jointCDF.orderedUnif: Joint cumulative distribution function of order statistics of...

In mutoss: Unified Multiple Testing Procedures

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.

mutoss documentation built on March 31, 2023, 8:46 p.m.