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A bivariate Levy process with negative binomial and gamma marginals

In English

Författare

Summary, in English

The joint distribution of X and N, where N has a geometric distribution and X is the sum of N IID exponential variables (independent of N), is infinitely divisible. This leads to a bivariate Levy process {(X(t), N(t)), t >= 0}, whose coordinates are correlated negative binomial and gamma processes. We derive basic properties of this process, including its covariance structure, representations, and stochastic self-similarity. We examine the joint distribution of (X(t), N(t)) at a fixed time t, along with the marginal and conditional distributions, joint integral transforms, moments, infinite divisibility, and stability with respect to random summation. We also discuss maximum likelihood estimation and simulation for this model.

Publiceringsår

2008

Språk

Engelska

Sidor

1418-1437

Publikation/Tidskrift/Serie

Journal of Multivariate Analysis

Volym

99

Issue

7

Dokumenttyp

Artikel i tidskrift

Förlag

Academic Press

Ämne

  • Probability Theory and Statistics

Nyckelord

  • operational time
  • random summation
  • random time transformation
  • stability
  • subordination self-similarity
  • negative binomial process
  • maximum likelihood estimation
  • divisibility
  • infinite
  • gamma Poisson process
  • discrete Levy process
  • gamma process

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0047-259X