Parameter Reduction of Complex Distributions Using a Tuning Method with Applications to Actuarial Data

When modeling more complex larger data sets, researchers/practitioners often use higher-order parametric distributions. However, such extensions pose various issues, prominently computational, and the significance of estimated parameters. For example, when estimating parameters of higher-order parametric distribution under the likelihood method, convergence problems and higher standard error of the estimated parameter can often be found. Therefore, considering these issues, we were motivated to look for a new avenue to remedy the situation. The parameter tuning method is introduced to reduce the number of parameters of higher-order parametric distribution with a minimal change of the likelihood value. Two different well-known actuarial data examples are used to demonstrate the procedure and illustrate the applicability and flexibility using well-known risk measures.