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M. A. Hussian
Department of Mathematical Statistics
Institute of Statistical Studies and Research (ISSR), Cairo University, Cairo, Egypt
In this paper, the estimation of R=P(Y < X), when X and Y are two generalized inverted exponential random variables with different parameters is considered. This problem arises naturally in the area of reliability for a system with strength X and stress Y. The estimation is made using simple random sampling (SRS) and ranked set sampling (RSS) approaches. The maximum likelihood estimator (MLE) of R is derived using both approaches. Assuming that the common scale parameter is known, MLEs of R are obtained. Monte Carlo simulations are performed to compare the estimators obtained using both approaches. . The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The comparison is based on biases, mean squared errors (MSEs) and the efficiency of the estimators of R based on RSS with respect to those based on SRS. The estimators based on RSS is found to dominate those based on SRS.
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