BLUEs of Parameters of Generalized Geometric Distribution Using Ordered Ranked Set Sampling

As an alternative to the best linear unbiased estimates based on order statistics (BLUE-OS) for general location-scale distributions given by Lloyd (1952) and Downton (1954), Bhoj and Ahsanullah (1996) presented the best linear unbiased estimates based on ranked set sample (BLUE-RSS) for the generalized geometric distribution. Hossain and Muttlak (2000) extended it to some other distributions, and gave the BLUE-RSS for the population mean and the standard deviation. Bhoj and Ahsanullah (1996) and Hossain and Muttlak (2000) arrived at the conclusion that the BLUE-RSS of the location parameter is more efficient than the BLUE-OS, while the BLUE-RSS of the scale parameter is not as efficient as the BLUE-OS for small n. In this article, we derive the best linear unbiased estimates using ordered ranked set sampling (BLUE-ORSS). These estimates are then compared with both BLUE-OS and BLUE-RSS for two special cases of the generalized geometric distribution. We show that BLUE-ORSS are uniformly better than BLUE-OS and BLUE-RSS not only for the location parameter but also for the scale parameter.