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
K. (1966) Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic. Ann. Inst. Statist. Math. 18: pp. 39-47Patil GP, Wani JK (1966) Minimum variance unbiased estimation of the distribution function admitting a sufficient statistics. Ann. Inst. Statist. ...
Alternatively, the F statistic can be transformed to a statistic, B that has a Beta distribution with parameters (k − 1)/2 and (N − k)/2, where B=(k−1)F(k−1)F+N−k=SSTreatSSTotalandSSTotal=SSTreat+SSE=∑j=1k∑i=1nj(Yij−Y¯)2. The null hypothesis is reject...
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 ...