Parametric Estimation of the Siler Mortality Model: Applications to Hazard Rate and Survivorship Analysis

This article investigates the approach to the Siler mortality model and it optimization techniques in modeling hazard rate intensities and survivorship experiences based on actuarial life table data sourced from Institute and Faculty of Actuaries (IFoA) ELT15 male mortality table for ages 20, 40, 60 and 80 with their respective values 0.00083, 0.000166, 0.01323 and 0.09675 following a parametric framework for the hazard rate intensities incorporating all age components. The five-parameters of the Siler model were estimated using non-linear optimization procedures assisted by numerical processes due to lack of closed-form solutions, the parameters are further used to construct vital actuarial life-table functions for hazard rates and survivorship experiences across all age groups. The fitted Siler model produced parameter estimates of all statistically significant. These estimates indicate high early-age hazard, a near-constant mid-age hazard and exponentially increasing senescent hazard at older ages and it really confirm adequacy of the model fitness and the Siler model shows superior fit over traditional models by validating its three-component structure for the data values. The study smooth curves uncover stable actuarial consistency and its coherences, the overall findings revealed appropriateness of Siler model optimization techniques providing tried-and-true framework for hazard rate intensities and provided answers to how the Siler model parameters are estimated using optimization techniques, how the hazard intensities be examine from optimizing Siler model parameters and to what extend does the survival experiences of a study lives be estimated. The research recommends that life insurance and pension fund administrators/regulators can follow the results of this article to carefully examine the risk effect of mortality on their clients. Hazard rate modeling remains cardinal in actuarial mathematics, demography and health population analysis.