A bivariate Levy process with negative binomial and gamma marginals
(2008) In Journal of Multivariate Analysis 99(7). p.14181437 Abstract
 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 selfsimilarity. 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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1186763
 author
 Kozubowski, Tomasz J; Panorska, Anna K and Podgorski, Krzysztof ^{LU}
 organization
 publishing date
 2008
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 operational time, random summation, random time transformation, stability, subordination selfsimilarity, negative binomial process, maximum likelihood estimation, divisibility, infinite, gamma Poisson process, discrete Levy process, gamma process
 in
 Journal of Multivariate Analysis
 volume
 99
 issue
 7
 pages
 1418  1437
 publisher
 Academic Press
 external identifiers

 wos:000257221700005
 scopus:45049087244
 ISSN
 0047259X
 DOI
 10.1016/j.jmva.2008.02.029
 language
 English
 LU publication?
 yes
 id
 8178ad0b9f3a4a1da6d751e6bfc3b442 (old id 1186763)
 date added to LUP
 20080903 16:34:24
 date last changed
 20170101 05:54:10
@article{8178ad0b9f3a4a1da6d751e6bfc3b442, abstract = {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 selfsimilarity. 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.}, author = {Kozubowski, Tomasz J and Panorska, Anna K and Podgorski, Krzysztof}, issn = {0047259X}, keyword = {operational time,random summation,random time transformation,stability,subordination selfsimilarity,negative binomial process,maximum likelihood estimation,divisibility,infinite,gamma Poisson process,discrete Levy process,gamma process}, language = {eng}, number = {7}, pages = {14181437}, publisher = {Academic Press}, series = {Journal of Multivariate Analysis}, title = {A bivariate Levy process with negative binomial and gamma marginals}, url = {http://dx.doi.org/10.1016/j.jmva.2008.02.029}, volume = {99}, year = {2008}, }