An Extended Inverse Lindley Distribution: Models, Properties and Applications

This research work proposed a new extension of the inverse Lindley distribution called exponential-inverse Lindley distribution. The study derived some statistical properties of the distribution such as its ordinary moments, moment generating and characteristics function. It also considered the survival and hazard functions and the distribution of ordered statistics. Some plots of the distribution revealed that it is a flexible and skewed distribution. The implications of the plots for the survival function indicate that the exponential-inverse Lindley distribution could be used to model time or age-dependent events, where survival rate decreases with time. The research also conducted a simulation study to check the consistency of the model parameters using maximum likelihood estimation. From the results of the simulation study, it was revealed that the average estimates tend to be closer to the true parameters when sample size increases and the biases and mean square errors all decrease as sample size increases which is in agreement with the theory of estimation. The performance of the proposed exponential-inverse Lindley distribution was evaluated by means of an applications of the model to a real life dataset.