No abstract

No abstract

Branching process, Discretizing, Failure rate, Fitting, Geometric distribution, 60E05, 62E99, 60J80,

No abstract

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modeled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al, 2016), Gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research. .es (V. Jordá). The modelLet Θ be a positive random variable with cdf F Θ (·) and Laplace-Stieltjes transform (hereinafter referred to as Laplace transform) L Θ (·), that is L Θ (s) = E[exp(−sΘ)] = ∞ 0 e −sz dF Θ (z). A distribution with support on (0, ∞) is identified by its Laplace transform. We consider the classical compound

This article proposes a model of foreign tourist expenditure, based on expenditure in the country of origin (i.e. reservation of accommodation and transport) and on goods and services at the destination. The study focuses on two measures reflecting the two types of expenditure: the tourist budget share and the difference in growth rates between expenditure at origin and at destination. The random nature of each of these variables is taken into account. The tourist budget share is determined using a fractional response model, based on the beta distribution. This approach allows us to accommodate certain aspects of the empirical budget share distribution, such as skewness, and to represent the results as bounded between 0 and 1, but also to include covariates. The empirical analysis was conducted using data obtained by the Canary Islands Tourist Expenditure Survey, focusing on German and British tourists in particular. The results obtained show that the fractional regression model proposed represents the behaviour of the relevant variables reasonably well and surpasses the performance of the linear regression model.

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed.

No abstract