Expository Moments for Pseudo Distributions

This book provides expository derivations for moments of a family of pseudo distributions, including the pseudo normal (PN) distributions, which have a wider variety of distributions than the skew normal (SN) and closed skew normal (CSN). The PN includes non-normal symmetric distributions, which are called "kurtic normal (KN)" distributions. The proofs of the moments and associated results are provided, often with multiple methods and didactic explanations.

Format: Hardback
Length: 343 pages
Publication date: 02 January 2023
Publisher: Springer Verlag, Singapore

This comprehensive book offers detailed expository derivations for moments of a remarkable family of pseudo distributions, which extends the realm of distributions encompassing the recently proposed pseudo normal (PN) distributions. This extended family includes notable members such as the skew normal (SN) derived by A. Azzalini and the closed skew normal (CSN) obtained by A. Domínguez-Molina, G. González-Farías, and A. K. Gupta, among others. Notably, the CSN encompasses the SN and a wide range of other distributions, highlighting the diverse nature of the PN.

Within this family, both the SN and CSN exhibit symmetric and skewed asymmetric distributions. However, it's important to note that symmetric distributions are solely confined to normal ones. Conversely, symmetric distributions within the PN can encompass both non-normal and normal characteristics. To address the non-normal symmetric distributions, a term called "kurtic normal (KN)" is introduced, where the term "kurtic" signifies "mesokurtic, leptokurtic, or platykurtic," which are terms commonly used in statistics.

The remarkable variety of the PN is made possible through the utilization of stripe (tigerish) and sectional truncation in univariate and multivariate distributions, respectively. The book meticulously presents the proofs of moments and associated results, ensuring that they are not omitted. Furthermore, these proofs are often presented in multiple methods, accompanied by comprehensive didactic explanations to enhance the understanding of the subject matter.

Weight: 699g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811935244
Edition number: 1st ed. 2022