jointCDF.orderedUnif: 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.
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)<="" li="">
Details
Following Shorack, Wellner (1986) or Finner, Roters (2002) by applying
Bolshev's recursion the joint distribution is calculated.
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.