Feller-Pareto and Related Distributions: Numerical Implementation and Actuarial Applications

Dutang, Christophe; Goulet, Vincent; Langevin, Nicholas

doi:10.18637/jss.v103.i06

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…Currently, coding skills form part of the body of knowledge of actuaries and actuarial science researchers. In R, an extensive implementation for aggregate loss modeling based on the collective risk theory is the actuar package (Dutang et al, 2008(Dutang et al, , 2022). An available library in Python is aggregate, which implements the computation of compound probability distributions via fast Fourier transform (FFT) convolution algorithm (Mildenhall, 2022).…”

Section: Context Scope and Contributionsmentioning

confidence: 99%

GEMAct: a Python package for non-life (re)insurance modeling

Pittarello,

Luini,

Marchione

2024

Ann. actuar. sci.

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This paper introduces gemact, a Python package for actuarial modeling based on the collective risk model. The library supports applications to risk costing and risk transfer, loss aggregation, and loss reserving. We add new probability distributions to those available in scipy, including the (a, b, 0) and (a, b, 1) discrete distributions, copulas of the Archimedean family, the Gaussian, the Student t and the Fundamental copulas. We provide an implementation of the AEP algorithm for calculating the cumulative distribution function of the sum of dependent, nonnegative random variables, given their dependency structure specified with a copula. The theoretical framework is introduced at the beginning of each section to give the reader with a sufficient understanding of the underlying actuarial models.

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Section: Context Scope and Contributionsmentioning

confidence: 99%

GEMAct: a Python package for non-life (re)insurance modeling

Pittarello,

Luini,

Marchione

2024

Ann. actuar. sci.

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“…Very recently, Dutang et al [16] provided functions in R for obtaining the MLE estimators for the whole family of Feller-Pareto distributions. Their asymptotic properties have been derived in Reference [17].…”

Section: The Singh-maddala Distributionmentioning

confidence: 99%

A new parametric approach to gender gap with application to EUSILC data in Poland and Italy

Greselin

Jędrzejczak

Trzcińska

2023

Statistical Analysis

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Real income distribution comparisons are of interest to policy makers across European countries. Nowadays, a crucial component of income inequality remains the discrepancy between men and women, often called the gender gap. Since the gender gap is related to the whole distribution of incomes in a population, popular single metrics are not adequate, and previous studies applied the relative distribution method, a non‐parametric approach to the comparison of distributions. Here, we propose a parametric approach for estimating the relative distribution. Then we extend it to assess the impact of selected covariates—related to the personal characteristics of the samples—on the existing gender gap in both countries. In more detail, models for income were fitted to empirical data from Poland and Italy, from the European Survey of Income and Living Conditions (wave 2018). Afterwards, their parameters were employed to obtain the estimates of relative distribution characteristics. The methods applied in the study turned out to be relevant to describe the gender gap over the entire income range. Finally, the results of the empirical analysis are discussed to reveal similarities and substantial differences between the countries.

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Data augmentation based methods for estimating the parameters of the Feller-Pareto distribution: theory and applications

Ghosh

2024

Research in Statistics

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Feller-Pareto and Related Distributions: Numerical Implementation and Actuarial Applications

Cited by 4 publications

References 14 publications

GEMAct: a Python package for non-life (re)insurance modeling

GEMAct: a Python package for non-life (re)insurance modeling

A new parametric approach to gender gap with application to EUSILC data in Poland and Italy

Data augmentation based methods for estimating the parameters of the Feller-Pareto distribution: theory and applications

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