Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Statistics and Probability

SelectedWorks

Skew

Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick Sep 2013

An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, …


An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick Jan 2013

An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick

Todd Christopher Headrick

This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of 𝐿-moments and 𝐿-correlations. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that 𝐿-moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of 𝐿-skew, 𝐿-kurtosis, …


A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick Oct 2012

A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with …


Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky Jan 2000

Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky

Todd Christopher Headrick

The power methods are simple and efficient algorithms used to generate either univariate or multivariate non-normal distributions with specified values of (marginal) mean, standard deviation, skew, and kurtosis. The power methods are bounded as are other transformation techniques. Given an exogenous value of skew, there is an associated lower bound of kurtosis. Previous approximations of the boundary for the power methods are either incorrect or inadequate. Data sets from education and psychology can be found to lie within, near or outside the boundary of the power methods. In view of this, we derived necessary and sufficient conditions using the Lagrange …