MODELLING INSURANCE DATA WITH THE PARETO ARCTAN DISTRIBUTION

2015 ◽  
Vol 45 (3) ◽  
pp. 639-660 ◽  
Author(s):  
Emilio Gómez-Déniz ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Scale Parameter ◽  
Survival Function ◽  
Inverse Gamma ◽  
Heavy Tailed Distributions ◽  
Fire Insurance ◽  
Tangent Function ◽  
Heavy Tailed ◽  
Limiting Case ◽  
Insurance Data ◽  
Theoretical Results

AbstractIn 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 illustrated. Its performance is compared, by means of the well-known Norwegian fire insurance data, with other existing heavy-tailed distributions in the literature such as Pareto, Stoppa, Shifted Lognormal, Inverse Gamma and Fréchet distributions.

scholarly journals Heavy-Tailed Distributions and Rating

2001 ◽  
Vol 31 (1) ◽  
pp. 37-58 ◽  
Author(s):  
J. Beirlant ◽  
G. Matthys ◽  
G. Dierckx
Keyword(s):  
Parametric Model ◽  
Extreme Value ◽  
Small Sample ◽  
Data Set ◽  
Large Claim ◽  
Heavy Tailed Distributions ◽  
Fire Insurance ◽  
Insurance Portfolio ◽  
Claim Size Distribution ◽  
Heavy Tailed

AbstractIn this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.

scholarly journals New methods to define heavy-tailed distributions with applications to insurance data

2020 ◽  
Vol 14 (1) ◽  
pp. 359-382 ◽  
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani ◽  
Omid Kharazmi
Keyword(s):  
New Methods ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Insurance Data

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

scholarly journals Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 56
Author(s):  
Haoyu Niu ◽  
Jiamin Wei ◽  
YangQuan Chen
Keyword(s):  
Research Work ◽  
Cauchy Distribution ◽  
Classification Model ◽  
Test Accuracy ◽  
Functional Link ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Improved Performance ◽  
Hidden Layer ◽  
Hidden Nodes

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.

Sign in / Sign up

Export Citation Format

Share Document