A mortality model based on a mixture distribution function

Abstract

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman–Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman–Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture ‘accident humps’).

Keywords:

• mortality model
• mixture distribution
• skew-bimodal-normal distribution
• accident hump
• half-normal distribution

Notes

1 Please direct all correspondence to Stefano Mazzuco, Department of Statistical Sciences, University of Padova, Via Cesare Battisti, 241, Padova 35121, Italy; or by E-mail: [email protected]

2 We are grateful to several scholars for insightful suggestions and comments on the preliminary versions of this paper. In particular, we thank Prof. Azzalini for providing references on the SBN distribution, Dr Lenart for suggesting the link with Pearson theory, and Prof. Canudas-Romo for many insightful comments on data to be used for estimation. We also thank research staff at the Max-Planck Odense Center on the Biodemography of Aging (MaxO) for providing several useful comments on this project. Finally, we thank two anonymous referees for the many suggestions provided to improve the manuscript.