The t-transformed power method distributions for simulating univariate and multivariate non-normal distributions. Issue 4 (2nd April 2020)

• Record Type: Journal Article
• Authors: Pant, Mohan D.
• Is Part Of: Communications in statistics. Volume 49:Issue 4(2020)
• Page Start: 825
• Page End: 846
• Publication Date: 2020-04-02
• Subjects: Monte Carlo -- Simulation -- Moments -- Non-normal distributions -- Correlated distributions; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1498894
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: This paper introduces a family of t -transformed power method distributions for fitting empirical and theoretical distributions with a wide range of skew and kurtosis values. Equations associated with the first four product moments (mean, variance, skew, and kurtosis) are derived and a methodology is subsequently illustrated for simulating univariate non-normal distributions based on the moment matching approach. Also included is a methodology for generating multivariate non-normal distributions correlated at the user-specified Pearson correlation matrix. The Monte Carlo simulation results indicate that the proposed methodology produces excellent agreement between estimates of Pearson correlations, skew, and kurtosis and their corresponding parameter values.