Parameter Estimation for Symmetric Stable Distribution

1980 ◽  
Vol 21 (1) ◽  
pp. 209 ◽  
Author(s):  
Ruth W. Arad
Keyword(s):  
Parameter Estimation ◽  
Stable Distribution ◽  
Symmetric Stable 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.

On the maximum of sums of random variables and the supremum functional for stable processes

1969 ◽  
Vol 6 (2) ◽  
pp. 419-429 ◽  
Author(s):  
C.C. Heyde
Keyword(s):  
Limit Theorem ◽  
Stable Distribution ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Law ◽  
Sums Of Random Variables ◽  
Symmetric Stable Distribution ◽  
General Limit ◽  
General Limit Theorem

Let Xi, i = 1, 2, 3, … be a sequence of independent and identically distributed random variables which belong to the domain of attraction of a stable law of index a. Write S0= 0, Sn = Σ i=1nXi, n ≧ 1, and Mn = max0 ≦ k ≦ nSk. In the case where the Xi are such that Σ1∞n−1Pr(Sn > 0) < ∞, we have limn→∞Mn = M which is finite with probability one, while in the case where Σ1∞n−1Pr(Sn < 0) < ∞, a limit theorem for Mn has been obtained by Heyde [9]. The techniques used in [9], however, break down in the case Σ1∞n−1Pr(Sn < 0) < ∞, Σ1∞n−1Pr(Sn > 0) < ∞ (the case of oscillation of the random walk generated by the Sn) and the only results available deal with the case α = 2 (Erdos and Kac [5]) and the case where the Xi themselves have a symmetric stable distribution (Darling [4]). In this paper we obtain a general limit theorem for Mn in the case of oscillation.

Parameter Estimation Based on Fractional Correlation under Alpha-Stable Distribution Noise Environment in Bistatic MIMO Radar System

2014 ◽  
Vol 989-994 ◽  
pp. 3710-3713
Author(s):  
Li Li
Keyword(s):  
Parameter Estimation ◽  
Stable Distribution ◽  
Impulsive Noise ◽  
Mimo Radar ◽  
Radar System ◽  
Noise Model ◽  
Distribution Model ◽  
Music Algorithm ◽  
Bistatic Mimo Radar ◽  
Noise Environment

This paper takes the-stable distribution as the noise model and works on the parameter estimation problem of bistatic Multiple-Input Multiple-Output (MIMO) radar system in the impulsive noise environment.This paper presents a signal model and a novel method for parameter estimation in bistatic MIMO radar system in the impulsive noise environment. Firstly, a signal array model is constructed based on the-stable distribution model. Secondly, Doppler parameters are jointly estimated by searching the optimal rotation angle to meet concentrated-energy of the FLOS-FC. Furthermore, two algorithms are presented for the estimation of DODs and DOAs, including based on FLOS-MUSIC algorithm and FLOS-ESPRIT algorithm. Simulation results are presented to verity the effectiveness of the proposed method.

scholarly journals REAL ZEROS OF ALGEBRAIC POLYNOMIALS WITH STABLE RANDOM COEFFICIENTS

2008 ◽  
Vol 85 (1) ◽  
pp. 81-86 ◽  
Author(s):  
K. FARAHMAND
Keyword(s):  
Stable Distribution ◽  
Random Coefficients ◽  
Algebraic Polynomials ◽  
Expected Number ◽  
Real Zeros ◽  
Number Of Zeros ◽  
Symmetric Stable Distribution ◽  
Number Of Real Zeros ◽  
Significant Interest ◽  
Special Case

AbstractWe consider a random algebraic polynomial of the form Pn,θ,α(t)=θ0ξ0+θ1ξ1t+⋯+θnξntn, where ξk, k=0,1,2,…,n have identical symmetric stable distribution with index α, 0<α≤2. First, for a general form of θk,α≡θk we derive the expected number of real zeros of Pn,θ,α(t). We then show that our results can be used for special choices of θk. In particular, we obtain the above expected number of zeros when $\theta _k={n\choose k}^{1/2}$. The latter generate a polynomial with binomial elements which has recently been of significant interest and has previously been studied only for Gaussian distributed coefficients. We see the effect of α on increasing the expected number of zeros compared with the special case of Gaussian coefficients.

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