logistic2_fn {drda}

2-parameter logistic function

Description

Evaluate at a particular set of parameters the 2-parameter logistic function.

Usage

logistic2_fn(x, theta)

Arguments

x

numeric vector at which the logistic function is to be evaluated.

theta

numeric vector with the four parameters in the form c(alpha, delta, eta, phi). alpha can only be equal to 0 or 1 while delta can only be equal to 1 or -1.

Details

The 2-parameter logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = 1 / (1 + exp(-eta * (x - phi)))⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

where theta = c(alpha, delta, eta, phi) and eta > 0. Only eta and phi are free to vary (therefore the name) while vector c(alpha, delta) is constrained to be either c(0, 1) (monotonically increasing curve) or c(1, -1) (monotonically decreasing curve).

This function allows values other than 0, 1, -1 for alpha and delta but will coerce them to their proper constraints.

Value

Numeric vector of the same length of x with the values of the logistic function.