Estimation of parameters of Alpha Logarithm Transformed Rayleigh distribution by using Maximum Likelihood Estimation method
Author(s):
M. Vijaya Lakshmi, K. V. Subrahmanyam, G. V. S. R. Anjaneyulu
Keywords:
ALTR, MLE, Average Estimate (AE), Variance (VAR), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Relative Absolute Bias (RAB) and Relative Efficiency (RE), Asymptotic confidence bounds.
Abstract
In this paper, we review the maximum likelihood method for estimating the statistical parameters which specify a probabilistic model and show that it generally gives an optimal estimator with minimum mean square error asymptotically. Thus, for most applications in information sciences, the maximum likelihood estimation suffices. Fisher information matrix, which defines the orthogonality between parameters in a probabilistic model, naturally arises from the maximum likelihood estimation. The parameters involved in the model are estimated using Maximum Likelihood Estimation (MLE) method. Maximum Likelihood estimation method under some risk function to estimate parameter of Alpha Logarithm Transformed Rayleigh distribution to know the best method. As the inverse of the Fisher information matrix gives the covariance matrix for the estimation errors of the parameters, the orthogonalization of the parameters guarantees that the estimates of the parameters distribute independently from each other. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTR distribution compared to some other well-known distributions. . We present MLE of the unknown parameters in this distribution using Newton-Raphson. We also computed Average Estimate (AE), Variance (VAR), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Relative Absolute Bias (RAB) and Relative Efficiency (RE) for both the parameters under sample based on 1000 simulations to assess the performance of the estimators. Also we derive the asymptotic confidence bounds for unknown parameters.
Article Details
Unique Paper ID: 150378

Publication Volume & Issue: Volume 7, Issue 5

Page(s): 91 - 97
Article Preview & Download


Share This Article

Conference Alert

ICM - STEP

International conference on Management, Science, Technology, Engineering, Pharmact and Humanities.

Latest Publication

Go To Issue



Call For Paper

Volume 7 Issue 9

Last Date 25 February 2020

About Us

IJIRT.org enables door in research by providing high quality research articles in open access market.

Send us any query related to your research on editor@ijirt.org

Social Media

Google Verified Reviews

Contact Details

Telephone:6351679790
Email: editor@ijirt.org
Website: ijirt.org

Policies

Important Links

Browse Rsearch papers