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One of the most important branch of statistics is survival and reliability analysis. There are various lifetime models available in literature that have applications in these fields. However the researchers always keep searching for more flexible models that are effective in more complex situations. With the same motivation, an effort has been made to introduce a new distribution named as Generalized Inverse Power Lindley distribution that is expected to turnout more constructive while dealing with complex real life data. Various statistical properties of the model have been derived. The parameter estimates are obatined using Maximum Likelihood Estimation (MLE) technique. Simulation study has been conducted to assess the performance of maximum likleihood estimators. Applicability of the proposed model to the real data has been investigated by comparing the model with some existing distributions.

In this work, the truncated version of Inverse Lindley Distribution has been introduced. Different statistical properties such as survival, hazard rate, reverse hazard rate, cumulative hazard rate of the new distribution have been derived. Quantile function and Order statistics have also been discussed. Method of Maximum Likelihood estimation have been employed to estimate the unknown parameters. The utility of the model have been illustrated using two real life datasets. It has been shown that the proposed model provides a better fit as compared to other existing models.

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