Continuous scaled phase-type distributions. Issue 2 (3rd April 2023)

• Record Type: Journal Article
• Authors: Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens; Yslas, Jorge
• Is Part Of: Stochastic models. Volume 39:Issue 2(2023)
• Page Start: 293
• Page End: 322
• Publication Date: 2023-04-03
• Subjects: Heavy tails -- parameter estimation -- phase-type -- scale mixtures; Primary: 60E05. Secondary: 60G70 -- 60J22 -- 62F10 -- 62N01 -- 62P05; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2022.2089683
• Languages: English
• ISSNs: 1532-6349

Abstract

Abstract: Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective statistical inference is derived and implemented using real-world datasets. In contrast to discrete scaling studied in earlier literature, in the present continuous case closed-form formulas for various functionals of the resulting distributions are obtained, which facilitates both their analysis and implementation. The resulting mixture distributions are very often heavy-tailed and yet retain various properties of phase-type distributions, such as being dense (in weak convergence) on the set of distributions with positive support.