Joint discrete and continuous matrix distribution modeling

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Joint discrete and continuous matrix distribution modeling. / Bladt, Martin; Gardner, Clara Brimnes.

In: Stochastic Models, Vol. 40, No. 1, 2023, p. 1-37.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bladt, M & Gardner, CB 2023, 'Joint discrete and continuous matrix distribution modeling', Stochastic Models, vol. 40, no. 1, pp. 1-37. https://doi.org/10.1080/15326349.2023.2185257

APA

Bladt, M., & Gardner, C. B. (2023). Joint discrete and continuous matrix distribution modeling. Stochastic Models, 40(1), 1-37. https://doi.org/10.1080/15326349.2023.2185257

Vancouver

Bladt M, Gardner CB. Joint discrete and continuous matrix distribution modeling. Stochastic Models. 2023;40(1):1-37. https://doi.org/10.1080/15326349.2023.2185257

Author

Bladt, Martin ; Gardner, Clara Brimnes. / Joint discrete and continuous matrix distribution modeling. In: Stochastic Models. 2023 ; Vol. 40, No. 1. pp. 1-37.

Bibtex

@article{d9f0eee4e2ce4121968c352ac4c0c853,
title = "Joint discrete and continuous matrix distribution modeling",
abstract = "In this paper, we introduce a bivariate distribution on (Formula presented.) arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on (Formula presented.) and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective EM algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.",
keywords = "EM-algorithm, Markov processes, mixed data, phase-type distributions",
author = "Martin Bladt and Gardner, {Clara Brimnes}",
note = "Publisher Copyright: {\textcopyright} 2023 Taylor & Francis Group, LLC.",
year = "2023",
doi = "10.1080/15326349.2023.2185257",
language = "English",
volume = "40",
pages = "1--37",
journal = "Stochastic Models",
issn = "1532-6349",
publisher = "Taylor & Francis",
number = "1",

}

RIS

TY - JOUR

T1 - Joint discrete and continuous matrix distribution modeling

AU - Bladt, Martin

AU - Gardner, Clara Brimnes

N1 - Publisher Copyright: © 2023 Taylor & Francis Group, LLC.

PY - 2023

Y1 - 2023

N2 - In this paper, we introduce a bivariate distribution on (Formula presented.) arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on (Formula presented.) and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective EM algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.

AB - In this paper, we introduce a bivariate distribution on (Formula presented.) arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on (Formula presented.) and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective EM algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.

KW - EM-algorithm

KW - Markov processes

KW - mixed data

KW - phase-type distributions

U2 - 10.1080/15326349.2023.2185257

DO - 10.1080/15326349.2023.2185257

M3 - Journal article

AN - SCOPUS:85151940964

VL - 40

SP - 1

EP - 37

JO - Stochastic Models

JF - Stochastic Models

SN - 1532-6349

IS - 1

ER -

ID: 371272681