A New Mixture of Exponential-Gamma Distribution

Abstract

A new distribution called New Mixture of Exponential-Gamma Distribution is presented in this paper. This new distribution contains exponential and standardized Lindley distributions as sub models. Some of the structural properties of the proposed distribution which include the survival function, hazard rate function, moments, moment generating function, quantile function, distribution of order statistics and Renyi entropy are obtained. The maximum likelihood method of estimation was used to estimate the parameters of the distribution. A Simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimates of the proposed distribution. An application of the proposed distribution to two real lifetime datasets is presented to illustrate its usefulness and superiority over some existing related models.

Keywords

• Gamma Mixture,Structural properties,Standardized Lindley,Maximum Likelihood Estimation

References

1. [1] Alzaatreh, A., Lee, C., Famoye, F., “A New Method for Generating Families of Continuous Distributions”, Metron, 71(1): 63-79, (2013).
2. [2] Amini, M., MirMostafaee, S. M. T. K and Ahmeadi, J., “Log-Gamma-Generated Families of Distributions”, Journal of Theoretical and Applied Statistics, 48 (4): 913-932, (2014)
3. [3] Eugene, N., Lee, C., Famoye, F., “Beta-Normal Distribution and its Applications”, Communication in Statistics-Theory and Methods, 31(4): 497-512, (2002).
4. [4] Gayan, W. L., and Mavis, P., “A Generalized Power Lindley Distribution with Applications”, Asian Journal of Mathematics and Applications, ID: ama0169, 23pages.
5. [5] Gupta, R.D., and Kundu. D. “Generalized Exponential Distributions” Australian and New Zealand Journal of Statistics. 41, 173 –188, (1999).
6. [6] Ibrahim E., Merovci, F., and Elgarhy, M., “A New Generalized Lindley Distribution”, Mathematical Theory and Modelling, 3(13):30-47, (3013).
7. [7] Lee, E. T., “Statistical Methods for Survival Data Analysis (2nd Edition)”, John Wiley and Sons Inc., New York, USA, (1992).[8] Mahdi, T. and A.K. Gupta, “A Generalization of The Gamma Distribution”, Journal of Data Science, 11:403-414, (2013).
8. [9] Michele D. Nichols and W. J. Padgett, “A Bootstrap Control Chart for Weibull Percentiles” Qual. Reliab. Engng. Int. 22:141–151, 691, (2006).

9. [10] Nadarajah, S. and A.K. Gupta, “A Generalized Gamma Distribution with Application to Drought Data”, Mathematical Computation and Simulation, 74: 1-7, (2007).
10. [11] Nichols, M. D., & Padgett, W. J., “A bootstrap control chart for Weibull percentiles”, Quality & Reliability Engineering International, 22(2), 141-151, (2006).
11. [12] Patil, G.P. and C.R. Rao, “Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families”, Biometrics, 34: 179-189, (1978).
12. [13] Patill, G.P., C.R. Rao and M.V. Ratnaparkhi, “On Discrete Weighted Distributions and Their Use in Model Choice for Observed Data”, Communication in Statistics- Theory and Methods, 15: 907-918, (1986).
13. [14] Peter H. W., “Kurtosis as Peakedness”, The American Statistician, 68:3, 191-195, (2014).[15] Rényi, A, (1961). On measure of entropy and information. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1, University of California Press, Berkeley, page 547-561, (1961).
14. [16] Resti, Y., N. Ismail and S.H. Jamaan, “Estimation of Claim Cost Data Using Zero Adjusted Gamma and Inverse Gaussian Regression Models” Journal of Mathematical Statistics., 9: 186-192, (2013).
15. [17] Samir A., Darwish D. and Ahmad S., “Log-Gamma-Rayleigh Distribution: Properties and Applications”, GU Journal of Science, (2018).
16. [18] Satsayamon S. and Winai B., “A New Family of Generalized Gamma Distribution and its Application”, Journal of Mathematical. Statistics, 10 (2): 211-220, (2014).
17. [19] Stacy, E.W., “A Generalization of the Gamma Distribution”, Annals Mathematical Statistics, 33: 1187-1192, (1962).