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Springer Handbook of Engineering Statistics pp 79–95Cite as

Characterizations of Probability Distributions

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Abstract

A characterization is a certain distributional or statistical property of a statistic or statistics that uniquely determines the associated stochastic model. This chapter provides a brief survey of the huge literature on this topic. Characterizations based on random (complete or censored) samples from common univariate discrete and continuous distributions, and some multivariate continuous distributions are presented. Characterizations that use the properties of sample moments, order statistics, record statistics, and reliability properties are reviewed. Applications to simulation, stochastic modeling and goodness-of-fit tests are discussed. An introduction to further resources is given.

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Abbreviations

BVE:

bivariate exponential

CDF:

cumulative distribution function

CF:

characteristic function

CFE:

Cauchy functional equation

FR:

failure rate

LMP:

lack-of-memory property

MGF:

moment generating function

MLE:

maximum likelihood estimation

MRL:

mean residual life

MVN:

multivariate normal

PDF:

probability density function

RV:

random variable

SF:

survival function

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Authors and Affiliations

  1. Department of Statistics, Ohio State University, 404 Cockins Hall, 1958 Neil Avenue, 43210-1247, Columbus, OH, USA

    H. Nagaraja

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  1. H. Nagaraja
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Correspondence to H. Nagaraja .

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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers the State University of New Jersey, 96 Frelinghuysen Road, 08854, Piscataway, NJ, USA

    Hoang Pham Prof.

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© 2006 Springer-Verlag

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Nagaraja, H. (2006). Characterizations of Probability Distributions. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_4

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  • DOI: https://doi.org/10.1007/978-1-84628-288-1_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-806-0

  • Online ISBN: 978-1-84628-288-1

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