RichardsCurve Class

public class RichardsCurve : NonlinearCurve

Public Class RichardsCurve
	Inherits NonlinearCurve

public ref class RichardsCurve : public NonlinearCurve

type RichardsCurve = 
    class
        inherit NonlinearCurve
    end

Inheritance

Object  →  Curve  →  NonlinearCurve  →  RichardsCurve

Use the RichardsCurve class to represent a five-parameter Richards curve, also known as the generalized logistic curve. It provides a flexible family of sigmoidal curves that includes the logistic and Gompertz curves as special cases.

The Richards curve is widely used in growth modeling because it can accommodate asymmetric growth patterns through its shape parameter ν. When ν = 1, it reduces to the logistic curve; as ν approaches infinity, it approaches the Gompertz curve; and when ν = 2, it yields a symmetric curve similar to the logistic but with different parameterization.

The equation is:

Parameters:

• A – Upper asymptote (maximum value minus baseline). See Amplitude.
• ν – Shape parameter (controls asymmetry). See Shape.
• k – Growth rate parameter. See GrowthRate.
• x₀ – Inflection point location. See InflectionPoint.
• C – Baseline offset (lower asymptote). See Offset.

Applications:

• Flexible growth modeling (population, tumor, crop)
• Pharmacokinetic dose-response with asymmetry
• Epidemic modeling with varied progression rates
• Product adoption curves
• Learning curves and skill acquisition

For details on how to fit a curve of this type, see the NonlinearCurveFitter class.

Reference