Rangvariable bei Vorliegen von Bindungen

Summary The family of distributions of the random sampleX ₁,...,X _N not being specified solution of different statistical problems is obtained by methods based on ranks, because these methods are distribution-free under the assumption ofQ:=P(X _i =X _j )=0. Frequently, in case ofQ>0, the use of midranks is proposed, though only few is known about their distribution depending on the (usually unknown) distribution of the random sample. Here general formulas of variance and covariance of midranks are derived, after the importance of the termQ determining variance and covariance has been briefly pointed out.