CooccurrenceAffinity (version 1.0)

EHypQuInt: Interval of alpha values for which X is a specified q'th quantile

Description

This function outputs the largest interval of log-odds parameter values alpha for which the Extended Hypergeometric distribution function at x is >= q and the complementary distribution function 1 - F(x-) is >= 1-q.

Usage

EHypQuInt(x, marg, q, scal = log(2 * marg[3]^2))

Value

This function returns the vector (a1, a2) defined above, the endpoints of the set of alpha values for which x is a q'th quantile of the Extended Hypergeometric distribution.

Arguments

x

integer co-occurrence count that should properly fall within the closed interval [max(0,mA+mB-N), min(mA,mB)]

marg

a 3-entry integer vector (mA,mB,N) consisting of the first row and column totals and the table total for a 2x2 contingency table

q

a quantile falling strictly between 0 and 1

scal

an integer parameter (default 2*N^2, capped at 10 within the function) that should be 2 or greater

Author

Eric Slud

Details

This function outputs the endpoints a1, a2 defined by

F(x, a1) = q and F(x-1, a2) = q

where F(z, a) = F(z, mA,mB,N, exp(a)) is the extended Hypergeometric distribution function.

The interval of alpha values with these endpoints a1, a2 is viewed as the set of alpha values "compatible" with x being a q'th quantile for the Extended Hypergeometric.

Examples

EHypQuInt(30,c(50,80,120), 0.95)
EHypQuInt(30,c(50,80,120), 0.05)

EHypQuInt(30,c(50,80,120), 0.5)
AlphInts(30,c(50,80,120), lev=0.9)$MedianIntrvl