Family Of Skewed Distributions Research Articles

Some Extensions of the Asymmetric Exponentiated Bimodal Normal Model for Modeling Data with Positive Support

It is common in many fields of knowledge to assume that the data under study have a normal distribution, which often generates mistakes in the results, since this assumption does not always coincide with the characteristics of the observations under analysis. In some cases, the data may have degrees of skewness and/or kurtosis greater than what the normal model can capture, and in others, they may present two or more modes. In this work, two new families of skewed distributions are presented that fit bimodal data with positive support. The new families were obtained from the extension of the bimodal normal distribution to the alpha-power family class. The proposed distributions were studied for their main properties, such as their probability density function, cumulative distribution function, survival function, and hazard function. The parameter estimation process was performed from a classical perspective using the maximum likelihood method. The non-singularity of Fisher’s information was demonstrated, which made it possible to find the stochastic convergence of the vector of the maximum likelihood estimators and, based on the latter, perform statistical inference via the likelihood ratio. The applicability of the proposed distributions was exemplified using real data sets.

A new family of skewed distributions with application to some daily closing prices

A new family of skewed distributions with application to some daily closing prices

Properties and Applications of a New Family of Skew Distributions

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.

Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution

In this paper, we consider a stochastic representation of the epsilon–skew–Cauchy distribution, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005). The stochastic representation facilitates derivation of distributional properties of the model. In addition, we introduce symmetric and asymmetric extensions of the Cauchy distribution, together with an extension of the epsilon–skew–Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.

Two-Piece location-scale distributions based on scale mixtures of normal family

ABSTRACTIn this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm.

Robust quantile regression using a generalized class of skewed distributions

It is well known that the widely popular mean regression model could be inadequate if the probability distribution of the observed responses do not follow a symmetric distribution. To deal with this situation, the quantile regression turns to be a more robust alternative for accommodating outliers and the misspecification of the error distribution because it characterizes the entire conditional distribution of the outcome variable. This paper presents a likelihood‐based approach for the estimation of the regression quantiles based on a new family of skewed distributions. This family includes the skewed version of normal, Student‐t, Laplace, contaminated normal and slash distribution, all with the zero quantile property for the error term and with a convenient and novel stochastic representation that facilitates the implementation of the expectation–maximization algorithm for maximum likelihood estimation of the pth quantile regression parameters. We evaluate the performance of the proposed expectation–maximization algorithm and the asymptotic properties of the maximum likelihood estimates through empirical experiments and application to a real‐life dataset. The algorithm is implemented in the R package lqr, providing full estimation and inference for the parameters as well as simulation envelope plots useful for assessing the goodness of fit. Copyright © 2017 John Wiley & Sons, Ltd.

A proof for the conjecture of characteristic function of the generalized skew-elliptical distributions

In the paper of Genton and Loperfido (Genton and Loperfido (2005)), the authors introduced the multivariate generalized skew-elliptical distributions, which is a family of skewed distributions that contains the more familiar skew-normal and skew-Student-t distributions. In the same paper the authors conjectured the structure of the characteristic function of the proposed family of distributions. In this short letter we prove their conjecture.

Libby and Novick's generalized beta exponential distribution

A new family of skewed distributions is presented. Some properties and estimation procedures for Libby and Novick's generalized beta exponential distribution, a particular member of the family, are derived. Real applications using two original data sets are described to show superior performance versus at least six known models.

Hidden Truncation and Additive Components : Two Alternative Skewing Paradigms

The two parameter skew-normal distribution can be viewed as having arisen from a standard normal density by hidden truncation or by an additive component construction. It is of interest to determine whether the two skewing mechanisms can yield the same asymmetric distribution when applied to other symmetric or asymmetric distributions. It is conjectured that the phenomenon only occurs in the normal case. In other cases, hidden truncation and additive components typically lead to different families of skewed distributions. Some examples are provided to illustrate the phenomenon. AMS (2000) Subject Classification : 60E05, 62E10.

Characterization of Continuous Symmetric Distributions Based on Families of Skewed Distributions

A characterization of a symmetric probability density function based on certain properties of its associated skewed family is presented. This characterization is then applied to various well-known distributions.

On the generalized Zipf distribution. Part I

This article is concerned with a class of informetric distribution, a family of skew distributions found to describe a wide range of phenomena both within or outside of information sciences and ref...

PERFORMANCE OF PROCESS CAPABILITY INDICES FOR WEIBULL AND LOGNORMAL DISTRIBUTIONS OR AUTOREGRESSIVE PROCESSES

The usual definitions of process capability indices assume that observations are independent and identically normally distributed. The process mean may shift and from that point forward the process is out of control but the observations are still independent and normally distributed. When the observations are non-normal or correlated, the estimation of the standard capability indices can be greatly affected. In this paper comparison of estimators of capability indices is presented when the process measurements are from one of two families of skewed distributions, Weibull or lognormal. Also, an investigation of estimators of the standard index, Cpk, is presented for normally distributed process measurements which follow an autoregressive model of order one.

Statistical properties of Winsorized means for skewed distributions

SUMMARY Sampling properties of estimators of the mean of a positive random variable that Winsorize the largest or the two largest observations in the sample are investigated. Exact and approximate expressions for the mean squared errors of these estimators are derived. Optimal Winsorization schemes are obtained for various skewed distributions. Efficiency comparisons between the sample mean and Winsorized means are presented for several families of skewed distributions. A nearly unbiased estimator of the mean squared error of the Winsorized mean is proposed.