Journal ArticleDOI
Estimation in Univariate and Multivariate Stable Distributions
TLDR
In this paper, the authors proposed several methods of estimating parameters in stable distributions, which involve sample characteristic functions, and one of the methods which is based upon the method of moments is treated in some detail.Abstract:
This paper proposes several methods of estimating parameters in stable distributions. All the methods involve sample characteristic functions. One of the methods which is based upon the method of moments is treated in some detail. Asymptotic normal distributions for the proposed moment estimators are provided. Moreover, all methods provide consistent estimators. The estimation problem is treated for both univariate and multivariate stable distributions.read more
Citations
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Journal ArticleDOI
Signal processing with fractional lower order moments: stable processes and their applications
M. Shao,Chrysostomos L. Nikias +1 more
TL;DR: A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented, focusing on the differences and similarities between stable signal processors based on fractional lower-order moments and Gaussian signal processing methods based on second-order Moments.
Journal ArticleDOI
Simple consistent estimators of stable distribution parameters
TL;DR: In this paper, the authors proposed estimators of a and c are similar to those of Fama and Roll, except that the small asymptotic bias in their estimators has been eliminated, and their restrictions that a be no less than 1.0 and that the distribution be symmetrical have been relaxed.
Book
Chance and Stability: Stable Distributions and Their Applications
TL;DR: In this article, the authors introduce the theory of stable laws and apply it to some probabilistic models correlated systems and fractals anomalous diffusion and chaos physics radiophysics astrophysics and cosmology.
Journal ArticleDOI
Regression-Type Estimation of the Parameters of Stable Laws
TL;DR: In this paper, a regression-type method of estimating the four parameters of a stable distribution is presented, and the estimators found are consistent and approximately unbiased for moderately large sample sizes.
Journal ArticleDOI
The Empirical Characteristic Function and Its Applications
TL;DR: In this article, it was shown that the empirical characteristic function converges uniformly almost surely to the population characteristic function (ecf) under some general restrictions, and that the ecf may be a useful tool in numerous statistical problems.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.