Abstract: In this article, a new family of probability distributions with domain in ?+ is introduced. This class can be considered as a natural extension of the exponential-inverse Gaussian distribution in Bhattacharya and Kumar (1986 Bhattacharya , S. K. , Kumar , S. ( 1986 ). E-IG model in life testing . Calcutta Statist. Assoc. Bull. 35 : 85 ? 90 . [Google Scholar] ) and Frangos and Karlis (2004 Frangos , N. , Karlis , D. ( 2004 ). Modelling losses using an exponential-inverse Gaussian distribution . Insur. Math. Econo. 35 : 53 ? 67 . [Crossref], [Web of Science ®], , [Google Scholar] ). This new family is obtained through the mixture of gamma distribution with generalized inverse Gaussian distribution. We also show some important features such as expressions of probability density function, moments, etc. Special attention is paid to the mixture with the inverse Gaussian distribution, as a particular case of the generalized inverse Gaussian distribution. From the exponential-inverse Gaussian distribution two one-parameter family of distributions are obtained to derive risk measures and credibility expressions. The versatility of this family has been proven in numerical examples.
Authorship: Gómez-Déniz E., Calderín-Ojeda E., Sarabia J.,
Fuente: Communications in Statistics. Theory and Methods, 2013, 42(6), 919-933
Publisher: Taylor and Francis Ltd.
Year of publication: 2013
No. of pages: 14
Publication type: Article
DOI: 10.1080/03610926.2011.588360
ISSN: 0361-0926,1532-415X
Publication Url: https://doi.org/10.1080/03610926.2011.588360