Non-Linear Models

09.03.2021

A series of pre-defined models exist that are classified into different categories. For almost all of these models, the partial derivatives are specified so that they can be calculated analytically and no approximation of the derivatives is necessary.

EXPONENTIAL FUNCTIONS

Box and Lucas (variant 1)

2 Parameters

Constant: MODEL_EXP_BOXLUCAS1

Box and Lucas (variant 2)

2 Parameters

Constant: MODEL_EXP_BOXLUCAS2

Box and Lucas (variant 3)

2 Parameters

Constant: MODEL_EXP_BOXLUCAS3

Chapman model

3 Parameters

Constant: MODEL_EXP_CHAPMAN

Exponential function

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL

Exponential associate

 

5 Parameters

Constant: MODEL_EXP_EXPONENTIAL_ASSOCIATE

Exponential decay function (variant 1)

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY1

Exponential decay function (variant 2)

5 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY2

Exponential decay function (variant 3)

 

 

7 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY3

Exponential decay function (variant 4)

4 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY4

Exponential decay function (variant 5)

6 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY5

Exponential decay function (variant 6)

8 Parameters

Constant: MODEL_EXP_EXPONENTIAL_DECAY6

Exponential growth function (variant 1)

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW1

Exponential growth function (variant 2)

5 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW2

Exponential growth function (variant 3)

7 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW3

Exponential growth function (variant 4)

4 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW4

Exponential growth function (variant 5)

6 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW5

Exponential growth function (variant 6)

8 Parameters

Constant: MODEL_EXP_EXPONENTIAL_GROW6

Exponential linear combination

4 Parameters

Constant: MODEL_EXP_EXPONENTIAL_LINEAR

Exponential function with 1 parameter (variant 1)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA1

Exponential function with 1 parameter (variant 2)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA2

Exponential function with 1 parameter (variant 3)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA3

Exponential function with 1 parameter (variant 4)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA4

Exponential function with 1 parameter (variant 5)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA5

Exponential function with 1 parameter (variant 6)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA6

Exponential function with 1 parameter (variant 7)

1 Parameter

Constant: MODEL_EXP_EXPONENTIAL_ONEPARA7

Exponential function with 2 parameters (variant 1)

2 Parameters

Constant: MODEL_EXP_EXPONENTIAL_TWOPARA1

Exponential function with 2 parameters (variant 2)

2 Parameters

Constant: MODEL_EXP_EXPONENTIAL_TWOPARA2

Exponential function with 2 parameters (variant 3)

2 Parameters

Constant: MODEL_EXP_EXPONENTIAL_TWOPARA3

Exponential function with 3 parameters (variant 1)

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL_THREEPARA1

Exponential function with 3 parameters (variant 2)

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL_THREEPARA2

Exponential function with 3 parameters

(variant 3)

 

3 Parameters

Constant: MODEL_EXP_EXPONENTIAL_THREEPARA3

Monomolecular growth model (variant 1)

3 Parameters

Constant: MODEL_EXP_MONOMOLECULAR1

Monomolecular growth model (variant 2)

3 Parameters

Constant: MODEL_EXP_MONOMOLECULAR2

Shaw model

4 Parameters

Constant: MODEL_EXP_SHAW

Stirling model

3 Parameters

Constant: MODEL_EXP_STIRLING

Time-power model

3 Parameters

Constant: MODEL_EXP_TIMEPOWER

Asymptotic regression model (variant 1)

3 Parameters

Constant: MODEL_EXP_YIELDFERTILIZER1

Asymptotic regression model (variant 2)

3 Parameters

Constant: MODEL_EXP_YIELDFERTILIZER2

GROWTH FUNCTIONS

Boltzmann model

4 Parameters

Constant: MODEL_GROWTH_BOLTZMANN

Gompertz model

3 Parameters

Constant: MODEL_GROWTH_GOMPERTZ

Hill model

3 Parameters

Constant: MODEL_GROWTH_HILL

Logistic Dose response model

4 Parameters

Constant: MODEL_GROWTH_LOGISTICDOSERESPONSE

Logistic model (variant 1)

3 Parameters

Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC1

Logistic model (variant 2)

3 Parameters

Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC2

Logistic model (variant 3)

