Five-Parameter Generalised Logistic (Richards) Forward Function

A five-parameter generalised logistic curve with asymmetry: $$y = a + (d - a)\,\bigl(1 + g\,\exp(-b\,(x - c))\bigr)^{-1/g}$$

Usage

loglogistic5(x, a, b, c, d, g)

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).

g

Numeric scalar. Asymmetry (Richards) parameter (\(g > 0\)).

Value

Numeric vector of predicted response values.

Details

When \(g = 1\) this reduces to logistic4() (after rescaling \(b\)). Works with any real \(x\) (including log10-transformed).

See also

Other forward-models: gompertz4(), logistic4(), logistic5(), loglogistic4()