Modelling count data is one of the most important issues in statistical research. In this paper, a new probability mass function introduced by discretizing continuous failure model Lindley distribution. The obtained over-dispersed and competitive with Poisson distribution to fit automobile claim frequency data. After revising some its properties compound discrete closed form. This suitable be applied collective risk when both number claims size single are implemented into model. fades away...

This article presents an extended distribution that builds upon the exponential distribution. extension is based on a scale mixture between and beta distributions. By utilizing this approach, we obtain offers increased flexibility in terms of kurtosis coefficient. We explore general density, properties, moments, asymmetry, coefficients Statistical inference performed using both moments maximum likelihood methods. To show performance new model, it applied to real dataset with atypical...

New expressions and bounds for Catalan's Apery's constants, derived from the half hyperbolic secant distribution, are presented. These constants obtained by using Lorenz curve, Gini Theil indices, convolutions a mixture of distributions, among other approaches. The new presented both in terms integral (simple double) representation also as an interesting series representation. Some these features well known, while others new. In addition, some representations Euler's numbers obtained.

This article proposes a model of foreign tourist expenditure, based on expenditure in the country origin (i.e. reservation accommodation and transport) goods services at destination. The study focuses two measures reflecting types expenditure: budget share difference growth rates between random nature each these variables is taken into account. determined using fractional response model, beta distribution. approach allows us to accommodate certain aspects empirical distribution, such as...

In this article, a new mixed Poisson distribution is introduced. This obtained by utilizing mixing process, with as and Transmuted Exponential distribution. Distributional properties like unimodality, moments, over-dispersion, infinite divisibility are studied. Three methods viz. Method of moment, moment proportion, Maximum-likelihood method used for parameter estimation. Further, an actuarial application in context aggregate claim presented. Finally, to show the applicability superiority...

Abstract In this paper, a new methodology based on the use of inverse circular tangent function that allows us to add scale parameter (say α) an initial survival is presented. The latter determined as limiting case when α tends zero. By choosing parent classical Pareto function, ArcTan (PAT) distribution obtained. After providing comprehensive analysis its statistical properties, theoretical results with reference insurance are illustrated. Its performance compared, by means well-known...

Abstract The distribution of the sum dependent risks is a crucial aspect in actuarial sciences, risk management and many branches applied probability. In this paper, we obtain analytic expressions for probability density function (pdf) cumulative (cdf) aggregated risks, modelled according to mixture exponential distributions. We first review properties multivariate distributions, then analytical formulation pdf cdf distribution. study detail some specific families with Pareto (Sarabia et al....

Abstract There are different citation habits in the research fields that influence obsolescence of literature. We analyze distinctive literature disciplinary journals eight scientific subfields based on cited references distribution, as a synchronous approach. use both negative binomial (NB) and Poisson distributions to capture this obsolescence. The corpus being examined is published 2019 covers 22,559 papers citing 872,442 references. Moreover, three measures tail distribution proposed:...

In this paper, we introduce a new parameterization for the scale mixture of Rayleigh distribution, which uses mean linear regression model indexed by and precision parameters to asymmetric positive real data. To test goodness fit, two residuals model. A Monte Carlo simulation study is performed evaluate parameter estimation proposed We compare our with existing alternatives illustrate its advantages usefulness using Gilgais data in R software version 4.2.3 gamlss package.