The Truncated Cauchy Power Family of Distributions with Inference and Applications

Entropy

Ibrahim Elbatal¹  Christophe Chesneau²  MahaA. Aldahlan³  Farrukh Jamal⁴  Mohammed Elgarhy⁵ 

[1] Department of Mathematics and Statistics-College of Science, Imam Muhammad ibn Saud Islamic University, Riyadh 11432, Saudi Arabia;Department of Mathematics, LMNO, Campus II, Science 3, Université de Caen, 14032 Caen, France;Department of Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia;Department of Statistics, Government Postgraduate College Der Nawab Bahawalpur, Punjab 63351, Pakistan;Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt;

关键词: cauchy distribution;    truncated distribution;    general family of distributions;    entropy;    estimation;    simple random sampling;    ranked set sampling;    data analysis;   

DOI  :  10.3390/e22030346

来源: DOAJ

【 摘 要 】

As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families.

【 授权许可】

Unknown