scholarly journals Reconstructed Quantized Coefficients Modeled with Generalized Gaussian Distribution with Exponent 1/3

2016 ◽  
Vol 21 (4) ◽  
pp. 5-12 ◽  
Author(s):  
Robert Krupiński
Keyword(s):  
Uniform Distribution ◽  
Gaussian Distribution ◽  
Shape Parameter ◽  
Gaussian Distributions ◽  
Generalized Gaussian Distribution ◽  
Impulse Function ◽  
Special Case

Abstract Generalized Gaussian distribution (GGD) includes specials cases when the shape parameter equals p = 1 and p = 2. It corresponds to Laplacian and Gaussian distributions respectively. For p → ∞, f(x) becomes a uniform distribution, and for p → 0, f(x) approaches an impulse function. Chapeau-Blondeau et al. [4] considered another special case p = 0.5. The article discusses more peaky case in which GGD p = 1/3.

scholarly journals Approximated fast estimator for the shape parameter of generalized Gaussian distribution for a small sample size

2015 ◽  
Vol 63 (2) ◽  
pp. 405-411 ◽  
Author(s):  
R. Krupiński
Keyword(s):  
Sample Size ◽  
Gaussian Distribution ◽  
Shape Parameter ◽  
Small Sample Size ◽  
Estimation Method ◽  
Small Sample ◽  
Time Data ◽  
Generalized Gaussian Distribution ◽  
Root Finding ◽  
Real Time Data Processing

Abstract Most estimators of the shape parameter of generalized Gaussian distribution (GGD) assume asymptotic case when there is available infinite number of observations, but in the real case, there is only available a set of limited size. The most popular estimator for the shape parameter, i.e., the maximum likelihood (ML) method, has a larger variance with a decreasing sample size. A very high value of variance for a very small sample size makes this estimation method very inaccurate. A new fast approximated method based on the standardized moment to overcome this limitation is introduced in the article. The relative mean square error (RMSE) was plotted for the range 0.3-3 of the shape parameter for comparison with other methods. The method does not require any root finding, any long look-up table or multi step approach, therefore it is suitable for real-time data processing

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