Applied Mathematics & Information Sciences

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A three parameter Burr distribution is considered. Two measures of reliability are discussed, namely R(t) = P(X > t) and P = P(X > Y). Point and interval estimation procedures are developed for the parameters, R(t) and P based on records. Two types of point estimators are developed – uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES). A comparative study of different methods of estimation is done through simulation studies and asymptotic confidence intervals of the parameters based on MLE and log(MLE) are constructed. Confidence intervals for the MLE and UMVUE of the parametric functions are obtained. Testing procedures are also developed for various hypotheses. Real example is used to illustrate the results.

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