Multivariate Matrix-Exponential Distributions

DOI10.1080/15326340903517097zbMath1196.60021OpenAlexW2160314116MaRDI QIDQ3562369

Bo Friis Nielsen, Mogens Bladt

Publication date: 21 May 2010

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://drops.dagstuhl.de/opus/volltexte/2008/1397/

zbMATH Keywords

continued fractionsHankel matricesmultivariate phase-type distributionmultivariate matrix-exponential

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05)

Related Items (15)

A NEW SHOCK MODEL WITH A CHANGE IN SHOCK SIZE DISTRIBUTION ⋮ Characterisation of multivariate phase type distributions ⋮ Queues and Risk Processes with Dependencies ⋮ Parisian types of ruin probabilities for a class of dependent risk-reserve processes ⋮ Multivariate matrix-exponential affine mixtures and their applications in risk theory ⋮ Ruin problems for risk processes with dependent phase-type claims ⋮ On a Construction of Stationary Processes via Bilateral Matrix-Exponential Distributions ⋮ Joint densities of hitting times for finite state Markov processes ⋮ On two families of bivariate distributions with exponential marginals: aggregation and capital allocation ⋮ On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient ⋮ Convolutions of multivariate phase-type distributions ⋮ A semi-explicit density function for Kulkarni's bivariate phase-type distribution ⋮ A note on compound renewal risk models with dependence ⋮ Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times ⋮ Ruin probabilities in models with a Markov chain dependence structure

Cites Work

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• The waiting-time distribution and its moments of the PH/PH/1 queue
• Multivariate risk model of phase type
• Multivariate Phase-Type Distributions
• On matrix exponential distributions
• A duality theorem for the matrix paradigms in queueing theory
• A New Class of Multivariate Phase Type Distributions
• Ph-distributions arising through conditioning
• A Multivariate Exponential Distribution
• On the Limitations of Multivariate Phase-Type Families

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