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.

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In recent years, composite models based on the lognormal distribution have become popular in actuarial sciences and related areas. In this short note, we present a new R package for computing the probability density function, cumulative density function, and quantile function, and for generating random numbers of any composite model based on the lognormal distribution. The use of the package is illustrated using a real data set.

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In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements.

The first ever real data application of a two-component Burr mixture distribution is provided. It is fitted to three loss data sets: fire loss claims in Denmark, fire loss claims for three building categories in Belgium and fire loss data in Norway. Each of these data sets exhibits significant bimodality. The fits of the two-component Burr mixture distribution are compared to those of five other two-component mixture distributions: the two-component Weibull mixture, two-component gamma mixture, two-component Pareto mixture, two-component lognormal mixture and the two-component exponential mixture distributions. The Burr mixture distribution is shown to give the best fit for each data set. The relative performances of the fitted distributions was assessed in terms of Akaike information criterion values, Bayesian information criterion values, consistent Akaike information criterion values, corrected Akaike information criterion values, Hannan-Quinn criterion values, density plots and probability-probability plots.