R: Joint cumulative distribution function of order statistics of...
jointCDF.orderedUnif
R Documentation
Joint cumulative distribution function of order statistics of n iid. U(0,1)-distributed random variables
Description
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.
Usage
jointCDF.orderedUnif(vec)
Arguments
vec
a numeric vector. The length of the vector also
determines the number of random variables considered.
Details
Following Shorack, Wellner (1986) or Finner, Roters (2002) by applying
Bolshev's recursion the joint distribution is calculated.
Value
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)
Author(s)
MarselScheer
References
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.