A bivariate Lévy process with negative binomial and gamma marginals

DOI10.1016/j.jmva.2008.02.029zbMath1144.60310OpenAlexW2085396093MaRDI QIDQ935337

Krzysztof Podgórski, Anna K. Panorska, Tomasz J. Kozubowski

Publication date: 6 August 2008

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2008.02.029

zbMATH Keywords

stabilitysubordinationmaximum likelihood estimationself-similarityinfinite divisibilitygamma processnegative binomial processrandom summationdiscrete Lévy processgamma Poisson processoperational timerandom time transformation

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Estimation in multivariate analysis (62H12) Central limit and other weak theorems (60F05) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Self-similar stochastic processes (60G18)

Related Items (12)

The Joint Distribution of the Sum and the Maximum of IID Exponential Random Variables ⋮ The joint distribution of the sum and maximum of dependent Pareto risks ⋮ Compound zero-truncated Poisson normal distribution and its applications ⋮ A bivariate infinitely divisible law for modeling the magnitude and duration of monotone periods of log‐returns ⋮ A new multivariate model involving geometric sums and maxima of exponentials ⋮ Bivariate gamma-geometric law and its induced Lévy process ⋮ A bivariate infinitely divisible distribution with exponential and Mittag-Leffler marginals ⋮ Geometric skew normal distribution ⋮ On a general class of discrete bivariate distributions ⋮ A new trivariate model for stochastic episodes ⋮ A general stochastic model for bivariate episodes driven by a gamma sequence ⋮ A generalized linear model for multivariate events

Cites Work

• A mixed bivariate distribution with exponential and geometric marginals
• Invariance properties of the negative binomial Levy process and stochastic self-similarity
• On simulation from infinitely divisible distributions
• Financial Modelling with Jump Processes
• Fractional Laplace motion
• A Representation of Independent Increment Processes without Gaussian Components
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