Abstract

In describing the system behavior accurately through various mathematical models include parametric dynamic models, statistical probability distribution functions etc, parameter estimation plays a critical role. The Lomax distribution has played a very important role in different contexts. It was originally introduced for modeling business failure data but its limits has been extended. It also has been used for reliability modeling and life testing. Also, a new measure called Kullback-Leibler divergence for survival function is used and is a very much easier to compute in continuous distributions than the K-L divergence. It measures the distance between an empirical and a prescribed survival function. In this paper, we have estimated, Maximum Likelihood Estimator, Uniform Minimum Variance Unbiased Estimator and Kullback-Leibler Divergence for survival function of the Reliability Function of the Lomax Distribution. Also, Mean Square Error (MSE) values have been generated. Rth order raw moments and Mean Square Errors are presented in the form of theorems. Comparisons among UMVUE, MLE and KLS have been made to find out the best estimator. Detailed simulations show a greater performance of the KLS estimation method than the commonly used Uniform Minimum Variance Unbiased Estimation and Maximum Likelihood method in Lomax scale parameter estimation as this distance converges to zero with increasing sample size. The numerical results obtained from simulation has been illustrated.

Author: Kirandeep Kour, Ather Aziz Raina, Parmil Kumar and Srikant Gupta

Received on: April, 2020

Accepted on: July, 2021