Power laws appear widely in many branches of economics, geography, demography and other social sciences. In particular, the upper tail of city size distributions appear to follow power laws, as many researchers have shown for different countries and different periods of times. A crucial point in...

This note revisits the ideas of the so-called semiparametric methods that we consider to be very useful when applying machine learning in insurance. To this aim, we first recall the main essence of semiparametrics like the mixing of global and local estimation and the combining of explicit...

It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss...

Grouped data in the form of income shares have conventionally been used to estimate income inequality due to the lack of individual records. We provide guidance on the choice between parametric and nonparametric methods and its estimation, for which we develop the GB2group R package. We present...

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM...

Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull-Pareto (CWL) distribution. On this note, this distribution is...

In the classical bonus-malus system the premium assigned to each policyholder is based only on the number of claims made without having into account the claims size. Thus, a policyholder who has declared a claim that results in a relatively small loss is penalised to the same extent as one who...

In this research, trade credit is analysed form a seller (supplier) perspective. Trade credit allows the supplier to increase sales and profits but creates the risk that the customer will not pay, and at the same time increases the risk of the supplier's insolvency. If the supplier is a small or...

In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the...

In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and...