Mortality modeling and regression with matrix distributions
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Mortality modeling and regression with matrix distributions. / Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens; Yslas, Jorge.
I: Insurance: Mathematics and Economics, Bind 107, 2022, s. 68-87.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Mortality modeling and regression with matrix distributions
AU - Albrecher, Hansjörg
AU - Bladt, Martin
AU - Bladt, Mogens
AU - Yslas, Jorge
N1 - Publisher Copyright: © 2022 The Author(s)
PY - 2022
Y1 - 2022
N2 - In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can lead to reasonably accurate and relatively parsimonious models for mortality curves across the entire lifespan. A particular feature of the proposed model framework is that it allows for a more direct interpretation of the implied underlying aging process than some previous approaches. Subsequently, towards applications of the approach for multi-population mortality modeling, we introduce regression via the concept of proportional intensities, which are more flexible than proportional hazard models, and we show that the two classes are asymptotically equivalent. We illustrate how the model parameters can be estimated from data by providing an adapted EM algorithm for which the likelihood increases at each iteration. The practical feasibility and competitiveness of the proposed approach, including the right-censored case, are illustrated by several sets of mortality and survival data.
AB - In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can lead to reasonably accurate and relatively parsimonious models for mortality curves across the entire lifespan. A particular feature of the proposed model framework is that it allows for a more direct interpretation of the implied underlying aging process than some previous approaches. Subsequently, towards applications of the approach for multi-population mortality modeling, we introduce regression via the concept of proportional intensities, which are more flexible than proportional hazard models, and we show that the two classes are asymptotically equivalent. We illustrate how the model parameters can be estimated from data by providing an adapted EM algorithm for which the likelihood increases at each iteration. The practical feasibility and competitiveness of the proposed approach, including the right-censored case, are illustrated by several sets of mortality and survival data.
KW - Inhomogeneous Markov processes
KW - Inhomogeneous phase-type distributions
KW - Phase-type distributions
KW - Regression models
KW - Survival analysis
UR - http://www.scopus.com/inward/record.url?scp=85136478979&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2022.08.001
DO - 10.1016/j.insmatheco.2022.08.001
M3 - Journal article
AN - SCOPUS:85136478979
VL - 107
SP - 68
EP - 87
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -
ID: 343343582