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198 results on '"Vernic, Raluca"'

59. Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Author

Bolancé Losilla, Catalina, Vernic, Raluca, and Xarxa de Referència en Economia Aplicada (XREAP)

Subjects
Teoria de distribucions (Anàlisi funcional), Accident insurance, Linear models (Statistics), Variables aleatòries, Teoria de l'estimació, 33 - Economia, Variables (Matemàtica), Theory of distributions (Functional analysis), Variables (Mathematics), Models lineals (Estadística), Anàlisi de regressió, Assegurances d'accidents, Random variables, Estimation theory, Regression analysis, 311 - Estadística
Abstract

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Published
2017

60. Multivariate count data generalized linear models: Three approaches based on the Sarmanov Distribution [WP]

Author

Bolancé Losilla, Catalina and Vernic, Raluca

Subjects
Teoria de distribucions (Anàlisi funcional), Theory of distributions (Functional analysis), Variables (Mathematics), Variables aleatòries, Teoria de l'estimació, Random variables, Estimation theory, Variables (Matemàtica)
Abstract

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Published
2017

66. On the bivariate Sarmanov distribution and copula. An application on insurance data using truncated marginal distributi

Author

Bahraoui, Zuhair, Bolancé, Catalina, Pelican, Elena, and Vernic, Raluca

Subjects
62 Statistics [Classificació AMS], Copula representation, Matemàtiques i estadística::Estadística matemàtica [Àrees temàtiques de la UPC], 62 Statistics::62F Parametric inference [Classificació AMS], 62-07, 62E15, 62F10, Truncated marginal distributions, Bivariate Sarmanov distribution, truncated marginal distributions, copula representation, risk measures, Bivariate sarmanov distribution, Risk measures, 62 Statistics::62E Distribution theory [Classificació AMS]
Abstract

The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log-likelihood function with the estimation based on maximizing the pseudo-log-likelihood function for copula (or partial estimation). Our aim is to estimate two statistics that can be used to evaluate the risk of the sum exceeding a given value. Numerical results using a real data set from the motor insurance sector are presented.

Published
2015

79. Inequalities for the De Pril approximation to the distribution of the number of policies with claims

Author

Vernic, Raluca, Dhaene, Jan, and Sundt, Bjorn

Abstract

In the present paper, we give su¢ cient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given. ispartof: pages:1-25 status: published

Published
2009

80. On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims.

Author

Răducan, Anişoara Maria, Vernic, Raluca, and Zbăganu, Gheorghiţă

Subjects
*PREDICTION models, *STOCHASTIC analysis, *PROBABILITY theory, *NUMERICAL analysis, *ERLANG (Computer program language)
Abstract

Recently, some recursive formulas have been obtained for the ruin probability evaluated at or before claim instants for a surplus process under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim revenues, which are assumed to be independent, identically distributed, following an arbitrary distribution. Based on numerical examples, a conjecture has also been stated relating the order in which the claims arrive to the magnitude of the corresponding ruin probability. In this paper, we prove this conjecture in the particular case when the claims are all exponentially distributed with different parameters. [ABSTRACT FROM AUTHOR]

Published
2017
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89. Statistical Inference for a New Class of Multivariate Pareto Distributions.

Author

Asimit, Alexandru V., Furman, Edward, and Vernic, Raluca

Subjects
INFERENTIAL statistics, MULTIVARIATE analysis, PARETO distribution, MAXIMUM likelihood sequence estimation, EXPECTATION-maximization algorithms, MOMENTS method (Statistics)
Abstract

Various solutions to the parameter estimation problem of a recently introduced multivariate Pareto distribution are developed and exemplified numerically. Namely, a density of the aforementioned multivariate Pareto distribution with respect to a dominating measure, rather than the corresponding Lebesgue measure, is specified and then employed to investigate the maximum likelihood estimation (MLE) approach. Also, in an attempt to fully enjoy the common shock origins of the multivariate model of interest, an adapted variant of the expectation-maximization (EM) algorithm is formulated and studied. The method of moments is discussed as a convenient way to obtain starting values for the numerical optimization procedures associated with the MLE and EM methods. [ABSTRACT FROM PUBLISHER]

Published
2016
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