Parametric and Parameter-Free Shape Moments

Haim Shore

doi:10.1002/9781118445112.stat08459

Parametric and Parameter-Free Shape Moments

Haim Shore

Department of Industrial Engineering and Management

Research output: Chapter in Book/Report/Conference proceeding › Entry for encyclopedia/dictionary › peer-review

Abstract

Abstract Skewness and kurtosis are commonly considered sufficient representatives of distributional shape, generally represented by the third and fourth standardized central moments (moments about the mean). Certain distributions own parametric shape moments, while others do not. In particular, the normal and exponential have parameter-free shape moments. In this article, we offer an in-depth explanation for this phenomenon, based on Pearson skewness measure and on a new ?Random-identity Paradigm,? recently published.

Original language	English
Title of host publication	Wiley StatsRef: Statistics Reference Online
Publisher	Wiley Online Library
Pages	1-5
Number of pages	5
ISBN (Print)	9781118445112
DOIs	https://doi.org/10.1002/9781118445112.stat08459
State	Published - 28 Nov 2023

Keywords

identity-full/less distributions
kurtosis
modeling process time
Pearson equation
random-identity paradigm
repetitiveness measure
shape moments
skewness

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10.1002/9781118445112.stat08459

Cite this

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abstract = "Abstract Skewness and kurtosis are commonly considered sufficient representatives of distributional shape, generally represented by the third and fourth standardized central moments (moments about the mean). Certain distributions own parametric shape moments, while others do not. In particular, the normal and exponential have parameter-free shape moments. In this article, we offer an in-depth explanation for this phenomenon, based on Pearson skewness measure and on a new ?Random-identity Paradigm,? recently published.",

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KW - kurtosis

KW - modeling process time

KW - Pearson equation

KW - random-identity paradigm

KW - repetitiveness measure

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KW - skewness

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Parametric and Parameter-Free Shape Moments

Abstract

Keywords

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