Continuous scaled phase-type distributions
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.
Cite
@article{arxiv.2103.02457,
title = {Continuous scaled phase-type distributions},
author = {Hansjoerg Albrecher and Martin Bladt and Mogens Bladt and Jorge Yslas},
journal= {arXiv preprint arXiv:2103.02457},
year = {2021}
}