TITLE:
Estimation of Aggregate Losses of Secondary Cancer Using PH-OPPL and PH-TPPL Distributions
AUTHORS:
Cynthia Mwende, Patrick Weke, Davis Bundi, Joseph Ottieno
KEYWORDS:
PH One Parameter Poisson Lindley, PH Two Parameter Poisson Lindley, PH Three Parameter Poisson Linldey, Discrete Fourier Transform, Discretization
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.5,
October
19,
2021
ABSTRACT: Kenyan
insurance firms have introduced insurance policies of chronic illnesses like
cancer; however, they have faced a huge
challenge in the pricing of these policies as cancer can transit into different
stages, which
consequently leads to variation in the cost of treatment. This has made the
estimation of aggregate losses of diseases which have multiple stages of
transitions such as cancer, an area
of interest of many insurance firms. Mixture phase type distributions can be
used to solve this setback as they can in-cooperate the transition in the
estimation of claim frequency while also in-cooperating the heterogeneity aspect of claim data. In this paper, we estimate the aggregate losses of
secondary cancer cases in Kenya using mixture phase type Poisson Lindley
distributions. Phase type (PH) distributions for one and two parameter Poisson
Lindley are developed as well their compound distributions. The matrix
parameters of the PH distributions are estimated using continuous Chapman
Kolmogorov equations as the disease process of cancer is continuous while
severity is modeled using Pareto, Generalized Pareto and Weibull distributions.
This study shows that aggregate losses for Kenyan data are best estimated using
PH-OPPL-Weibull model in the case of PH-OPPL distribution models and
PH-TPPL-Generalized Pareto model in the case of PH-TPPL distribution models. Comparing
the two best models, PH-OPPL-Weibull model provided the best fit for secondary
cancer cases in Kenya. This model is also recommended
for different diseases which are dynamic in nature like cancer.