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Bivariate life distributions from Pólya's urn model for contagion

Part of: Distribution theory - Probability Distribution theory

Published online by Cambridge University Press:  14 July 2016

Albert W. Marshall  and
Ingram Olkin
Albert W. Marshall*
Affiliation:
University of British Columbia and Western Washington University
Ingram Olkin*
Affiliation:
Stanford University
*
∗ Postal address: 2781 West Shore Drive, Lummi Island, WA 98262, USA.
∗∗ Postal address: Department of Statistics, Sequoia Hall, Stanford University, Stanford, CA 94305, USA.
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Abstract

Shock models based on Poisson processes have been used to derive univariate and multivariate exponential distributions. But in many applications, Poisson processes are not realistic models of physical shock processes because they have independent increments; expanded models that allow for possibly dependent increments are of interest. In this paper, univariate and bivariate Pólya urn schemes are used to derive models of shock sources. The life distributions obtained from these models form a large parametric family that includes the exponential distribution. Even in the univariate case these life distributions have not been widely used, though they form a large and flexible family. In the bivariate case, the family includes the bivariate exponential distributions of Marshall and Olkin as a special case.

Keywords

SHOCK MODELSPOISSON PROCESSESBIVARIATE EXPONENTIAL DISTRIBUTIONMIXTURES OF DISTRIBUTIONSGAMMA DISTRIBUTION

MSC classification

Primary: 60E05: Distributions
Secondary: 62E15: Exact distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 497 - 508
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Supported in part by the National Science Foundation and by the Natural Sciences and Engineering Research Council of Canada.

Supported in part by the National Science Foundation.

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