Estimation of parameters of the extreme value distribution using ranked set sampling

Abstract

The estimates of the location and scale parameters of the extreme value distribution are obtained by using ranked set sampling procedure. These linear unbiased estimators with minimum variance are compared with the ordered least squares estimates given by Lieblein and Zelen (1956). It is shown that the relative precisions of our estimators are higher than those of the ordered least squares estimators. Furthermore, the relative precision of our estimator for the population mean is higher than the usual estimator based on ranked set sampling procedure. The ranked set sampling procedure is modified to estimate a given parameter assuming that the value of the other parameter is known.

Keywords:

• Extreme value distribution
• least squares estimates
• minimum variance estimators
• modified ranked set sampling
• ordered observations
• relative precision
• unbiased estimators