The Pseudo-Lindley Alpha Power transformed distribution, mathematical characterizations and asymptotic properties
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We introduce a new generalization of the Pseudo-Lindley distribution by applying alpha power transformation. The obtained distribution is referred as the Pseudo-Lindley alpha power transformed distribution (PL-APT). Some tractable mathematical properties of the PL-APT distribution as reliability, hazard rate, order statistics and entropies are provided. The maximum likelihood method is used to obtain the parameters' estimation of the PL-APT distribution. The asymptotic properties of the proposed distribution are discussed. Also, a simulation study is performed to compare the modeling capability and flexibility of PL-APT with Lindley and Pseudo-Lindley distributions. The PL-APT provides a good fit as the Lindley and the Pseudo-Lindley distribution. The extremal domain of attraction of PL-APT is found and its quantile and extremal quantile functions studied. Finally, the extremal value index is estimated by the double-indexed Hill's estimator (Ngom and Lo, 2016) and related asymptotic statistical tests are provided and characterized.
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