International Journal of Statistics and Reliability Engineering

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Vol 6, No 2 :

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Maximum Product Spacing Method for Estimation of Entropy of Log-Logistic Probability Distribution and their Order Statistics

Ankita Sharma , Parmil Kumar

Abstract

Shannon (1948) introduced the term “Entropy” as a measure of information or uncertainty associated with a probabilistic scheme. As entropy is used to make certain inferences about the associated probability distribution so it has gained importance among researchers to study the various properties of the distributions and the associated random variable. Order statistics being the ordered random variables represents many real-world problems. Order statistics for continuous parent population have found important applications in many fields specially life time distributions. Nagaraja et al. (1996), and Balakrishan and Rao (1998) have discussed applications of order statistics in survival analysis, life testing, reliability, robustness studies, statistical quality control etc. Log-logistic distribution is one of the commonly used distribution in the study of reliability theory and survival analysis. In this paper, we have derived the expressions for entropy of Log-logistic distribution and of their associated 1^st and n^th order statistics corresponding to a sample of size n. Further, we have estimated the Entropy of Log-logistics distribution by using two methods of estimation namely maximum likelihood method and the method of product spacing. These methods of estimation used for estimating the entropy have been compared in terms of bias and MSE through simulation studies.

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ISSN(P) 2350-0174

ISSN(O) 2456-2378

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