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Estimation of the Parameters of Skewed Alpha-stable Distributions
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| Christopher Dance, Ercan kuruoglu |
| "Estimation of the parameters of skewed alpha-stable distributions" C Dance, E Kuruoglu. Proceedings of Applications of Heavy-Tailed Distributions in Finance and Engineering, 1999. |
| Estimation-of-the-parameters-of-skewed-alpha-stable-distribution.pdf |
Stable distributions have received great interest over the last few years in the signal processing community and have proved to be strong alternatives to the Gaussian distribution. There have been several works in the literature addressing the problem of estimating the parameters of stable distributions. However, most of these works consider only the special case of symmetric stable random variables. This is an important restriction though, since most real life signals are skewed. Previous work on estimating the parameters of general (possibly skewed) stable distributions has been limited. The existing techniques are either computationally too expensive or their estimates have high variances.
In this paper, we solve the general problem of stable parameter estimation analytically. We introduce three novel classes of estimators for the parameters of general stable distributions. These new classes of estimators are based on formulas we have developed for the fractional and negative order moments of skewed stable random variables. These are generalisations of methods previously suggested for paramater estimation with symmetric stable distributions.
Of all known techniques for the general problem, only the characteristic function technique and the methods we have suggested yield closed form estimates for the parameters which may be efficiently computed. Simulation results show that at least one of our new estimators has better performance than the characteristic function technique over most of the parameter space. Furthermore our techniques require substantially less computation.
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The research we conduct on expressive visual representations is applicable to visual search, object detection, image classification and the automatic extraction of 3D human poses and shapes that can be used for human behavior understanding and prediction, human-robot interaction or even avatar animation. We also extract 3D information from images that can be used for intelligent robot navigation, augmented reality and the 3D reconstruction of objects, buildings or even entire cities.
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