Distributional properties of the negative binomial Lévy process
(2009) In Probability and Mathematical Statistics 29(Fasc. 1). p.43-71- Abstract
- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3049633
- author
- Kozubowski, Tomasz and Podgorski, Krzysztof LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- 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
- in
- Probability and Mathematical Statistics
- volume
- 29
- issue
- Fasc. 1
- pages
- 43 - 71
- publisher
- Center for Probability and Mathematical Statistics, Wroclaw
- ISSN
- 0208-4147
- language
- English
- LU publication?
- yes
- id
- 226dbe23-3c63-4a43-aeea-776b7c7349a9 (old id 3049633)
- alternative location
- http://www.math.uni.wroc.pl/~pms/files/29.1/Article/29.1.3.pdf
- date added to LUP
- 2016-04-01 12:59:11
- date last changed
- 2018-11-21 20:11:04
@article{226dbe23-3c63-4a43-aeea-776b7c7349a9,
abstract = {{The geometric distribution leads to a Lévy process parameterized<br/><br>
by the probability of success. The resulting negative binomial process<br/><br>
(NBP) is a purely jump and non-decreasing process with general negative<br/><br>
binomial marginal distributions. We review various stochastic mechanisms<br/><br>
leading to this process, and study its distributional structure. These<br/><br>
results enable us to establish strong convergence of the NBP in the supremum<br/><br>
norm to the gamma process, and lead to a straightforward algorithm<br/><br>
for simulating sample paths.We also include a brief discussion of estimation<br/><br>
of the NPB parameters, and present an example from hydrology illustrating<br/><br>
possible applications of this model.}},
author = {{Kozubowski, Tomasz and Podgorski, Krzysztof}},
issn = {{0208-4147}},
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}},
language = {{eng}},
number = {{Fasc. 1}},
pages = {{43--71}},
publisher = {{Center for Probability and Mathematical Statistics, Wroclaw}},
series = {{Probability and Mathematical Statistics}},
title = {{Distributional properties of the negative binomial Lévy process}},
url = {{http://www.math.uni.wroc.pl/~pms/files/29.1/Article/29.1.3.pdf}},
volume = {{29}},
year = {{2009}},
}