A class of claim distributions: Properties, characterizations and applications to insurance claim data

被引:29
作者
Ahmad, Zubair [1 ]
Mahmoudi, Eisa [1 ]
Hamedani, Gholamhossien [2 ]
机构
[1] Yazd Univ, Dept Stat, POB 89175-741, Yazd, Iran
[2] Marquette Univ, Dept Math Stat & Comp Sci, Milwaukee, WI 53233 USA
关键词
Family of distributions; heavy tailed distributions; Weibull distribution; insurance claim; actuarial measures; fitness; estimation; PARAMETER; MIXTURES; MODELS;
D O I
10.1080/03610926.2020.1772306
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Actuaries are often in search of finding an adequate model for actuarial and financial risk management problems. In the present work, we introduce a class of claim distributions useful in a number of lifetime analyses. A special sub-model of the proposed family, called the Weibull claim model, is considered in detail. Some mathematical properties along with certain characterizations are derived and maximum likelihood estimates of the model parameters are obtained. A simulation study has been carried out to evaluate the performance of the maximum likelihood estimators. Furthermore, some actuarial measures such as value at risk, tail value at risk, tail variance and tail premium variance are calculated. A simulation study based on these actuarial measures is done. Finally, two applications of the proposed model to the insurance claim data set are presented.
引用
收藏
页码:2183 / 2208
页数:26
相关论文
共 32 条
  • [1] Modeling loss data using composite models
    Abu Bakar, S. A.
    Hamzah, N. A.
    Maghsoudi, M.
    Nadarajah, S.
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2015, 61 : 146 - 154
  • [2] [Anonymous], 2009, WILEY SERIES PROBABI
  • [3] [Anonymous], 2001, ASTIN BULL, DOI DOI 10.2143/AST.31.1.1002
  • [4] [Anonymous], 2012, LOSS MODELS DATA DEC
  • [5] Artzner P., 1999, N AM ACTUAR J, V3, P11, DOI [DOI 10.1080/10920277.1999.10595795, 10.1080/10920277.1999.10595795]
  • [6] Generalized inverse Lindley distribution with application to Danish fire insurance data
    Asgharzadeh, A.
    Nadarajah, S.
    Sharafi, F.
    [J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (10) : 5001 - 5021
  • [7] Skew mixture models for loss distributions: A Bayesian approach
    Bernardi, Mauro
    Maruotti, Antonello
    Petrella, Lea
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2012, 51 (03) : 617 - 623
  • [8] On generalized log-Moyal distribution: A new heavy tailed size distribution
    Bhati, Deepesh
    Ravi, Sreenivasan
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2018, 79 : 247 - 259
  • [9] Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses
    Brahimi, Brahim
    Meraghni, Djamel
    Necir, Abdelhakim
    Zitikis, Ricardas
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2011, 49 (03) : 325 - 334
  • [10] Folded and log-folded-t distributions as models for insurance loss data
    Brazauskas, Vytaras
    Kleefeld, Andreas
    [J]. SCANDINAVIAN ACTUARIAL JOURNAL, 2011, (01) : 59 - 74