Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.
Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.
Statistical Modelling with Quantile Functions adds a new dimension to the practice of statistical modelling that will be of value to anyone faced with analyzing data. Not intended to replace classical approaches but to supplement them, it will make some of the traditional topics easier and clearer, and help readers build and investigate models for their own practical statistical problems.
Table of Contents
Describing the Sample
Describing the Population
QUANTILE MODELS AND THEIR CONSTRUCTION
Distributional Model Building
THE STATISTICAL MODELLING PROCESS
EXTENDING THE MODELS
Regression Quantile Models
Bivariate Quantile Models
"The author's writing is clear, and there are excellent problems presented in each chapter. This book is a very good self-contained resource for professionals who are seeking a gentle introduction to the topic of data modeling via quantile functions."
"…the book is a good introduction to the subject and will serve statisticians, researchers, etc. in their modelling work…researchers will undoubtedly gain a lot of knowledge and insight of the core modelling ideas and techniques by reading this book. … I enjoyed reading this book; it is well written, easy to read and it would be worth considering as a text for honour students or as a seminar course at a graduate level."
Short Book Reviews, Vol. 21, No. 1, April, 2001
"The methodology developed in this book provides a fundamentally different approach to modeling the stochastic behavior of data in comparison to the standard statistical approach. In the standard approach, models are selected from a library of potentially useful models, with attention generally focused on a few standard models. As the author points out, when there are thousands of observations, standard probability models that are controlled by one or two parameter values may not fit the data very well, especially in the tail area of the distribution. There are no such limitations on models built using the methodology presented here.... I think this book provides a valuable starting point for anyone interested in quantile methods and it makes a strong case for the adoption of these methods as part of the applied statistician's toolbox."
-Technometrics, Vol 43, No. 4, Nov. 2001
"This book stands the traditional approach on its head by attempting, wherever possible, to develop statistical methodology with quantiles... This approach turns out to be surprisingly successful. …In summary Statistical Modeling with Quantile Functions is an interesting and unorthodox book, whose intentions I applaud. Any book that brings together interesting material on quantiles, particularly their use in statistical inference should be welcomed.
-Journal of the American Statistical Association, December 2001
"The references are up-to-date and contain several seminal articles by the author Warren G.Gilchrist. …This book is easy to read and comprehend with a basic level of mathematical statistics knowledge. There are several unsolved problems in this topic, and this book is timely and valuable for a resolution of these unsolved problems. The tables, graphs and chosen exercise problems in each chapter make the readability of the book even better."
-Journal of Statistical Computation and Simulation, Vol. 76, No. 8, August 2006