Journal of Risk Model Validation

Risk.net

Analytical expressions of risk quantities for composite models

José María Sarabia and Enrique Calderín-Ojeda

  • We derive composite models from the McDonald’s family.
  • Analytic expressions of actuarial quantities are obtained.
  • Applications of these models to two sets of unimodal and positively--skewed insurance claim size data are given.

Composite models have received a lot of attention in the recent actuarial literature. In this paper, we obtain analytic expressions of different actuarial and statistical quantities for a general class of composite models derived from the McDonald’s family of probability distributions. These quantities include probability density functions, cumulative distribution functions, quantile functions, raw moments, value-at-risk, tail moments, moments of loss variables and the quantile density function, which is very useful for the computation of expectations of order statistics. Finally, applications of these models to two sets of unimodal and positively skewed insurance claim size data are provided.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here