THE PSEUDO-LINDLEY ALPHA POWER TRANSFORMED DISTRIBUTION, MATHEMATICAL CHARACTERIZATIONS AND ASYMPTOTIC PROPERTIES

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. Modou Ngom † Work Affiliation : Ministry of High School (SENEGAL) LERSTAD, Gaston Berger University, Saint-Louis, Sénégal Imhotep Mathematical Center Email:ngom.modou1@ugb.edu.sn, ngomodoungom@gmail.com. Moumouni Diallo †† Work Affiliation : Université des Sciences Sociale et de Gestion de Bamako(USSGB) Imhotep Mathematical Center Email: moudiallo1@gmail.com Adja Mbarka Fall ††† Work Affiliation : Université Iba Der Thiam de Thiés (UIDT) Imhotep Mathematical Center LERSTAD, Gaston Berger University, Saint-Louis, Sénégal Email:adjambarka.fall@univ-thies.sn Gane Samb Lo †††† LERSTAD, Gaston Berger University, Saint-Louis, Sénégal (main affiliation) LSTA, Pierre and Marie Curie University, Paris VI, France AUST African University of Sciences and Technology, Abuja, Nigeria Imhotep Mathematical Center Email:gane-samb.lo@edu.ugb.sn, gslo@aust.edu.ng, ganesamblo@ganesamblo.net Permanent address : 1178 Evanston Dr NW T3P 0J9,Calgary, Alberta, Canada.