2015
DOI: 10.1017/asb.2015.9
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Modelling Insurance Data With the Pareto Arctan Distribution

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

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Cited by 22 publications
(24 citation statements)
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“…Our results suggest that there exists enough statistical evidence to reject the null hypothesis that the data come from any of the models considered. 4 However, it is relevant to mention that these tests reject the Gamma distribution earlier than the EAT distribution for almost all the years examined.…”
Section: Resultsmentioning
confidence: 92%
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“…Our results suggest that there exists enough statistical evidence to reject the null hypothesis that the data come from any of the models considered. 4 However, it is relevant to mention that these tests reject the Gamma distribution earlier than the EAT distribution for almost all the years examined.…”
Section: Resultsmentioning
confidence: 92%
“…showing an outstanding performance in three different scenarios, to model claim size data [4], to describe city size data [5] and finally to derive a parametric family of Lorenz curves [12]. The survival function and pdf of the EAT distribution are provided bȳ…”
Section: The Exponential Arctan Distributionmentioning
confidence: 99%
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“…That is, particular attentions was made to define models with new features in this regard, motivating the development of general families of distributions having the ability to generate flexible distributions. Among these families, we may mention the skew-normal family pioneered by [1], the exponentiated-generated (Exp-G) family proposed by [2], the Marshall-Olkin-generated (MO-G) family studied by [3], the order statistics-generated family introduced by [4], the Sinh-arcsinh-generated family developed by [5], the beta-generated (B-G) family introduced by [6], the transmuted-generated (T-G) family developed by [7], the gamma-generated (Gam-G) family proposed by [8] and the Pareto ArcTan family developed by [9]. Each of them has generated a plethora of distributions and statistical models, widely used in practice.…”
Section: Introductionmentioning
confidence: 99%
“…For this reason, researchers developed various extensions and modified forms of the P distribution to obtain a more flexible model with different numbers of parameters. Some of them can be cited as follows: Exponentiated P (EP) (Stoppa 1990;Gupta et al 1998), Beta P (BP) (Akinsete et al 2008), Kumaraswamy P (KwP) (Bourguignon et al 2013), Kumaraswamy generalized P (Nadarajah and Eljabri 2013), P ArcTan (PAT) (Gómez-Déniz and Calderín-Ojeda 2015), exponentiated Weibull P and Weibull P 1 − exp − G(x; ξ) G(x; ξ)…”
Section: Introductionmentioning
confidence: 99%