On the mixture of Shanker and gamma distributions with applications to engineering data

There are several reliability and life testing challenges that may be solved using the gamma and Shanker distributions. In this paper, a new lifetime model of two parameters is suggested, referred to as Shanker-Gamma distribution (SGD). The SGD is developed by mixing two well-known distributions, namely; Shanker distribution of one parameter and gamma distribution of two parameters to propose a new continuous more flexibility distribution for modeling real data in different areas. Some important statistical and mathematical properties of the distribution are derived such as the distribution function, moment generating function, rth moment, the coefficients of variation, skewness and kurtosis, and the distributions of order statistics. The maximum likelihood estimation (MLE) method is adopted to estimate the model parameters and a simulation study is conducted investigate the efficiency of the MLE. Also, the Renyi entropy, stochastic ordering, Lorenz and Bonferroni curves and the Gini index are obtained. Additionally, some reliability functions are presented and it is noted that the model have decreasing hazard rate function based on its parameters. Numerical calculations are provided to study the various statistical properties of the SG distribution for various values of the distribution parameters. Finally, two real data sets include tensile strength of polyester fibers and failure time explore the potentiality of the suggested model as compared with some alternatives models. For both data sets, it is revealed that the SGD is more flexible than its competitors considered in this paper. Also, the MLE values decrease as the sample size increases