Finite mixture of gamma distributions and applications
About this article
Abstract
In this paper a new one parameter probability distribution “Finite Mixture of Gamma Distributions” is suggested from three com-ponent mixture of Exponential (θ), Gamma (4, θ) and Gamma (3,θ) with mixing proportions θ^2/(〖(θ〗^2+6θ+2)),6θ/(〖(θ〗^2+6θ+2)) and 2/(〖(θ〗^2+6θ+2)) respectively. Its first four moments and expressions for skew-ness, kurtosis, and coefficient of variation have been given. Various mathematical and statistical properties of the proposed distribu-tion, including hazard rate function, mean residual life function, and stress strength reliability, have been discussed. Estimation of the parameter has been discussed. The goodness of fit of the distribution has been discussed with two real-life data set and second-ary data. The fit has been compared with one-parameter life time distributions, including Exponential, Lindley, and Chris Jerry distributions.
Keywords
- Finite Mixture Distributions
- Estimation of Parameters
- Hazard Rate Function
- Kurtosis
- Moments
- Mean Residual Life Function
References
B.S Everitt and D.J. Hand (1981). “Finite Mixture Distributions”, Chapman & Hall, New York. https://doi.org/10.1007/978-94-009-5897-5.
C. K. Onyekwere and O. J. Obulezi,” (2023) Chris-Jerry distribution and its applications”, Asian Journal of Probability and Statistics vol.20,130480 ,16-30. https://doi.org/10.9734/ajpas/2022/v20i130480.
Lindley (1958).” Fiducial distributions and Bayes theorem”, Journal of the Royal Statistical Society, Series B,20,102-107. https://doi.org/10.1111/j.2517-6161.1958.tb00278.x.
Rama Shanker (2016). “Amarendra Distribution and Its Applications” ,6(1), 44-56.
Rama Shanker (2017). “Rama Distribution and Its Application”International Journal of Statistics and Applications,7(1), , 26-35.
View more references (9)
Shanker, R. (2015). “Akash distribution and its Applications” ,International Journal of Probability and Statistics, 4(3), , 65–75. https://doi.org/10.15406/bbij.2016.03.00075.
Shanker R(2016 b). “Aradhana distribution and its applications”, International Journal of Statistics and Applications,6(1), 23 – 34.
Shanker (2016 c). “Sujatha distribution and its applications” ,Statistics in Transition-new series, 17(3),1–20. https://doi.org/10.59170/stattrans-2016-023.
Shanker R (2017). “Suja Distribution and Its Application” International Journal of Probability and Statistics 6(2):11-19. https://doi.org/10.15406/bbij.2017.06.00155.
Shanker R (2023). “Komal Distribution with properties and Application in Survival Analysis” ,Biometrics & Biostatistics. International Jour-nal.;12(2), 40–44. https://doi.org/10.15406/bbij.2023.12.00381.
Shanker R (2023).” Pratibha distribution with properties and application” Biom Biostat Int J.12(5),136-142. https://doi.org/10.15406/bbij.2023.12.00397.
Shanker R (2015 b). “Shanker distribution and its Applications” ,International Journal of Statistics and Applications, 5(6), , 338 – 348.
Shukla KK (2018).” Pranav distribution with properties and its applications”. Biom Biostat Int J. 7(3): 244-254. https://doi.org/10.15406/bbij.2018.07.00215.
https://www.kaggle.com/dataset/ iam sourav banarjee/life-expectancy-at-birth-across-the-globe.