A gamma kernel density estimation for insurance loss data

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Fitting insurance loss data can be challenging because of their non-negativity, asymmetry, skewness, and possible multi-modality. Though many parametric models have been used in the actuarial literature, these difficulties call for more flexible models for actuarial applications. In this paper, we propose a new class of gamma kernel density estimators (GKDEs) based on the gamma density. We prove that the density of the proposed model converges to that of any loss random variable which is non-negative and continuous, and establish its rate of convergence, under some technical conditions. The proposed model has several advantages over the existing gamma kernel class by Chen (2000) in that it is a valid density for any finite sample and has standard distributional quantities, such as the moments, the conditional tail moments, and the compound distribution with GKDE claim amounts, in analytic form. The model is also a competing model of the Erlang mixture by Lee and Lin (2010) in its flexibility, but with a straightforward implementation and optimization. As numerical examples, we fit the gamma kernel density estimator to actual insurance data and find that the proposed model gives adequate results compared to the Erlang mixture and the Phase-type models.

Original languageEnglish
Pages (from-to)569-579
Number of pages11
JournalInsurance: Mathematics and Economics
Volume53
Issue number3
DOIs
Publication statusPublished - 2013 Nov 1

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Kernel Density Estimation
Insurance
Kernel Density Estimator
Model
Compound Distribution
Moment
Multimodality
Nonnegativity
Skewness
Kernel density estimation
Parametric Model
Asymmetry
Tail
Rate of Convergence
Random variable
Flexibility
Non-negative
Valid
kernel
Converge

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

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A gamma kernel density estimation for insurance loss data. / Jeon, Yongho; Kim, Joseph H.T.

In: Insurance: Mathematics and Economics, Vol. 53, No. 3, 01.11.2013, p. 569-579.

Research output: Contribution to journalArticle

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