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Shaw, W. and Buckley, I. (2009) The Alchemy of Probability Distributions: Beyond Gram-Charlier Expansions, and a Skew-Kurtotic Normal Distribution from a Rank Transmutation Map. ArXiv: 0901.0434.

has been cited by the following article:

• TITLE: The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

  AUTHORS: Jacob C. Ehiwario, John N. Igabari, Peter E. Ezimadu

  KEYWORDS: Alpha Power Transformation, Topp-Leone Distribution, Quantiles, Moments

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.1, January 31, 2023

  ABSTRACT: This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.