is invaluable for studies into distribution theory and related fields, providing a consolidated knowledge base and facilitating the development of novel families of distributions and their members. The book's significance lies in its consolidated and comprehensive treatment of contemporary distribution families, which have revolutionized real-life data fitting. The book presents mechanisms, properties, and inferential methods for families like Beta, T-X, and Transmuted families in one place. Key topics on cumulative distribution function, reliability analysis, and maximum likelihood estimation are discussed for the reader's learning. The inclusion of R codes for maximum likelihood estimation offers practical utility in applying these distributions. Furthermore, the book actively encourages the development of new distribution families and members, fostering innovation in the field. Its detailed coverage of various families and their properties, coupled with accessible explanations, makes it a crucial asset for both established researchers and those new to distribution theory.The target audience includes graduate and postgraduate statistics students, research fellows in distribution theory, and readers in allied fields like mathematics and physics.

This book offers a comprehensive exploration of popular continuous distribution families, including Exponentiated, Beta, Kumaraswamy, T-X, and Transmuted. It details methods for developing new distribution families, their properties, and inference. Practical applications of the members of families are enhanced by R code for maximum likelihood estimation.This resource is invaluable for studies into distribution theory and related fields, providing a consolidated knowledge base and facilitating the development of novel families of distributions and their members. The book's significance lies in its consolidated and comprehensive treatment of contemporary distribution families, which have revolutionized real-life data fitting. The book presents mechanisms, properties, and inferential methods for families like Beta, T-X, and Transmuted families in one place. Key topics on cumulative distribution function, reliability analysis, and maximum likelihood estimation are discussed for the reader's learning. The inclusion of R codes for maximum likelihood estimation offers practical utility in applying these distributions. Furthermore, the book actively encourages the development of new distribution families and members, fostering innovation in the field. Its detailed coverage of various families and their properties, coupled with accessible explanations, makes it a crucial asset for both established researchers and those new to distribution theory.The target audience includes graduate and postgraduate statistics students, research fellows in distribution theory, and readers in allied fields like mathematics and physics.

This book offers a comprehensive exploration of popular continuous distribution families, including Exponentiated, Beta, Kumaraswamy, T-X, and Transmuted. It details methods for developing new distribution families, their properties, and inference. Practical applications of the members of families are enhanced by R code for maximum likelihood estimation. This resource is invaluable for studies into distribution theory and related fields, providing a consolidated knowledge base and facilitating the development of novel families of distributions and their members. The book's significance lies in its consolidated and comprehensive treatment of contemporary distribution families, which have revolutionized real-life data fitting. The book presents mechanisms, properties, and inferential methods for families like Beta, T-X, and Transmuted families in one place. Key topics on cumulative distribution function, reliability analysis, and maximum likelihood estimation are discussed for the reader’s learning. The inclusion of R codes for maximum likelihood estimation offers practical utility in applying these distributions. Furthermore, the book actively encourages the development of new distribution families and members, fostering innovation in the field. Its detailed coverage of various families and their properties, coupled with accessible explanations, makes it a crucial asset for both established researchers and those new to distribution theory. The target audience includes graduate and postgraduate statistics students, research fellows in distribution theory, and readers in allied fields like mathematics and physics.

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 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.

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 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 new book presents the latest research in the field.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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).

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).

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.

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.

In many fields of research, such as, biology, computer science, control theory, economics, engineering, genetics, hydrology, medicine, number theory, statistics, physics, psychology, reliability, risk management, etc., the shapes of probability distributions of non-normal data exhibit J-shaped distributions. The shapes of such distributions may be skewed to the left or the right depending on whether a large percentage of data is at the lower or upper extreme. In this book, we have studied the J-shaped distributions and their applications. As a motivation, we have discussed several real-world examples which can be modeled through J-shaped distribution. We have presented the mathematical formulation of the family of J-shaped probability distributions which was first proposed by Topp and Leone (1955). We also have discussed several variations of Topp–Leone’s family of J-shaped distribution. We have considered the general form of J-shaped distribution and derived its moments independently. We also have discussed other distributional properties of the J-shaped distribution. Some distributional properties of order statistics of the J-shaped distribution such as moment, variance, product moments, and covariance are also provided. To describe the shapes of the J-shaped distribution, the plots of the and for various values of the parameter have been provided. Entropy provides an excellent tool to quantify the amount of information (or uncertainty) contained in a random observation regarding its parent distribution (population). A large value of entropy implies greater uncertainty in the data. As such, Shannon entropy of the J-shaped distribution is provided. The distributional properties of order statistics of the J-shaped distribution such as moment, variance, product moments, and covariance, have also been presented. The numerical computations of these for selected values of the parameters are provided. The distributional properties of the record values of the J-shaped distribution are also investigated. Some discussions on the sum, product and ratio of the J-shaped distributions are provided. Characterizations of the J-shaped distribution are given by using the method of truncated moment, order statistics and record values.