Document Type

Article

Source Publication Title

Applied Mathematical Sciences

First Page

6437

Last Page

6475

Abstract

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 specified valued of L-skew, L-kurtosis, and L-correlation. Evaluation of the proposed doubling technique indicated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moments in terms of relative bias and relative efficiency when extreme non-normal distributions are of concern.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 specified valued of L-skew, L-kurtosis, and L-correlation. Evaluation of the proposed doubling technique indicated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moments in terms of relative bias and relative efficiency when extreme non-normal distributions are of concern.

Disciplines

Curriculum and Instruction | Education

Publication Date

1-1-2012

Language

English

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