Simulation of the p-generalized Gaussian distribution

Abstract

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.

Keywords:

• random numbers
• simulation
• p-generalized Gaussian distribution
• power exponential distribution
• exponential error distribution
• p-generalized polar method
• p-generalized rejecting polar method
• stopping time
• p-generalized uniform distribution on the p-circle
• generalized arc-length measure
• goodness of fit
• Monte Carlo simulation
• Monty Python method
• Ziggurat method
• tail algorithm

MSC 2010:

• 65C10
• 60G40
• 68U20