Gilchrist Statistical Modelling with Quantile Functions

Erscheinungsjahr 2002
ISBN: 978-1-4200-3591-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 344 Seiten

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.

Zielgruppe

Applied statisticians; Graduate students in statistics

Autoren/Hrsg.

Gilchrist, Warren

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

INTRODUCTION
An Overview
Describing the Sample
Describing the Population
Statistical Foundations
QUANTILE MODELS AND THEIR CONSTRUCTION
Foundation Distributions
Distributional Model Building
THE STATISTICAL MODELLING PROCESS
Identification
Estimation
Validation
Application
EXTENDING THE MODELS
Regression Quantile Models
Bivariate Quantile Models
Postscript