Estimation of the Shape Parameter of Ged Distribution for a Small Sample Size

• Authors: Jan Purczyński , Kamila Bednarz-Okrzyńska
• Languages of publication: EN

Abstracts

EN

In this paper a new method of estimating the shape parameter of generalized error distribution (GED), called ‘approximated moment method’, was proposed. The following estimators were considered: the one obtained through the maximum likelihood method (MLM), approximated fast estimator (AFE), and approximated moment method (AMM). The quality of estimator was evaluated on the basis of the value of the relative mean square error. Computer simulations were conducted using random number generators for the following shape parameters: s = 0.5, s = 1.0 (Laplace distribution) s = 2.0 (Gaussian distribution) and s = 3.0.

Keywords

EN

estimating parameters of GED distribution

• Publisher: Sciendo
• Journal: Folia Oeconomica Stetinensia
• Year: 2014
• Volume: 14
• Issue: 1
• Pages: 35-46

Dates

published

2014-06-01

received

2013-10-28

accepted

2014-07-01

online

2014-12-11

Contributors

author

Jan Purczyński

• Szczecin University Faculty of Management and Economics of Services Department of Quantitative Methods Cukrowa 8, 71-004 Szczecin, Poland

author

Kamila Bednarz-Okrzyńska

• MA Szczecin University Faculty of Management and Economics of Services Department of Quantitative Methods Cukrowa 8, 71-004 Szczecin, Poland

References

• Box, G.E.P. & Tiao, G.C. (1962). A further look at robustness via Bayes theorem. Biometrika, 49 (3/4).[Crossref]
• Hsieh, D.A. (1989). Testing for nonlinear dependence in daily foreign exchange rate changes. Journal of Business, 62.[Crossref]
• Kokkinakis, K. & Nandi, A.K. (2005). Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling. Signal Processing, 85.[Crossref]
• Krupiński, R. & Purczyński, J. (2006). Approximated fast estimator for the shape parameter of generalized Gaussian distribution. Signal Processing, 86 (4).[Crossref][WoS]
• Krupiński, R. & Purczyński, J. (2007). Modeling the distribution of DCT coefficients for JPEG reconstruction. Signal Processing: Image Communication, 22 (5).[Crossref][WoS]
• Meigen, S. & Meigen, H. (2006). On the modeling of small sample distributions with generalized Gaussian density in a maximum likelihood framework. IEEE Transactions on Image Processing, 15 (6).
• Nelson, D.B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59 (2).[Crossref]
• Subbotin, M.T.H. (1923). On the law of frequency of error. Mathematicheski Sbornik, 31.
• Weron, A. & Weron, R. (1998). Inżynieria finansowa. Warszawa: WNT

Identifiers

DOI

10.2478/foli-2014-0103