English

Continuous scaled phase-type distributions

Probability 2021-11-25 v2 Statistics Theory Statistics Theory

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.

Keywords

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}
}