Analyzing Non-Monotonic Hazard Rate Data Using the Harris Extended Inverted Lindley Distribution

In this paper, we introduce a new three-parameter extension of the inverse Lindley distribution known as the Harris extended inverted Lindley (HEIL) distribution, which offers more flexibility in modeling upside-down bathtub lifetime data. Some statistical properties of the proposed model were explicitly derived. These include density and hazard rate functions with their behavior, ordinary and incomplete moments, skewness, kurtosis measures, moment generating functions, reliability properties, and the quantile function. The maximum likelihood estimation of the parameters, their estimated asymptotic distribution and confidence intervals were derived. Renyi entropy as a measure of the uncertainty in the model is derived. The simulation study is conducted to evaluate the performance of the maximum likelihood estimator. Finally, to assess the superiority of the proposed model three real data sets were examined. Mathematics Subject Classification (2020) 60E05 · 62E10 ·