Statistical Science

Quantile Probability and Statistical Data Modeling

Emanuel Parzen

Source: Statist. Sci. Volume 19, Number 4 (2004), 652-662.

Abstract

Quantile and conditional quantile statistical thinking, as I have innovated it in my research since 1976, is outlined in this comprehensive survey and introductory course in quantile data analysis. We propose that a unification of the theory and practice of statistical methods of data modeling may be possible by a quantile perspective. Our broad range of topics of univariate and bivariate probability and statistics are best summarized by the key words. Two fascinating practical examples are given that involve positive mean and negative median investment returns, and the relationship between radon concentration and cancer.

Keywords: Mid-distribution transform; percent function; percentile function; quantile function; monotone transform; parameter inverse pivot quantile function; confidence Q–Q curve; quantile–quartile function QIQ(u); density quantile; quantile density; conditional quantile; comparison distribution; comparison density; Bayesian inference using quantile simulation; bivariate dependence; component correlations

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ss/1113832730
Digital Object Identifier: doi:10.1214/088342304000000387
Mathematical Reviews number (MathSciNet): MR2185587
Zentralblatt MATH identifier: 1100.62500

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