A Finite Mixture of Convex Combination of Probability Models: Properties and Application
K. M. Sakthivel
Department of Statistics, Bharathiar University, Coimbatore, India.
G. Vidhya *
Department of Statistics, Bharathiar University, Coimbatore, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new continuous probability distribution is developed by using a mixture of exponential and Rayleigh distributions for modeling lifetime data. It has been developed to increase flexibility and shows it can perform better than the existing mixture distributions. The forms of the probability density function and cumulative distribution function along with statistical properties such as moments, incomplete moments, survival function, hazard function, mean residual life, stochastic ordering, order statistics, and stress strength reliability of the proposed distribution are explained. We also obtained the Bonferroni index and Lorenz curve of the proposed distribution. The parameters of the proposed distribution are estimated using the maximum likelihood technique. Finally, data analysis is performed using real-time data to illustrate the suitability of the proposed distribution.
Keywords: Lifetime distribution, hazard function, mean residual life function, order statistic, parameter estimation