Statistical Methods for Non-Precise Data: 1st Edition (Hardback) book cover

Statistical Methods for Non-Precise Data

1st Edition

By Reinhard Viertl

CRC Press

208 pages

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Hardback: 9780849382420
pub: 1995-11-29

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The formal description of non-precise data before their statistical analysis is, except for error models and interval arithmetic, a relatively young topic. Fuzziness is described in the theory of fuzzy sets but only a few papers on statistical inference for non-precise data exist. In many cases, for example when very small concentrations are being measured, it is necessary to describe the imprecision of data. Otherwise, the results of statistical analysis can be unrealistic and misleading. Fortunately, there is a straightforward technique for dealing with non-precise data. The technique - the generalized inference method - is explained in Statistical Methods for Non-Precise Data. Anyone who understands elementary statistical methods and simple stochastic models will be able to use this book to understand and work with non-precise data.

The book includes explanations of how to cope with non-precise data in different practical situations, and makes an excellent graduate level text book for students, as well as a general reference for scientists and practitioners.


Table of Contents

Non-Precise Data and Their Formal Description

Non-Precise Data

Non-Precise Numbers and Characterizing Functions

Construction of Characterizing Functions

Non-Precise Vectors

Functions of Non-Precise Quantities and Non-Precise Functions

Descriptive Statistics with Non-Precise Data

Non-Precise Samples

Histograms for Non-Precise Data

Cumulative Sums for Non-Precise Data

Empirical Distribution Function for Non-Precise Data

Empirical Fractiles for Non-Precise Data

Foundations for Statistical Inference with Non-Precise Data

Combination of Non-Precise Observations

Sample Moment for Non-Precise Observations

Sequences of Non-Precise Observations

Classical Statistical Inference for Non-Precise Data

Point Estimators for Parameters

Confidence Regions for Parameters

Nonparametric Estimation

Statistical Tests and Non-Precise Data

Bayesian Inference for Non-Precise Data

Bayes' Theorem for Non-Precise Data

Bayesian Confidence Regions Based on Non-Precise Data

Non-Precise Predictive Distributions

Non-Precise a priori Distributions

Bayes Theorem for Non-Precise a priori Distribution and Non-Precise Data

Bayesian Decisions Based on Non-Precise Information



List of Symbols


Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General