Rani Distribution and Its Application

In the present world the modeling and analyzing lifetime data are essential in almost all applied sciences including medicine, engineering, insurance and finance, amongst others. The two classical one parameter lifetime distributions which are popular and are in use for modeling lifetime data from biomedical science and engineering are exponential and Lindley introduced by Lindley [1]. Shanker, et al. [2] have detailed comparative study on modeling of lifetime data from various fields of knowledge 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 functions, amongst others. In search for new one parameter lifetime distributions which gives better fit than exponential and Lindley distributions, recently Shanker has introduced several one parameter lifetime distributions in statistical literature namely Akash [3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Akshaya [10] and showed that these distributions gives better fit than the classical exponential and Lindley distributions. The probability density function (pdf) and the corresponding cumulative distribution function (cdf) of Akash[3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Lindley [1] distributions are presented in Table (1). It has also been discussed by Shanker that although each of these lifetime distributions has advantages and disadvantages over one another due to its shapes, hazard rate functions and mean residual life functions, there are still many lifetime data where these distributions are not suitable for modeling lifetime data 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 these one parameter lifetime 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 parameter θ and a gamma distribution having shape parameter