A Simulation Study of Estimator for the Stable Index - Innovative Management in Information and Production - page 15

0.5 1.0 1.5

alpha

The MSE of the estimators, U − 1
n

and V − 1
n

Fig. 2 ( h ) ( h ) ,for σ = 1, β = 0, μ = 0, and n = 200

Our estimator is not only very easy to compute, but also has asymptotic normality
property.

Acknowledgements The author sincerely thanks anonymous referees for helpful comments and
suggestions, leading to many improvements in the paper.

References

I.A. Bolov, On the computation of the probability density function of -stable distributions.

In: Mathematical Modelling and Analysis Proceedings of the 10th International Conference
MMA2005 and CMAM2 , Trakai, pp. 333-341, 2005
Z. Fan, Parameter estimation of stable distributions. Commun. Stat. Theor. Methods 35 , 245-255
(2006)
E.F. Fama, R. Roll, Parameter estimates for symmetric stable distribution. J. Am. Stat. Assoc. 66 ,
331-338 (1971)
W. Hoeffding, A class of statistics with asymptotically normal distribution. Ann. Math. Stat. 19 ,
293-325 (1948)
R. Ihaka, R. Gentleman, R: A language for data analysis and graphics. J. Comput. Graph. Stat. 5 ,
299-314 (1996)
I.A. Kouttrouvelis, Regression-type estimation of the parameters of stable laws. J. Am. Stat. Assoc.
75 , 918-928 (1980)
A.J. Lee, U-Statistics: Theory and Practice (Marcel Dekker, New York, 1990)
F. Marohn, Estimating the index of a stable laws via the POT-method. Stat. Probab. Lett. 41 ,
413-423 (1999)

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