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Applications of skew models using generalized logistic distribution. (English) Zbl 1415.60018

Summary: We use the skew distribution generation procedure proposed by A. Azzalini [Scand. J. Stat. 12, 171–178 (1985; Zbl 0581.62014)] to create three new probability distribution functions. These models make use of normal, student-\(t\) and generalized logistic distribution, see P. N. Rathie and P. K. Swamee [On a new invertible generalized logistic distribution approximation to normal distribution. Techn. Rep., University of Brasilia (2006)]. Expressions for the moments about origin are derived. Graphical illustrations are also provided. The distributions derived in this paper can be seen as generalizations of the distributions given by S. Nadarajah and S. Kotz [Acta Appl. Math. 91, No. 1, 1–37 (2006; Zbl 1117.62014)]. 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 and (c) waiting time between eruptions of the Old Faithful Geyser in the Yellow Stone National Park, Wyoming, USA. We compare the fit of the distributions introduced in this paper with the distributions given by Nadarajah and Kotz [loc. cit.]. The results show that our distributions, in general, fit better the data sets. The general \(R\) codes for fitting the distributions introduced in this paper are given in Appendix A.

MSC:

60E05 Probability distributions: general theory
62B15 Theory of statistical experiments
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
60E10 Characteristic functions; other transforms

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[17] Health expenditure, total (
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