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Distributional properties of the negative binomial Lévy process

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Author

Summary, in English

The geometric distribution leads to a Lévy process parameterized

by the probability of success. The resulting negative binomial process

(NBP) is a purely jump and non-decreasing process with general negative

binomial marginal distributions. We review various stochastic mechanisms

leading to this process, and study its distributional structure. These

results enable us to establish strong convergence of the NBP in the supremum

norm to the gamma process, and lead to a straightforward algorithm

for simulating sample paths.We also include a brief discussion of estimation

of the NPB parameters, and present an example from hydrology illustrating

possible applications of this model.

Publishing year

2009

Language

English

Pages

43-71

Publication/Series

Probability and Mathematical Statistics

Volume

29

Issue

Fasc. 1

Document type

Journal article

Publisher

Center for Probability and Mathematical Statistics, Wroclaw

Topic

  • Probability Theory and Statistics

Keywords

  • Borehole data
  • Cluster Poisson process
  • Compound Poisson process: Count data: Cox process
  • Discrete Lévy process
  • Doubly stochastic Poisson process
  • Fractures
  • Gamma-Poisson process
  • Gamma process: Geometric distribution
  • Immigration birth process
  • Infinite divisibility
  • Logarithmic distribution: Over-dispersion
  • Pascal distribution
  • Point process
  • Random time transformation
  • Subordination
  • Simulation

Status

Published

ISBN/ISSN/Other

  • ISSN: 0208-4147