R_bounds function

Bounds for the correlation of two (or more) Benrnoulli random variables

Replaces impossible correlations (values too small or too large) with minimum and maximum correlations, respectively.

min_r(p1, p2)
max_r(p1, p2)
R.bounds(p, R, pad = 0.001)

Arguments

• p1: Probability of success for first random variable
• p2: Probability of success for second random variable
• p: Vector of marginal probabilities for multivariate Bernoulli random variables, for R.bounds.
• R: Raw correlation matrix for random variables
• pad: Padding (in correlation units) to adjust the returned correlation matrix with respect extremal values.

Details

The functions r.min and r.max define minimum and maximimum possible correlations. The function R.bounds replaces impossibly large or small values with maximally large or small values repectively.

Returns

Functions return a scalar defining minimum or maximimum possible correlations. See Aho et al. (2023).

Author(s)

Ken Aho

References

Aho, K., Derryberry, D., Godsey, S. E., Ramos, R., Warix, S., Zipper, S. (2023) The communication distance of non-perennial streams. EarthArXiv https://eartharxiv.org/repository/view/4907/

Examples

min_r(0.6, 0.9)
max_r(0.1, 0.2)

x1 <- rep(c(1,0),5)
x2 <- c(rep(1,7), rep(0,3))
x3 <- c(rep(1,3), rep(0,7))
R <- cor(cbind(x1, x2, x3))
R.bounds(c(0.5, 0.7, 1), R)