A Marshall–Olkin family of heavy-tailed distributions which includes the lognormal one

Abstract

A new class of heavy-tailed distribution functions,, containing the lognormal distribution as a particular case is introduced. The class thus obtained depends on a set of three parameters, incorporating an additional distribution to the classical lognormal one. This new class of heavy-tailed distribution is presented as an alternative to other useful heavy-tailed distributions, such as the lognormal, Weibull, and Pareto distributions. The density and distribution functions of this new class are given by a closed expression which allows us to easily compute probabilities, quantiles, moments, and related measurements. Finally, some applications are shown as examples.

Keywords:

• Heavy-Tailed
• Insurance
• Lognormal Distribution
• Loss
• Subexponential Distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60E05
• Secondary: 62H05

Acknowledgments

The authors are indebted to the referees for helpful comments which, without doubt, helped to improve an earlier version of the paper.

Funding

Research partially funded by ECO2009–14152 (MICINN, Spain), ECO2013-47092 (MINECO, Spain) and SEJ–02814 (Junta de Andalucía, Spain).