3 Parameters

Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC3

Richards model

4 Parameters

Constant: MODEL_GROWTH_SIGMOIDALRICHARDS2

Weibull model (variant 1)

4 Parameters

Constant: MODEL_GROWTH_SIGMOIDALWEIBULL1

Weibull model (variant 2)

4 Parameters

Constant: MODEL_GROWTH_SIGMOIDALWEIBULL2

HYPERBOLA FUNCTIONS

Hyperbola function (variant 1)

2 Parameters

Constant: MODEL_HYPERBOLA_HYPERBOLA1

Hyperbola function (variant 2)

5 Parameters

Constant: MODEL_HYPERBOLA_HYPERBOLA2

Hyperbola function (variant 3)

4 Parameters

Constant: MODEL_HYPERBOLA_HYPERBOLA3

Hyperbola function (variant 4)

2 Parameters

Constant: MODEL_HYPERBOLA_HYPERBOLA4

Hyperbola function (variant 5)

2 Parameters

Constant: MODEL_HYPERBOLA_HYPERBOLA5

LOGARITHM FUNCTIONS

Bradley function

2 Parameters

Constant: MODEL_LOGARITHM_BRADLEY

Logarithm function (variant 1)

2 Parameters

Constant: MODEL_LOGARITHM_LOG1

Logarithm function (variant 2)

2 Parameters

Constant: MODEL_LOGARITHM_LOG2

Logarithm function (variant 3)

3 Parameters

Constant: MODEL_LOGARITHM_LOG3

Logarithm function (variant 4)

1 Parameters

Constant: MODEL_LOGARITHM_LOG4

PEAK FUNCTIONS

Asymmetric double sigmoidal model

5 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_ASYMMETRICDOUBLESIG

Beta function

5 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_BETA

Extreme function

3 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_EXTREME

Gauss model (variant 1)

3 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_GAUSS

Gauss model (variant 2)

3 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_GAUSSAMPLITUDE

Gram-Charlier model

5 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_GRAMCHARLIER

Inverse polynomial function

6 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_INVERSEPOLYNOMIAL

Logistic peak function

5 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_LOGISTICPEAK

Lognormal function

3 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_LOGNORMAL

Lorentz peak function

3 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_LORENTZIANPEAK

Pseudo-Voigt function (variant 1)

4 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_PSEUDOVOIGT1

Pseudo-Voigt function (variant 2)

5 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_PSEUDOVOIGT2

Weibull model

4 parameters + baseline parameter

Peak Function

Constant: MODEL_PEAK_WEIBULL

POWER FUNCTIONS

Belehradek model

3 Parameters

Constant: MODEL_POWER_BELEHRADEK

Bleasdale Nelder model

4 Parameters

Constant: MODEL_POWER_BLEASDALENELDER

Freundlich model (variant 1)

2 Parameters

Constant: MODEL_POWER_FREUNDLICH1

Freundlich model (variant 2)

3 Parameters

Constant: MODEL_POWER_FREUNDLICH2

Freundlich model (variant 3)

3 Parameters

Constant: MODEL_POWER_FREUNDLICHEXT

Gunary model

3 Parameters

Constant: MODEL_POWER_GUNARY

Harris model

3 Parameters

Constant: MODEL_POWER_HARRIS

Langmuir model (variant 1)

3 Parameters

Constant: MODEL_POWER_LANGMUIREXT1

Langmuir model (variant 2)

3 Parameters

Constant: MODEL_POWER_LANGMUIREXT2

Pareto model

1 Parameters

Constant: MODEL_POWER_PARETO

Exponential function (variant 1)

1 Parameters

Constant: MODEL_POWER_POWER1

Exponential function (variant 2)

2 Parameters

Constant: MODEL_POWER_POWER2

Exponential function (variant 3)

2 Parameters

Constant: MODEL_POWER_POWER3

Exponential function (variant 4)

2 Parameters

Constant: MODEL_POWER_POWER4

RATIONAL FUNCTIONS

BET model (variant 1)

2 Parameters

Constant: MODEL_RATIONAL_BET1

BET model (variant 2)

2 Parameters

Constant: MODEL_RATIONAL_BET2

Holliday model (variant 1)

3 Parameters

Constant: MODEL_RATIONAL_HOLLIDAY

Holliday model (variant 2)

