Continuous scaled phase-type distributions

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