logistic4_fn {drda}R Documentation

4-parameter logistic function


Evaluate at a particular set of parameters the 4-parameter logistic function.


logistic4_fn(x, theta)



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


numeric vector with the four parameters in the form c(alpha, delta, eta, phi).


The 4-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), alpha is the value of the function when x -> -Inf, delta is the (signed) height of the curve, eta > 0 is the steepness of the curve or growth rate (also known as the Hill coefficient), and phi is the value of x at which the curve is equal to its mid-point.

When delta < 0 the curve is monotonically decreasing while it is monotonically increasing for delta > 0.

The mid-point ⁠f(phi; theta)⁠ is equal to alpha + delta / 2 while the value of the function for x -> Inf is alpha + delta.


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

[Package drda version 2.0.3 Index]