* Corresponding author, e-mail: heba_nagy_84@yahoo.com Research Article GU J Sci35(x): x-x (2022) DOI:10.35378/gujs.776277 Gazi University Journal of Science http://dergipark.gov.tr/gujs Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution Mohamed ELGARHY 1 , Amal HASSAN 2 , Heba NAGY 2,* 1 Al Mahalla Al Kubra, Algharbia – The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, 31951, Algharbia, Egypt 2 5 Dr. Ahmed Zoweil St., Dokki – Faculty of Graduate Studies for Statistical Research (Cairo University, Department of Mathematical Statistics), 12613, Giza, Egypt Highlights • We propose a new generalization for Topp-Leone (PTL) distribution with one more shape parameter. • PTL is argued through different estimation procedures. • A comparison is implemented between different estimates through a simulation study. Article Info Abstract We display the power Topp-Leone (PTL) distribution with two parameters. The following major features of the PTL distribution are investigated: quantile measurements, certain moment’s measures, residual life function, and entropy measure. Maximum likelihood, least squares, Cramer von Mises, and weighted least squares approaches are used to estimate the PTL parameters. A numerical illustration is prepared to compare the behavior of the achieved estimates. Data analysis is provided to scrutinize the flexibility of the PTL model matched with Topp-Leone distribution. Received: 02 Aug 2020 Accepted: 05 May 2021 Keywords Cramer von Mises estimators Maximum likelihood estimators Moments Topp-Leone distribution 1. INTRODUCTION The origin of Topp-Leone (TL) distribution can be referred to [1] who introduced it. They obtained moments of the TL distribution as well as modeled it for some failure data. General formulae for some measures of moments and hazard rate function (hrf) motivation to the distribution have been discussed in [2]. [3] proposed the reflected generalized TL model, explored its properties and applied financial data in fitting income distribution. Some reliability measures of the TL model have been studied in [4]. Formulae of single and product moments based on order statistics were given in [5]. The density function of the TL distribution is J-shaped. A TL distribution's probability density function (pdf) is denoted by -1 1 (1 )(2 ) , 0 1, ( ; ) = 2 > 0. z z z f z z     − − −   (1) The cumulative distribution function (cdf) related to Equation (1) is given by: (;) (2 ). Fz z z    = − (2) Constructions of the TL distribution have been found to be useful in several fields. Many efforts have been made by notable authors to propose new generalized and extended forms of TL model, for instance; TL inverse Weibull distribution [6]; TL geometric distribution [7], TL Nadarajah-Haghighi distribution [8],