A new statistical model for non-monotone survival data is proposed with some of its statistical properties as an extension of power Lindley distribution. These include the density and hazard rate functions with their behavior, moments, moment generating function, skewness, kurtosis measures, and quantile function. Maximum likelihood estimation of the parameters and their estimated asymptotic distribution and confidence intervals are derived. Rényi entropy as a measure of the uncertainty in the model is derived. An application of the model to a real data set is presented and compared with the fit attained by other well-known existing distributions.
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