mutoss (version 0.1-10)

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

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)<="" dl="">

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.