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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, before demonstrating this method
through examples of standard normal, logistic, and uniform power
method pdfs. It also discusses methods for improving the
performance of a simulation based on power method polynomials. The
book then develops simulation procedures for systems of linear
statistical models, intraclass correlation coefficients, and
correlated continuous variates and ranks. Numerical examples and
results from Monte Carlo simulations illustrate these procedures.
The final chapter describes how the g-and-h and generalized lambda
distribution (GLD) transformations are special applications of the
more general multivariate nonnormal data generation approach.
Throughout the text, the author employs Mathematica (R) in a range
of procedures and offers the source code for download online.
Written by a longtime researcher of the power method, this book
explains how to simulate nonnormal distributions via easy-to-use
power method polynomials. By using the methodology and techniques
developed in the text, readers can evaluate different
transformations in terms of comparing percentiles, measures of
central tendency, goodness-of-fit tests, and more.
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, before demonstrating this method
through examples of standard normal, logistic, and uniform power
method pdfs. It also discusses methods for improving the
performance of a simulation based on power method polynomials. The
book then develops simulation procedures for systems of linear
statistical models, intraclass correlation coefficients, and
correlated continuous variates and ranks. Numerical examples and
results from Monte Carlo simulations illustrate these procedures.
The final chapter describes how the g-and-h and generalized lambda
distribution (GLD) transformations are special applications of the
more general multivariate nonnormal data generation approach.
Throughout the text, the author employs Mathematica (R) in a range
of procedures and offers the source code for download online.
Written by a longtime researcher of the power method, this book
explains how to simulate nonnormal distributions via easy-to-use
power method polynomials. By using the methodology and techniques
developed in the text, readers can evaluate different
transformations in terms of comparing percentiles, measures of
central tendency, goodness-of-fit tests, and more.
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