Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Simulating Univariate And Multivariate Tukey G-And-H Distributions Based On The Method Of Percentiles, Tzu-Chun Kou, Todd C. Headrick
Simulating Univariate And Multivariate Tukey G-And-H Distributions Based On The Method Of Percentiles, Tzu-Chun Kou, Todd C. Headrick
Todd Christopher Headrick
This paper derives closed-form solutions for the 𝑔-and-ℎ shape parameters associated with the Tukey family of distributions based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew and kurtosis functions. The MOP methodology is also extended from univariate to multivariate data generation. A procedure is described for simulating nonnormal distributions with specified Spearman correlations. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the …
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. …
Simulating Multivariate G-And-H Distributions, Rhonda K. Kowalchuk, Todd C. Headrick
Simulating Multivariate G-And-H Distributions, Rhonda K. Kowalchuk, Todd C. Headrick
Todd Christopher Headrick
The Tukey family of g-and-h distributions is often used to model univariate real-world data. There is a paucity of research demonstrating appropriate multivariate data generation using the g-and-h family of distributions with specified correlations. Therefore, the methodology and algorithms are presented to extend the g-and-h family from univariate to multivariate data generation. An example is provided along with a Monte Carlo simulation demonstrating the methodology. In addition, algorithms written in Mathematica 7.0 are available from the authors for implementing the procedure.
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, …
Simulating Controlled Variate And Rank Correlations Based On The Power Method Transformation, Todd C. Headrick, Simon Y. Aman, T. Mark Beasley
Simulating Controlled Variate And Rank Correlations Based On The Power Method Transformation, Todd C. Headrick, Simon Y. Aman, T. Mark Beasley
Todd Christopher Headrick
The power method transformation is a popular algorithm used for simulating correlated non normal continuous variates because of its simplicity and ease of execution. Statistical models may consist of continuous and (or) ranked variates. In view of this, the methodology is derived for simulating controlled correlation structures between non normal (a) variates, (b) ranks, and (c) variates with ranks in the context of the power method. The correlation structure between variate-values and their associated rank-order is also derived for the power method. As such, a measure of the potential loss of information is provided when ranks are used in place …
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 …
Fast Fifth-Order Polynomial Transforms For Generating Univariate And Multivariate Nonnormal Distributions, Todd C. Headrick
Fast Fifth-Order Polynomial Transforms For Generating Univariate And Multivariate Nonnormal Distributions, Todd C. Headrick
Todd Christopher Headrick
A general procedure is derived for simulating univariate and multivariate nonnormal distributions using polynomial transformations of order five. The procedure allows for the additional control of the fifth and sixth moments. The ability to control higher moments increases the precision in the approximations of nonnormal distributions and lowers the skew and kurtosis boundary relative to the competing procedures considered. Tabled values of constants are provided for approximating various probability density functions. A numerical example is worked to demonstrate the multivariate procedure. The results of a Monte Carlo simulation are provided to demonstrate that the procedure generates specified population parameters and …
Simulating Correlated Multivariate Nonnormal Distributions: Extending The Fleishman Power Method, Todd C. Headrick, Shlomo S. Sawilowsky
Simulating Correlated Multivariate Nonnormal Distributions: Extending The Fleishman Power Method, Todd C. Headrick, Shlomo S. Sawilowsky
Todd Christopher Headrick
A procedure for generating multivariate nonnormal distributions is proposed. Our procedure generates average values of intercorrelations much closer to population parameters than competing procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random deviates, and it is simpler to code in a programming language (e.g,, FORTRAN). Numerical examples demonstrating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, and kurtosis.