Asymptotic properties of maximum likelihood estimator for some discrete distributions generated by

Authors

  • Davood Farbod Yerevan State University
  • Karen V. Gasparian Yerevan State University

DOI:

https://doi.org/10.6092/issn.1973-2201/3537

Abstract

In large-scale biomolecular sysrems there are frequency distribuions with properties like Stable Laws. It is of interest to construct such frequency distributions. In the present article we consider Cauchy stable law. The large-sample distribution of the Maximum Likelihood Estimator (M.L.E.) of the scale parameter for some discrete distributions generated by Cauchy stable law are investigated. The existence, strong consistency, asymptotic normality and asymptotic efficiency of that is established.

References

J. ASTOLA, E. DANIELIAN, (2006), Frequency Distributions in Biomolecular Systems and Growing Networks, TICSP Series, No. 31, Tampere, Finland.

J. ASTOLA, K.V. GASPARIAN, E. DANIELIAN, (2007), The Maximum Likelihood Estimators for Distributions with Moderate Growth, Proceedings of CSIT Conf., 24-28 Sept., Yerevan, Armenia, pp. 91-94.

A. A. BOROVKOV, (1998), Mathematical Statistics, Gordon and Breach Sciences Publishers, Translated from the Russian into English.

W.H. DUMOUCHEL, (1973), On the Asymptotic Normality of the Maximum Likelihood Estimate when Sampling from a Stable Distribution, Annals of Statistics, 1, pp. 948-957.

D. FARBOD, (2008), The Asymptotic Properties of Some Discrete Distributions Generated by Levy᾽s Law, Far East Journal of Theoretical Statistics, 26 (1), pp. 121-128.

W. FELLER, (1971), Introduction to Probability Theory and its Applications, Vol. 2, John Wiley and Sons, New York.

E. L. LEHMANN, (1983), Theory of Point Estimation, John and Wiley Sons.

J. P. NOLAN, (2007), Stable Distributions - Models for Heavy Tailed Data, Boston: Brikhauser, in progress, chapter 1 online at academic 2, American.edu/~Jpnolan.

V. M. ZOLOTAREV, (1986), One-dimensional Stable Distributions, Vol. 65, of Translation of Mathematical Monographs, American Mathematical Society, Translation of the Original 1983 Russian edition.

Downloads

Published

2008-12-31

How to Cite

Farbod, D., & Gasparian, K. V. (2008). Asymptotic properties of maximum likelihood estimator for some discrete distributions generated by. Statistica, 68(3/4), 321–326. https://doi.org/10.6092/issn.1973-2201/3537

Issue

Vol. 68 No. 3/4 (2008)

Section

Articles

License

Copyright (c) 2008 Statistica

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.