Modelling claim number using a new mixture model: negative binomial gamma distribution


GENÇTÜRK Y. , YİĞİTER A.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, cilt.86, sa.10, ss.1829-1839, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 86 Konu: 10
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00949655.2015.1085987
  • Dergi Adı: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Sayfa Sayıları: ss.1829-1839

Özet

In actuarial applications, mixed Poisson distributions are widely used for modelling claim counts as observed data on the number of claims often exhibit a variance noticeably exceeding the mean. In this study, a new claim number distribution is obtained by mixing negative binomial parameter p which is reparameterized as p = exp( -lambda) with Gamma distribution. Basic properties of this new distribution are given. Maximum likelihood estimators of the parameters are calculated using the Newton-Raphson and genetic algorithm (GA). We compared the performance of these methods in terms of efficiency by simulation. A numerical example is provided.