3 Parameters

Constant: MODEL_RATIONAL_HOLLIDAYEXT

Nelder function

4 Parameters

Constant: MODEL_RATIONAL_NELDER

Rational function (variant 1)

3 Parameters

Constant: MODEL_RATIONAL_RATIONAL1

Rational function (variant 2)

3 Parameters

Constant: MODEL_RATIONAL_RATIONAL2

Rational function (variant 3)

3 Parameters

Constant: MODEL_RATIONAL_RATIONAL3

Rational function (variant 4)

3 Parameters

Constant: MODEL_RATIONAL_RATIONAL4

Rational function (variant 5)

3 Parameters

Constant: MODEL_RATIONAL_RATIONAL5

Reciprocal function (variant 1)

2 Parameters

Constant: MODEL_RATIONAL_RECI1

Reciprocal function (variant 2)

1 Parameters

Constant: MODEL_RATIONAL_RECI2

Reciprocal function (variant 3)

1 Parameters

Constant: MODEL_RATIONAL_RECI3

Reciprocal function (variant 4)

2 Parameters

Constant: MODEL_RATIONAL_RECI4

OTHER FUNCTIONS

Binding curve (variant 1)

2 Parameters

Constant: MODEL_PHARMA_BINDING1

Binding curve (variant 2)

4 Parameters

Constant: MODEL_PHARMA_BINDING2

Biphasic model

7 Parameters

Constant: MODEL_PHARMA_BIPHASIC

Competition curve (variant 1)

3 Parameters

Constant: MODEL_PHARMA_COMPETITION1

Competition curve (variant 2)

5 Parameters

Constant: MODEL_PHARMA_COMPETITION2

Dose response model

4 Parameters

Constant: MODEL_PHARMA_DOSERESPONSE

Sine function

3 Parameters

Constant: MODEL_WAVE_SINE

Damped sine function

4 Parameters

Constant: MODEL_WAVE_SINEDAMP

Square sine function

3 Parameters

Constant: MODEL_WAVE_SINESQUARE

NIST model Bennet5

3 Parameters

Constant: MODEL_NIST_BENNET5

NIST model Boxbod

2 Parameters

Constant: MODEL_NIST_BOXBOD

NIST model Chwirut

3 Parameters

Constant: MODEL_NIST_CHWIRUT

NIST model Danwood

2 Parameters

Constant: MODEL_NIST_DANWOOD

NIST model Eckerle4

3 Parameters

Constant: MODEL_NIST_ECKERLE4

NIST model Enso

9 Parameters

Constant: MODEL_NIST_ENSO

NIST model Gauss

8 Parameters

Constant: MODEL_NIST_GAUSS

NIST model Hahn1

7 Parameters

Constant: MODEL_NIST_HAHN1

NIST model Kirby2

6 Parameters

Constant: MODEL_NIST_KIRBY2

NIST model Lanczos

6 Parameters

Constant: MODEL_NIST_LANCZOS

NIST model MGH09

4 Parameters

Constant: MODEL_NIST_MGH09

NIST model MGH10

3 Parameters

Constant: MODEL_NIST_MGH10

NIST model MGH17

5 Parameters

Constant: MODEL_NIST_MGH17

NIST model Misra1A

2 Parameters

Constant: MODEL_NIST_MISRA1A

NIST model Misra1B

2 Parameters

Constant: MODEL_NIST_MISRA1B

NIST model Misra1C

2 Parameters

Constant: MODEL_NIST_MISRA1C

NIST model Misra1D

2 Parameters

Constant: MODEL_NIST_MISRA1D

NIST model RAT42

3 Parameters

Constant: MODEL_NIST_RAT42

NIST model RAT43

4 Parameters

Constant: MODEL_NIST_RAT43

NIST model Roszman1

4 Parameters

Constant: MODEL_NIST_ROSZMAN1

References

Seber G. A. F., Wild C. J. Nonlinear Regression. Wiley, New York, 2003.

The NIST models can be found on the Internet at: http://www.itl.nist.gov/div898/strd

See Also

Non-Linear Curve Fitting Analysis Object

Non-Linear Curve Fitting Tutorial

NonLinCurveFit Function

ParameterEstimation Function

NonLinModel Function

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