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THE PSEUDO-LINDLEY ALPHA POWER TRANSFORMED DISTRIBUTION, MATHEMATICAL CHARACTERIZATIONS AND ASYMPTOTIC PROPERTIES
Keywords:
alpha power transformation of distribution functions, Lindley’s distribution, pseudo-Lindley distribution, extreme value theory, doubly indexed Hill’s estimator, reliability, hazard rate, maximum likelihood method, quantile function, extreme quantile function, asymptotic laws, Lambert functionDOI:
https://doi.org/10.17654/0972086322004Abstract
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 distributions. The extremal domain of attraction of PL-APT is found and its quantile and extremal quantile functions are studied. Finally, the extremal value index is estimated by the double-indexed Hill’s estimator (Ngom and Lo [19]) and related asymptotic statistical tests are provided and characterized.
Received: February 14, 2022
Accepted: March 26, 2022
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