Year: 2012
Type: article
Abstract: Power method polynomials are used for simulating non-normal dis-tributions 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 method-ology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivari-ate non-normal distributions with specified values of L-skew, L-kurtosis, and L-correlation. Evaluation of the proposed doubling technique in-dicates that estimates of L-skew, L-kurtosis, and L-correlation are su-perior to conventional product-moments in terms of relative bias and relative efficiency when extreme non-normal distributions are of con-cern.
Authors: Mohan D. Pant, Todd C. Headrick
Institution: Southern Illinois University Carbondale
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1506102011