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In this research paper, we introduce an extension of the Gamma-Lindley distribution using a particular exponentiation of its cumulative distribution function, which offers a more flexible model for lifetime data. Another attractive feature of this extension is that it has several particular cases: Weibull, generalized Pareto, Lindley, exponential and Gamma-Lindley distributions. Different statistical properties of this distribution are explored, such as the density, failure rate and the  r   th  moments. We attempt to prove that the extended Gamma-Lindley distribution is characterized by its truncated moment of order statistics. One of the main merits of this work lies in the fact that it provides the ability of this characterization to simulate the new distribution compared with the inverse transform sampling method. Estimation of the parameters using the tailed regression method is investigated. The COVID-19 real data evolution in Tunisia illustrates the performance of the EGL distribution compared with its special cases through some criteria such as the Kolmogorov-Smirnov test, Mean Squared error and Kullback-Leibler divergence. The predictive ability of the extended Gamma-Lindley distribution proved to provide a better fit to expect the number of deaths by Corona-virus in Tunisia in the future period.

An Extended Gamma-Lindley Model and Inference for the Prediction of Covid-19 in Tunisia