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Distributional properties of the negative binomial Lévy process

Publiceringsår: 2009
Språk: Engelska
Sidor: 43-71
Publikation/Tidskrift/Serie: Probability and Mathematical Statistics
Volym: 29
Nummer: Fasc. 1
Dokumenttyp: Artikel
Förlag: Center for Probability and Mathematical Statistics, Wroclaw


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.



  • Probability Theory and Statistics
  • 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


  • ISSN: 0208-4147

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