Class Of Skewed Distributions Research Articles

Family of extended mean mixtures of multivariate normal distributions: Properties, inference and applications

<abstract><p>A new class of skewed distributions, with a matrix skewness parameter, called extended mean mixtures of multivariate normal (EMMN) distributions, is constructed. The family of EMMN distributions includes the SN and MMN distributions as special cases. Some basic properties of this family, such as characteristic function, moment generating function, affine transformation and canonical forms of the distributions are derived. An EM-type algorithm is developed to carry out the maximum likelihood estimation of the parameters. Two special cases of this family are studied in detail. A simulation is carried out to examine the performance of the estimation method, and the flexibility is illustrated by fitting a special case of this family to a real data. Finally, the theoretical formula of the multivariate tail conditional expectation of the EMMN distribution is derived.</p></abstract>

Frontier Quantile Model Using a Generalized Class of Skewed Distributions

© 2017 American Scientific Publishers All rights reserved. One of the classical ways to predict manufacturing production is to use Stochastic frontier model. At present, the most accurate predictions obtained by using this model involve the use of quantiles and asymmetric Laplace distributions for the noise and inefficiency. In this paper, we analyze the possibility of using more general skew distributions. We show that skew normal distributions lead to better predictions.

Moments of Standardized Fernandez-Steel Skewed Distributions: Applications to the Estimation of GARCH-Type Models

We provide general expressions for obtaining raw, absolute and conditional moments for a standardized version of the class of skewed distributions proposed by Fernandez and Steel (1998). We show that these expressions are readily programmable in addition of greatly reducing the computational cost. We discuss several applications that are relevant for the purpose of estimating asymmetric conditional volatility models under skewed distributions.

A generalization of Tukey’s g-h family of distributions

A new class of distribution function based on the symmetric densities is introduced, these transformations also produce nonnormal distributions and its pdf and cd f can be expressed in parametric form. This class of distributions depend on the two parameters, namely g and h which controls the skewness and the elongation of the tails, respectively. This class of skewed distributions is a generalization of Tukey’s g−h family of distributions. In this paper, we calculate a closed form expression for the density and distribution of the Tukey’s g−h family of generalized distributions, which allows us to easily compute probabilities, moments and related measures.

A Generalized Class of Skew Distributions and Parametric Quantile Regression Models

This paper proposes a generalized class of univariate skew distributions that are constructed through mixture of two scaled normal distributions. The proposed skew distributions with the skewness parameter defined in the (0,1) interval allow us to have an application on parametric quantile regression. Expressing a skew distribution as a scale mixture of normal can facilitate the estimation procedure via the Bayesian Markov Chain Monte Carlo methods. We conduct two simulation studies on skew error regression models and parametric quantile regression models with two corresponding empirical studies on the U.S. market return and infant birthweight data where we obtain satisfactory results.

A new skew generalization of the normal distribution: Properties and applications

A new class of distribution functions with not-necessarily symmetric densities, which contains the normal one as a particular case, is introduced. The class thus obtained depends on a set of three parameters, with an additional one to the classical normal distribution being inserted. This new class of skewed distributions is presented as an alternative to the class of skew-normal and Balakrishnan skew-normal distributions, among others. The density and distribution functions of this new class are given by a closed expression which allows us to easily compute probabilities, moments and related measurements. Certain interesting regularity properties reduce the study of this class to one of a subset of standardized distributions. Finally, some applications are shown as examples.

Testing Conditional Asymmetry: A Residual-Based Approach

We propose three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and nonparametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters in the first step. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests and an empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.

Class of skew-distributions: theory and applications in biology

In this paper, we study a class of skew-normal distributions driven by the convolution of two independent random variables: a normal and a beta distributed random variables. This problem is motivated by the numerical simulation of the oviductal egg transport in mammals, expressed as a series of microsphere instant velocities regulated by ovarian hormones including estradiol. We propose a closed form convolution formula, represented in terms of the infinite series expanded using Hermite polynomials. We also analyse the convergence of such series and perform the numerical experiments to illustrate these formulae.

On the consistency of tests of symmetry

It is important to determine whether a distribution is symmetric or skewed, as this might affect inferences of interest. There are a number of concepts that define classes of skewed distributions, and many tests for symmetry have been suggested in the literature. We find the appropriate class of skewed distributions for which each of the tests of symmetry is consistent.