Extended Inverse Lindley distribution

Modeling survival data depends on the shape of the hazard rate. In this paper, a distribution called the Extended Inverse Lindley distribution, will be introduced. Extended Inverse Lindley distribution is a distribution that is formed from the transformation of the two-parameter Lindley distribution. The transformations used are power transformation and inverse transformation. Thus, the Extended Inverse Lindley distribution can model heavy-tailed data with an upside-down bathtub hazard rate. In this essay, we discuss how to construct Extended Inverse Lindley distribution and characteristics of these distributions. These include the probability density function, cumulative distribution function, survival function, hazard rate, r-th moment, and mode. The parameters of the Extended Inverse Lindley distribution were estimated using the maximum likelihood method. At the end of this paper, the Extended Inverse Lindley distribution is used to illustrate the repairing time data (in hours) for 46 failures of an airborne communications receiver and shown that the Extended Inverse Lindley distribution is more suitable for modeling data than other distributions.