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International Journal of Statistika and Mathematika, ISSN: 2277- 2790 E-ISSN: 2249-8605

Volume 6, Issue 2, June 2013 pp 96-100

Research Article

Information theoretic approach in Parameter Estimation

 Sandeep Kumar¹, Parmil Kumar², Mamta Khajuria³, Ameena Rajput⁴

Academic Editor:  Dr. Dase R.K.

Let  be the probability density function of a random variable X, where functional form of pdf is known except for the parameter. This parameter  can be a scalar or a vector. One of the most important tasks in statistical inference is of estimating  on basis of a random sample  drawn from the population. The traditional methods of parameter estimation are methods of moments, least squares, minimum chi-square, maximum likelihood, minimum distance and recent one called method of probability weighted moment due to Greenwood et al [4]. Amongst all methods, Fisher [3] method of maximum likelihood is widely accepted and is considered as one of the best method for parameter estimation. Akaike [1] work paved the way for the information theoretic approach in parameter estimation.  Lind and Solana [8] method is based on the principle of least information.  Kapur [6] compared the Gauss’ method of estimation with a method based on the principle of maximum entropy. In the present communication we have used Parameter estimation methods using entropy optimization principles and compare these with classical methods such as method of moments and method of m.l.e. The basic principle is that, subject to the information available we should choose   in such a way that the entropy is as large as possible or the distribution as nearly uniform as possible. We have also derived some parameter estimation methods from entropy optimization principles, while their relation among methods of parameter estimation is also discussed. Further, the asymptotic behaviour of the estimator is also studied for exponential and geometric distribution.