期刊名称：Pakistan Journal of Statistics and Operation Research
印刷版ISSN：2220-5810
出版年度：2015
卷号：11
期号：3
页码：267-282
DOI：10.18187/pjsor.v11i3.685
语种：English
出版社：College of Statistical and Actuarial Sciences
摘要：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.
其他摘要：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.
关键词：skew type I generalized logistic distribution; moment generating function; skewness; kurtosis; mean deviation; order statistics
