Modeling loss data using composite models

Abstract

We develop several new composite models based on the Weibull distribution for heavy tailed insurance loss data. The composite model assumes different weighted distributions for the head and tail of the distribution and several such models have been introduced in the literature for modeling insurance loss data. For each model proposed in this paper, we specify two parameters as a function of the remaining parameters. These models are fitted to two real insurance loss data sets and their goodness-of-fit is tested. We also present an application to risk measurements and compare the suitability of the models to empirical results.

Composite Models Used in Actuarial Practice

“…There are other composite models studied in the literature like, e.g. : composite truncation models [13], composite lognormal -Burr [1], composite Stoppa models [2], inverse Weibull composite models [4], composite lognormal -Pareto model with random threshold [9].…”

“…Also, the number of parameters is reduced from four to two. The other two parameters are expressed using the relationships = 0 and = ( 0 + 1) 1 . Thus, the constant c of the density function definition is, in [10]…”

“…However in [5], it is underlined that Pareto fits well the tail, but on the other hand, lognormal and Weibull distributions produce an overall good fit but fit badly the tail. Several works have introduced composite models for insurance loss data modeling [1,6]. Cooray and Ananda [3] in 2005 were the first to open the way for research into composite models using a longnormal distribution to a certain threshold and then the Pareto distribution.…”

New methods to define heavy-tailed distributions with applications to insurance data

“…Another promising approach for obtaining new flexible heavy-tailed families of distributions, which gives reasonably good fit for heavy-tailed losses, is the method of composition; see Paula et al [11], Klugman et al [12], Nadarajah and Abu Bakar [13], and Bakar et al [14]. However, it should be noted that the new distributions obtained by the composition approach involve more than three parameters causing difficulties in the estimation process and computational efforts are required.…”

Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions

“…Other distributions for the body such as the Weibull distribution (Ciumara, 2006;Scollnik and Sun, 2012) or the log-normal distribution (Cooray and Ananda, 2005;Scollnik, 2007;Pigeon and Denuit, 2011) have also been used. Nadarajah and Bakar (2014); Bakar et al (2015); Calderín-Ojeda and Kwok (2016) investigate the splicing of the log-normal or Weibull distribution with various tail distributions. Lee et al (2012) consider the splicing of a mixture of two exponentials and the GPD.…”