Titlebook: Expository Moments for Pseudo Distributions; Haruhiko Ogasawara Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

有偏见

The Sectionally Truncated Normal Distribution,runcation, moments and cumulants of the distribution are obtained. As an associated result of the Hermite polynomials found in the derivation, the product sum of natural numbers is introduced with its properties.

浅滩

capillaries

The Pseudo-Normal (PN) Distribution, published), 2021). The moment generating functions of the variables and their functions for the PN are obtained giving various moments. Closed properties of affine transformation, marginal/conditional and independent distributions are shown as in the CSN.

CON

使混合

高歌

激怒

补角

misshapen

The Truncated Pseudo-Normal (TPN) and Truncated Normal-Normal (TNN) Distributions,. When the observable variables are sectionally truncated, we have the truncated pseudo normal (TPN) and normal-normal (TNN). The properties of the TPN and TNN e.g., the moment generating functions and closure, are given. Using a non-recursive formula, the moments of the TPN are derived.

终点

Multivariate Measures of Skewness and Kurtosis,sized with the by-products of the explicit expressions of the elements. The vectors of the multivariate cumulants up to the fourth order are shown by the multiple commutators and their inverses. Properties of multivariate measures of skewness and kurtosis are discussed.