Abstract
In this article, we have presented a new three-parameter probability distribution called the Lindley Gompertz distribution. The proposed model can exhibit increasing, increasing-decreasing, j-shaped, and bathtub, and a broad variety of monotone failure rates. Some properties of this model are studied and calculated. Three extensively used estimation methods are used to estimate the model parameters namely maximum likelihood estimators (MLE), least-square (LSE), and Cramer-Von-Mises (CVM) methods. By using the maximum likelihood estimate we have constructed the asymptotic confidence interval for the model parameters. All the computations are performed in R software. The potentiality of the proposed distribution is revealed by using some graphical methods and statistical tests taking a real dataset, where the proposed distribution provided a better fit and more flexible in comparison with some other lifetime distributions.
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