Finite mixture of gamma distributions and applications

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.