Overview

Understanding Kurtosis offers a comprehensive exploration of one of the most misunderstood concepts in statistics. Beginning with the historical development and mathematical foundations of kurtosis, the book examines classical moment-based measures and their limitations, then introduces modern alternatives based on quantiles, tail means and distributional orderings. Through rigorous theory, illustrative examples and clear geometric interpretations, it explains how peakedness and tail heaviness can be compared across families of symmetric distributions.The book also presents new constructions of symmetric non-normal distributions with kurtosis three, discusses mixture models, discrete analogues and multivariate extensions, and highlights practical applications such as image sharpness analysis and data modelling. Designed for students, researchers and practitioners, the book provides both theoretical depth and practical insight, offering a unified framework for understanding kurtosis and its role in statistical analysis.

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