Continuous scaled phase-type distributions
Hansjörg Albrecher, Martin Bladt, Mogens Bladt, Jorge Yslas · Stochastic Models · 2022
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.