Hypothesis testing of the location and scale parameters using order statistics (Q801417)

An asymptotically most powerful test of the null hypothesis \(H_ 0: \mu =\mu_ 0\), \(\sigma =\sigma_ 0\) versus the alternative hypothesis \(H_ 1: \mu =\mu_ 1\), \(\sigma =\sigma_ 1\) using a few selected order statistics is derived in this paper. The order statistics are chosen from a large complete or censored (singly-censored, doubly-censored, or multiply-censored) sample taken from a distribution with probability density function of the form (1/\(\sigma)\)f[(X-\(\mu)\)/\(\sigma\) ], where \(\mu\) and \(\sigma\) are location and scale parameters, respectively.