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.

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.

Value

The left inverse of the CDF evaluated at p.

Details

This algorithm works by progressively cutting the specified range in half, moving into the left or right half depending on where the solution is.

Examples

d <- distribution(cdf = \(x) pmin(pmax(x, 0), 1))
distionary:::directional_inverse(
  d,
  p = 0.2, low = 0, high = 1, tol = 1e-9, maxiter = 200L,
  direction = "left"
)
#> [1] 0.2