Abstract
This contribution deals with Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed for many applications in science and engineering to describe physical phenomena. Its use also seems interesting in modeling economic and financial data. For low values of the shape parameter α, the distribution presents heavy tails. In particular, α = 1/2 is considered and for such a value of the shape parameter, different simulation methods are assessed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alefeld, G.: On the convergence of Halley’s method. The American Mathematical Monthly, 88(7), 530–536 (1981)
Chapeau-Blondeau, F., Monir, A.: Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Transactions on Signal Processing, 50(9), 2160–2165 (2002)
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., Knuth, D. E.: On the Lambert W function. Advances in Computational Mathematics, 5, 329–359 (1996)
Domínguez-Molina, J.A., González-Farías, G., Rodríguez-Dagnino, R.M.: A practical procedure to estimate the shape parameter in the generalized Gaussian distribution. Technique Report, 1-01-18 (http://www.cimat.mx) (2001)
Kokkinakis, K., Nandi, A. K.: Exponentparameter estimation for a generalized Gaussian probability density functions with application to speech modeling. Signal Processing, 85, 1852–1858 (2005)
Michael, J.R., Schucany, W. R., Haas, R.W.: Generating random variates using transformations with multiple roots. The American Statistician, 30, 88–90 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer, Milan
About this paper
Cite this paper
Nardon, M., Pianca, P. (2008). Simulating a Generalized Gaussian Noise with Shape Parameter 1/2. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods in Insurance and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-0704-8_22
Download citation
DOI: https://doi.org/10.1007/978-88-470-0704-8_22
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0703-1
Online ISBN: 978-88-470-0704-8
eBook Packages: Business and EconomicsEconomics and Finance (R0)