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Axioms 2016, 5(2), 10; doi:10.3390/axioms5020010

Applications of Skew Models Using Generalized Logistic Distribution

1
Department of Statistics and Applied Mathematics, Federal University of Ceara, Fortaleza, CE 60020-181, Brazil
2
DICRE, Credit Risk Management, Bank of Brazil—BB, Brasilia 70073-901, Brazil
3
Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: Humberto Bustince and Hans J. Haubold
Received: 12 February 2016 / Revised: 6 April 2016 / Accepted: 7 April 2016 / Published: 15 April 2016

Abstract

We use the skew distribution generation procedure proposed by Azzalini [Scand. J. Stat., 1985, 12, 171–178] to create three new probability distribution functions. These models make use of normal, student-t and generalized logistic distribution, see Rathie and Swamee [Technical Research Report No. 07/2006. Department of Statistics, University of Brasilia: Brasilia, Brazil, 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 Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. 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 [Acta Appl. Math., 2006, 91, 1–37]. 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. View Full-Text
Keywords: generalized logistic distribution; normal distribution; Student-t distribution; skew distributions generalized logistic distribution; normal distribution; Student-t distribution; skew distributions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Rathie, P.N.; Silva, P.; Olinto, G. Applications of Skew Models Using Generalized Logistic Distribution. Axioms 2016, 5, 10.

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