Abstract
Generalized logistic distributions are very versatile and give useful representations of many physical situations. Skew-symmetric densities recently received much attention in the literature. In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. We derive, the probability density function (pdf) and cumulative distribution function (CDF) of the skew type I generalized logistic distribution denoted by S'GLD . The general statistical properties of the S'GLD such as: the moment generating function (mgf), characteristic function (chf), Laplace and Fourier transformations are obtained in explicit form. Expressions for the n th moment, skewness and kurtosis are discussed. Mean deviation about the mean and about the median, Renye entropy and the order statistics are also given. We consider the general case by inclusion of location and scale parameters. The results of Nadarajah (2009) are obtained as special cases. Graphical illustration of some results has been represented. Further we present a numerical example to illustrate some results of this paper.
Highlights
The fundamental properties and characterization of symmetric distributions about origin are widely used in many applications as stated in Johnson et al (1995)
There has been quite an intense activity connected to a broad class of continuous probability distribution which are generated starting from a symmetric distribution and applying a suitable form perturbation of the symmetry
Azzalini (1985) showed that any symmetric distribution was viewed as a member of more general class of skewed distribution
Summary
The fundamental properties and characterization of symmetric distributions about origin are widely used in many applications as stated in Johnson et al (1995). The logistic distribution has important uses in describing growth and as alternative for the normal distribution. It has several important applications in population modeling, biological, geological issues, psychological issues, actuarial, industrial and engineering felids. Different properties and applications of logistic distribution are studied extensively by, Ojo (1997, 2002, 2003), Olapade (2004), Alvarez et al (2011), and Nassar and Elmasry (2012). Univariate skewsymmetric models have been defined by several authors, using the concept described in the article by Azzalini (1985). The skew-symmetric models defined based on the skew-normal distribution as ( )
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