Estimation of control improvement benefit with α–stable distribution

2017 ◽  
pp. 128-137 ◽  
Author(s):  
Paweł D. Domański ◽  
Piotr M. Marusak
Keyword(s):  
Stable Distribution

Radar Clutter Recognition Using Alpha Stable Distribution

2011 ◽  
Vol 30 (9) ◽  
pp. 2042-2045 ◽  
Author(s):  
Xu-tao Li ◽  
Shou-yong Wang ◽  
Lian-wen Jin
Keyword(s):  
Stable Distribution ◽  
Radar Clutter ◽  
Alpha Stable Distribution

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

Generalized spectral coherence for cyclostationary signals with α-stable distribution

2021 ◽  
Vol 159 ◽  
pp. 107737
Author(s):  
Piotr Kruczek ◽  
Radosław Zimroz ◽  
Jerome Antoni ◽  
Agnieszka Wyłomańska
Keyword(s):  
Stable Distribution ◽  
Spectral Coherence ◽  
Cyclostationary Signals

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family

2019 ◽  
Vol 12 (4) ◽  
pp. 171
Author(s):  
Ashis SenGupta ◽  
Moumita Roy
Keyword(s):  
Entire Range ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Real Life ◽  
Circular Statistics ◽  
Directional Statistics ◽  
Symmetric Stable Distribution ◽  
Stable Family ◽  
Family Of Distributions ◽  
Better Than

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

scholarly journals Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions

2013 ◽  
Vol 14 (4) ◽  
pp. 504-520 ◽  
Author(s):  
Anthony Fiche ◽  
Jean-Christophe Cexus ◽  
Arnaud Martin ◽  
Ali Khenchaf
Keyword(s):  
Pattern Recognition ◽  
Stable Distribution ◽  
Belief Functions
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