Calculates the joint cumulative distribution function of order statistics of n iid. U(0,1)-distributed random variables at argument vec. Because of numerical issues n should not be greater than 100.
jointCDF.orderedUnif(vec)The return value is the following probability P(U_(1:n) <= vec[1], ..., U_(n:n) <= vec[n]), where U_1, ..., U_n are assumed to be iid. uniformly distributed on [0,1]. The i-th ordered value is denoted by U_(i:n) and n equals length(vec)
MarselScheer
a numeric vector. The length of the vector also determines the number of random variables considered.
Following Shorack, Wellner (1986) or Finner, Roters (2002) by applying Bolshev's recursion the joint distribution is calculated.
Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.
Finner, H. and Roters, M. (2002). Multiple hypotheses testing and expected type I errors. Ann. Statist. 30, 220-238.