Four-Parameter Gompertz Forward Function

Computes the response for a Gompertz saturation curve: $$y = a + (d - a)\,\exp\!\bigl(-\exp(-b\,(x - c))\bigr)$$

Usage

gompertz4(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.

Details

The Gompertz is intrinsically asymmetric (skewed toward the upper asymptote) without requiring a fifth parameter.

See also

Other forward-models: logistic4(), logistic5(), loglogistic4(), loglogistic5()