Composite Lognormal–Pareto model with random threshold

Pigeon, Mathieu; Denuit, Michel

doi:10.1080/03461231003690754

Cited by 78 publications

(37 citation statements)

References 11 publications

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“…Pigeon and Denuit (2011) consider a situation in which heterogeneity of the threshold parameter in a composite lognormal-Pareto model is allowed in order so that it can vary among observations. Specifically, these authors show how a gamma or a lognormal mixing distribution can be imposed on in the context of the second lognormal-Pareto model in Scollnik (2007).…”

Section: Discussionmentioning

confidence: 99%

Modeling with Weibull-Pareto Models

Scollnik

Sun

2012

North American Actuarial Journal

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In this paper we develop several composite Weibull-Pareto models and suggest their use to model loss payments and other forms of actuarial data. These models all comprise a Weibull distribution up to a threshold point, and some form of Pareto distribution thereafter. They are similar in spirit to some composite lognormal-Pareto models that have previously been considered in the literature. All of these models are applied, and their performance compared, in the context of a realworld fire insurance data set.

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Section: Discussionmentioning

confidence: 99%

Modeling with Weibull-Pareto Models

Scollnik

Sun

2012

North American Actuarial Journal

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“…Various new composite distributions have been developed in the literature including composite lognormal‐Burr,150 composite exponential‐Pareto,15,152 composite Weibull‐Pareto,153 composite lognormal‐Pareto,149,153,154 truncated composite lognormal‐Pareto,155 truncated composite Weibull‐Pareto,156 composite lognormal‐lognormal,158 composite inverse Weibull‐Weibull,158 and composite log‐Gauss‐Pareto 159…”

Section: Composite Methodsmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

145

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There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as ‘methods of combination’ for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed‐transformer method, and (5) composite method. WIREs Comput Stat 2013, 5:219–238. doi: 10.1002/wics.1255 This article is categorized under: Algorithms and Computational Methods > Random Number Generation Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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“…For the purpose of predicting large losses reasonably, we claim that the minimum density power divergence estimator is useful when considered alongside the maximum likelihood estimator. There are two more additional contributions on the composite lognormal-Pareto model by Scollnik (2007) and Pigeon and Denuit (2011). The comparison of estimation methods for those models should have been attempted for a contribution to the field of actuarial science or insurance; however, we have focused on the applicability of the minimum density power divergence estimator on composite models that considered only the original and basic model by Cooray and Ananada (2005).…”

Section: Discussionmentioning

confidence: 99%

A Robust Estimation for the Composite Lognormal-Pareto Model

Pak¹

2013

Communications for Statistical Applications and Methods

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Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

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Composite Lognormal–Pareto model with random threshold

Cited by 78 publications

References 11 publications

Modeling with Weibull-Pareto Models

Modeling with Weibull-Pareto Models

Methods for generating families of univariate continuous distributions in the recent decades

A Robust Estimation for the Composite Lognormal-Pareto Model

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