Suppose that distribution of Y = (Y_{1} , ... , Y_{n}) belongs to the parametric family \{f_{Y}(y | \theta): \theta \in \Theta \}. Then, the statistic S = S(Y_{1} , ... , Y_{n}) is sufficient for \theta if and only if there exit functions h of y and g of...
(which gives you the distribution of an order statistic) and to stats.stackexchange.com/questions/48496/… (the derivation for the memorylessness of the exponential distribution can be used in a similar way to say that the distribution of the other variables in the sample...
Statistical Estimation in the Space of a Certain Sufficient Statistic of the Extremal Value Distribution, and Group Classificationdoi:10.1023/A:1020260002659Journal of Mathematical Sciences -Abusev, R. A.Perm State University, Perm, RussiaKluwer Academic Publishers-Plenum PublishersJournal of Mathematical ...
(1966): Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic. Ann. Inst. Statist. Math., 18, 39–47.Patil GP., Wani JK. Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic. Ann Inst Stat Math Tokyo 1966,...