Research ArticleOpen AccessGoogle Scholar indexed
Gamma-Generalized Inverse Gaussian Class of Distributions
Kisii University, Kisii, Kenya
Kisii University, Kisii, Kenya
Kisii University, Kisii, Kenya
- 1 Kisii University, Kisii, Kenya
- 2 Kisii University, Kisii, Kenya
- 3 Kisii University, Kisii, Kenya
Open Journal of Statistics·Volume 11 (2021)·Pages 1026–1043·Published 29 November 2021·DOI10.4236/ojs.2021.116061
Copy link · social · email
Abstract
Gamma distribution nests exponential, chi-squared and Erlang distributions; while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture using Generalized inverse Gaussian mixing distribution. The rth moment of the mixture is obtained via the rth moment of the mixing distribution. Special cases and limiting cases of the mixture are deduced.
KeywordsGIGMixtureSpecial CasesLimiting CasesGammaMixing Distribution
- Bhattacharya, S.K. (1967) A Modified Bessel Function Model in Life Testing. Metrika, 11, 133-144. https://doi.org/10.1007/BF02613584
- Nadarajah, S. and Kotz, S. (2006) Compound Mixed Poisson Distributions I. Scandinavian Actuarial Journal, 3, 141-162. https://doi.org/10.1080/03461230600783384
- Gómez-Déniz, E., Calderín-Ojeda, E. and Sarabia, J.M. (2013) Gamma-Generalized Inverse Gaussian Class of Distributions with Applications. Communications in Statistics-Theory and Methods, 42, 919-933. https://doi.org/10.1080/03610926.2011.588360
- Willmot, G.E. (1993) Ruin Probabilities in the Compound Binomial Model. Insurance: Mathematics and Economics, 12, 133-142. https://doi.org/10.1016/0167-6687(93)90823-8
- Bhattacharya, S.K. and Kumar, S. (1986) E-IG Model in Life Testing. Calcutta Statistical Association Bulletin, 35, 85-90. https://doi.org/10.1177/0008068319860110
- Frangos, N. and Karlis, D. (2004) Modelling Losses Using an Exponential-Inverse Gaussian Distribution. Insurance: Mathematics and Economics, 35, 53-67. https://doi.org/10.1016/j.insmatheco.2004.04.005
- Wakoli, M. (2016) Hazard Functions of Exponential Mixtures and Their Link with Mixed Poisson Distributions. University of Nairobi, Nairobi.
- Barndorff-Nielsen, O. and Halgreen, C. (1977) Infinite Divisibility of the Hyperbolic and Generalized Inverse Gaussian Distributions. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 38, 309-311. https://doi.org/10.1007/BF00533162
- Sichel, H.S. (1971) On a Family of Discrete Distributions Particularly Suited to Represent Long-Tailed Frequency Data. Proceedings of the Third Symposium on Mathematical Statistics. SACSIR.
- Sichel, H.S. (1974) On a Distribution Representing Sentence-Length in Written Prose. Journal of the Royal Statistical Society: Series A (General), 137, 25-34. https://doi.org/10.2307/2345142
- Willmot, G. (1986) Mixed Compound Poisson Distributions. ASTIN Bulletin: The Journal of the IAA, 16, S59-S79. https://doi.org/10.1017/S051503610001165X
- Nyawade, K.O. (2018) Generalized Inverse Gaussian Distributions under Different Parametrizations Research Report in Mathematics. University of Nairobi, Nairobi.