The Arctan-Tan-G Family of Distributions: Properties and Applications

Abstract: We introduce a new family of continuous distributions, a so-called Arctan-Tan-G (or ATT-G) family. Some mathematical properties of the new family are studied including, in particular, asymptotics for the pdf and the cdf, order statistics, and stochastic ordering. A special case of this family, the ATT-Weibull (ATT-W) distribution, is discussed. The density function, the quantile function, Bowley's skewness and Moors' kurtosis are researched. Distribution of order statistics is obtained. The model parameters are estimated by maximum likelihood. Usefulness of the new family is proven empirically by means of a real data set.

probabilitystatistics theorydata analysis, statistics and probability

Audience: researchers in the topic

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Comments: Dr. Yevhen Tiurchyn is Associate Professor of Department of Statistics & Probability Theory in Oles Honchar National University of Dnipro (Ukraine).

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Asymptotic Methods in Statistics

Series comments: One can find video files and slides of talks at the seminar on Asymptotic Methods in Statistics here: www.youtube.com/@SeminarforAsymptoticMethods

A link to a slide is below the description of the video, namely shorturl.at/jUAhL and shorturl.at/6wjUA shorturl.at/rdpqs

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