The design of an optimal bonus-malus system based on the Sichel distribution

George Tzougas, Nicholas Frangos

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


This chapter presents the design of an optimal Bonus-Malus System (BMS) using the Sichel distribution to model the claim frequency distribution. This system is proposed as an alternative to the optimal BMS obtained by the traditional Negative Binomial model [19]. The Sichel distribution has a thicker tail than the Negative Binomial distribution and it is considered as a plausible model for highly dispersed count data. We also consider the optimal BMS provided by the Poisson-Inverse Gaussian distribution (PIG), which is a special case of the Sichel distribution. Furthermore, we develop a generalised BMS that takes into account both the a priori and a posteriori characteristics of each policyholder. For this purpose we consider the generalised additive models for location, scale and shape (GAMLSS) in order to use all available information in the estimation of the claim frequency distribution. Within the framework of the GAMLSS we propose the Sichel GAMLSS for assessing claim frequency as an alternative to the Negative Binomial Type I (NBI) regression model used by Dionne and Vanasse [9, 10]. We also consider the NBI and PIG GAMLSS for assessing claim frequency.
Original languageEnglish
Title of host publicationModern Problems in Insurance Mathematics
Number of pages22
ISBN (Electronic)9783319066530
ISBN (Print)9783319066523
Publication statusPublished - 2014

Publication series

NameEAA Series
ISSN (Print)1869-6929
ISSN (Electronic)1869-6937


  • Sichel Distribution
  • Bonus-malus System (BMS)
  • Generalized Additive Models For Location, Scale And Shape (GAMLSS)
  • Negative Binomial Inverse Gaussian-Poisson (PIG)


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