Simulation of the p-generalized Gaussian distribution

• Published in: Journal of statistical computation and simulation Vol. 83; no. 4; pp. 641 - 667
• Main Authors: Kalke, S., Richter, W.-D.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.04.2013; Taylor & Francis Ltd
• Subjects: Adequacy; Complexity; Computation; Computer simulation; exponential error distribution; generalized arc-length measure; Goodness of fit; Monte Carlo simulation; Monty Python method; Normal distribution; p-generalized Gaussian distribution; p-generalized polar method; p-generalized rejecting polar method; p-generalized uniform distribution on the p-circle; power exponential distribution; random numbers; Representations; Science; Simulation; Stochastic models; Stochasticity; stopping time; tail algorithm; Ziggurat method
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2011.631187

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box-Muller method and the Marsaglia-Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.