SOME BEST PARAMETER ESTIMATES FOR DISTRIBUTIONS WITH FINITE END-POINT

Consider n observations on R, generated independently by a distributio n function F which is only partially specified: We require that F has in its upper tail a density f such that f(x) = (exp(b/alpha)/alpha) (t heta - x)(1/alpha-1) (1 + 0((theta - x)(delta/alpha))) as x tends to t he right endpoint theta of F. The parameters of interest are alpha > 0 and b, theta is an element of R. Based on the largest order statistic s in the sample, we can define in case alpha > 1/2 estimates of alpha, b and theta that behave asymptotically like the BLUE of theta as if a lpha was known and like the UMVU estimates of a and b in some ideal mo del as if theta was known. We show in addition that the BLUE estimate of theta can be outperformed by a bias corrected largest order statist ic.