Algorithm to Compute a Directional Inverse — directional

Calculates the smallest value for which a function f evaluates to be greater than or equal to y – that is, the left inverse of f at y. Intended for internal use only.

Usage

directional_inverse(distribution, p, low, high, tol, maxiter, direction)

Arguments

distribution: A distribution having access to a cdf.
p: Single value for which to calculate the left inverse.
low, high: Single numeric values forming a range within which to search for the solution.
tol, maxiter: Tolerance (a small positive number) and maximum number of iterations
direction: One of "left" for calculating left-inverse, or "right" for calculating right-inverse.

Details

This algorithm works by progressively cutting the specified range in half, so that the width of the range after k iterations is 1/2^k times the original width.