Ishita Distribution and Its Applications

The analyzing and modeling real lifetime data are crucial in many applied sciences including medicine, engineering, insurance and finance, amongst others. The two important one parameter lifetime distributions namely exponential and Lindley [2] are popular for modeling lifetime data from biomedical science and engineering. Recently, Shanker et al. [3] have conducted a comparative and critical study on the modeling of lifetime data from biomedical science and engineering using exponential and Lindley distributions and observed that there are many lifetime data where these two distributions are not suitable due to their shapes, nature of hazard rate functions, and mean residual life, amongst others. While searching a lifetime distribution which gives better fit than exponential and Lindley, Shanker [1] has introduced a lifetime distribution named Akash distribution and showed that Akash distribution gives much better fit than both exponential and Lindley distributions. Shanker et al. [4] have comparative study on the modeling of lifetime data using Akash, Lindley and exponential distribution and observed that there are several situations where these lifetime distributions are not suitable either from theoretical or applied point of view. Therefore, an attempt has been made in this paper to obtain a new lifetime distribution which is flexible than Akash, Lindley and exponential distributions for modeling lifetime data in reliability and in terms of its hazard rate shapes. The new one parameter lifetime distribution is based on a twocomponent mixture of an exponential distribution having scale parameterθ and a gamma distribution having shape parameter 3 and scale parameter θ