Mathematica Eterna
Open Access

Abstract

On the New Skew distributions using Azzalini’s Formula

Rafael Oliveira Silva, Paulo H. D. Silva, Jo˜ao Maur´ıcio Ara´ujo Mota and Pushpa N. Rathie

We use the skew distribution generation procedure proposed by Azzalini [Scand. J. Stat., 12, 171-178, 1985] to create two new probability distribution functions. These models make use of Eirado-Rathie distribution ,see Eirado and Rathie [Statistics Research Letters, 3, 17-22, 2014] and Rathie-Swamee generalized logistic distribution, see Rathie and Swamee [University of Brasilia: Brasilia, Brazil, 2006]. Expressions for the moments about origin are derived. Graphical illustrations are also provided. Applications with unimodal and bimodal data are given to illustrate the applicability of the results derived in this paper. The applications include the analysis of the following data sets: (a) spending on public education in various countries in 2003; (b) total expenditure on health in 2009 in various countries, (c) waiting time between eruptions of the Old Faithful Geyser in the Yellow Stone National Park, Wyoming, USA and (d) pH concentration.