Continuous scaled phase-type distributions

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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.

Original languageEnglish
JournalStochastic Models
Issue number2
Pages (from-to)293-322
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2022 The Author(s). Published with license by Taylor and Francis Group, LLC.

    Research areas

  • Heavy tails, parameter estimation, phase-type, scale mixtures

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