Abstract
The largest, or smallest, observation in a finite sample is termed an extreme value. Its distribution converges with increasing sample size to one of three types. These three limiting distributions are of considerable interest in engineering. These distributions have been applied to a variety of problems in many fields of practical interest. If the initial distribution
f
(
x
,
θ
) has an unbounded upper tail, but not all of its moments are finite, then the asymptotic extreme value distribution is termed a type II maxima [Frèchet distribution (FD)]. In the present paper, we derive the best linear unbiased estimators of location and scale parameters of the FD and we obtain the best linear invariant estimations. Moreover, we use the maximum likelihood method to estimate the parameters of this distribution. Finally, we conduct a numerical experiment and draw conclusions.