Generalized Exponential Distribution - Estimation of parameters using modifications in methods of Ranked Set Sampling

Abstract

In this study, we estimate the parameters of the Generalized Exponential Distribution using Moving Extreme Ranked Set Sampling (MERSS). Using the maximum likelihood estimation method, we derive the expressions. MERSS estimates are compared with estimates obtained by simple random sampling (SRS) using a real data set. We also study the other variations of the methods of Ranked Set Sampling like Quartile Ranked Set Sampling(QRSS), Median Ranked Set Sampling(MRSS) and Flexible Ranked Set Sampling(FLERSS) (a scheme based on QRSS and MRSS). For known shape parameter values, we present coefficients for linear combinations of order statistics for least squares estimates. Here, the expressions are derived through maximum likelihood, and the estimates are calculated numerically. Simulated results indicate that estimates generated using least-squares and the maximum likelihood method for Ranked Set Sampling (RSS) perform better than those generated using Simple Random Sampling (SRS). Asymptotically, MERSS outperforms SRS, QRSS, MRSS, and FLERSS.