A Generalized Skew Logistic Distribution

Communications in Statistics - Theory and Methods, 2015

The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many di↵erent spheres a↵ecting human life. By far the most well-known application of logistic distribution is in the logistic regression which is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution is obtained using the technique by of mixing two distributions hereafter called as the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum and the distribution of the sample median. For illustrative purposes, a real life data set is considered as an application of the EEL distribution.

Communications in Statistics, 2018

This paper develops a skewed extension of the type III generalized logistic distribution and presents the analytical equations for the computation of its moments, cumulative probabilities and quantile values. It is demonstrated through an example that the distribution provides an excellent fit to data characterized by skewness and excess kurtosis.

Journal of science and engineering, 2023

In the domain of the univariate distribution a large number of new distributions were introduced by using different generators. In this paper, a three-parameter distribution called the 'Skew-Lomax' distribution is proposed, which is the special case of the Azzalini distribution to generalize the Lomax distribution. The Lomax distribution is also called Pareto type II distribution, which is a heavy-tailed continuous probability distribution for a non-negative random variable. The statistical properties of the proposed Skew-Lomax distribution, including mean, variance, moments about the origin, cumulative distribution function, hazard rate function, quantile function, and random number generation have been derived. Also, the method of maximum likelihood and the method of moment to estimate the parameters of this distribution have been proposed. Three real data sets have been used to illustrate the usefulness, flexibility, and application of the proposed distribution. The coefficient of determination, chi-square test statistics, and the sum of the square of error depict that the proposed model is more flexible than the Lomax distribution.

The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many different spheres affecting human life. By far, the most well-known application of logistic distribution is in the logistic regression that is used for modeling categorical response variables. The exponentiatedexponential logistic distribution, a generalization of the logistic distribution, is obtained using the technique proposed by of mixing two distributions, hereafter called the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum, and the distribution of the sample median. For illustrative purposes, a real-life data set is considered as an application of the EEL distribution. A cosh(Bx−C)−D . Written in terms of the upper tail of the distribution of income (not in income power) it will take the form

Journal of Statistical Research of Iran, 2010

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC (λ 1 , λ 2 ), that it has more flexible than the skew-Cauchy distribution (denoted by SC (λ)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC (λ 1 , λ 2 ) can fits the data better than SC (λ).

Journal of Statistical Theory and Applications

In this paper we consider a new class of asymmetric logistic distribution that contains both the type I and type II generalized logistic distributions of Balakrishnan and Leung (Commun Stat Simul Comput 17(1):25–50, 1988) as its special cases. We investigate some important properties of the distribution such as expressions for its mean, variance, characteristic function, measure of skewness and kurtosis, entropy etc. along with the distribution of its order statistics. A location-scale extension of the distribution is defined and discussed the maximum likelihood estimation of its parameters. Further, two real life medical data sets are utilized for illustrating the usefulness of the model and a simulation study is conducted for examining the performance of the maximum likelihood estimators of the parameters of the distribution.

Proyecciones (Antofagasta), 2010

The Fisher information matrix for Generalized skew-normal (GSN) distribution is derived. The expressions for the elements of the matrices require of integrals that are solved numerically using a suitable software.

Arxiv preprint arXiv:0912.4554, 2009

Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable X into a so-called Lambert W random variable Y, which allows a very flexible approach to model skewed data. Its shape depends on the shape of X and a skewness parameter γ. In particular, for symmetric X and nonzero γ the output Y is skewed. Its distribution and density function are particular variants of their input counterparts. Maximum likelihood and method of moments estimators are presented, and simulations show that in the symmetric case additional estimation of γ does not affect the quality of other parameter estimates. Applications in finance and biomedicine show the relevance of this class of distributions, which is particularly useful for slightly skewed data. A practical by-result of the Lambert W framework: data can be “unskewed.” The R package LambertW developed by the author is publicly available (CRAN).

Sankhya A, 2016

This paper constructs a family of multivariate distributions which extends the class of generalized skew-elliptical (GSE) distributions, introduced by Azzalini and Capitanio (J. Roy. Statist. Soc. Ser. B, 65, 367-389, 2003), and derives formulae for it's characteristics; mean and covariance. The extended GSE family is particularly relevant whenever the need arises to model data by skewed distributions, as is the case in actuarial science, risk management and other branches of science. The paper also generalizes the skewnormal distribution in the sense of Azzalini and Dalla Valle (Biometrika, 83, 715-726, 1996). Furthermore, for estimation purposes, the maximum likelihood equations are derived. Finally, a numerical examples is provided which demonstrates that the extended GSE distribution offers a better fit in comparison to the GSE distribution.

Pakistan Journalof Statistics, 2020

We propose a new family of continuous distributions with two extra parameters named Transmuted Exponential-G family of distributions. We provide a special member for the new family of distributions. An explicit expression for some of its mathematical and structural properties such as reliability function, failure rate, ordinary moments, incomplete moments, generating function, Renyi entropy and order statistics were derived and presented. The method of maximum likelihood is used to estimate the parameters of the developed family of distributions. A simulation study is carried out to assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors. Real-life data are used to validate the robustness of the developed family of distribution.

The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increasing, decreasing, bathtub and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fr´echet distribution, and illustrate its importance by means of two applications to real data sets. To appear in Communications in Statistics-Theory and Methods (USA)-Impact factor (2013) = 0.284

2015

In this paper we study a new class of skew-Cauchy distributions inspired on the family extended two-piece skew normal distribution. The new family of distributions encompasses three well known families of distributions, the normal, the two-piece skew-normal and the skew-normal-Cauchy distributions. Some properties of the new distribution are investigated, inference via maximum likelihood estimation is implemented and results of a real data application, which reveal good performance of the new model, are reported

Communications in Statistics: Case Studies, Data Analysis and Applications, 2019

In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira and Steel (2006, Journal of the American Statistical Association, 101: 823-829). In particular, we consider using the logistic kernel to derive a class of univariate distribution called the truncated-logistic skew symmetric (TLSS) distribution. We provide some structural properties of the proposed distribution and develop the statistical inference for the TLSS distribution. A simulation study is conducted to investigate the efficacy of the maximum likelihood method. For illustrative purposes, two real data sets from environmental studies are used to exhibit the applicability of such a model.

Journal of modern applied statistical methods: JMASM

A new generalization of the logistic distribution is defined and studied, namely, the gamma-logistic distribution. Various properties of the gamma-logistic are obtained. The structural analysis of the distribution includes moments, mode, quantiles, skewness, kurtosis, Shannon's entropy and order statistics. The method of maximum likelihood estimation is proposed for estimating the model parameters. For illustrative purposes, a real data set is analyzed as an application of the gamma-logistic distribution.

Proyecciones (Antofagasta), 2011

In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. This new class is an extension of other skew-symmetric distributions that have already been studied. We give special attention to a family from this class that could be seen as an extension of the skew-generalized-normal model introduced by Arellano- . We study the main properties, stochastic representation, moments and an extension of this new model.