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New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie
New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie
Electronic Thesis and Dissertation Repository
This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.
The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …
A Class Of Phase-Type Ageing Models And Their Lifetime Distributions, Boquan Cheng
A Class Of Phase-Type Ageing Models And Their Lifetime Distributions, Boquan Cheng
Electronic Thesis and Dissertation Repository
Ageing is a universal and ever-present biological phenomenon. Yet, describing the ageing mechanism in formal mathematical terms — in particular, capturing the ageing pattern and quantifying the ageing rate — has remained a challenging actuarial modelling endeavour. In this thesis, we propose a class of Coxian-type Markovian models. This class enables a quantitative description of the well-known characteristics of ageing, which is a genetically determined, progressive, and essentially irreversible process. The unique structure of our model features the transition rate for the ageing process and a functional form for the relationship between ageing and death with a shape parameter that …