J-shaped distributions and their applications / Mohammad Ahsanullah and Mohammad Shakil.
| Author/creator | Ahsanullah, Mohammad |
| Other author | Shakil, Mohammad (Professor of mathematics) |
| Format | Electronic |
| Publication Info | New York : Nova Science Publishers, [2023] |
| Description | xii, 143 pages : illustrations ; 22 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Life sciences research and development Mathematics research developments |
| Contents | Mathematical formulations -- Distributional properties -- Order statistics -- Record values -- Sum, product and ratio -- Characterizations -- Percentile points. |
| Abstract | "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"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references ( [131]-139) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2023039633 |
| ISBN | 9798891130135 (paperback) |
| ISBN | (adobe pdf) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |