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Full-Text Articles in Physical Sciences and Mathematics
Simulating Non-Normal Distributions With Specified L-Moments And L-Correlations, Todd C. Headrick, Mohan D. Pant
Simulating Non-Normal Distributions With Specified L-Moments And L-Correlations, Todd C. Headrick, Mohan D. Pant
Todd Christopher Headrick
This paper derives a procedure for simulating continuous non-normal distributions with specified L-moments and L-correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product-moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L-moment-based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L-skew and L-kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. …
Statistical Simulation: Power Method Polynomials And Other Transformations, Todd C. Headrick
Statistical Simulation: Power Method Polynomials And Other Transformations, Todd C. Headrick
Todd Christopher Headrick
Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data generation, Statistical Simulation: Power Method Polynomials and Other Transformations presents techniques for conducting a Monte Carlo simulation study. It shows how to use power method polynomials for simulating univariate and multivariate nonnormal distributions with specified cumulants and correlation matrices. The book first explores the methodology underlying the power method, …
The Power Method Transformation: Its Probability Density Function, Distribution Function, And Its Further Use For Fitting Data, Todd C. Headrick, Rhonda K. Kowalchuk
The Power Method Transformation: Its Probability Density Function, Distribution Function, And Its Further Use For Fitting Data, Todd C. Headrick, Rhonda K. Kowalchuk
Todd Christopher Headrick
The power method polynomial transformation is a popular algorithm used for simulating non-normal distributions because of its simplicity and ease of execution. The primary limitations of the power method transformation are that its probability density function (pdf) and cumulative distribution function (cdf) are unknown. In view of this, the power method’s pdf and cdf are derived in general form. More specific properties are also derived for determining if a given transformation will also have an associated pdf in the context of polynomials of order three and five. Numerical examples and parametric plots of power method densities are provided to confirm …