Four-Parameter Logistic (4PL) Forward Function

Computes the response for a four-parameter logistic curve: $$y = a + \frac{d - a}{1 + \exp\!\left(-\frac{x - c}{b}\right)}$$

Usage

logistic4(x, a, b, c, d)

Arguments

x

Numeric vector. Independent variable (typically log10-concentration).

a

Numeric scalar. Lower asymptote (baseline response).

b

Numeric scalar. Scale parameter (\(b > 0\)); controls steepness.

c

Numeric scalar. Inflection-point location on the x-axis.

d

Numeric scalar. Upper asymptote (saturation response).

Value

Numeric vector of predicted response values, same length as x.

Details

Symmetric about its inflection point at \((c, (a+d)/2)\). Always monotonically increasing when \(b > 0\) and \(a < d\).

See also

Other forward-models: gompertz4(), logistic5(), loglogistic4(), loglogistic5()