CurveExpert Professional 1000-Model Regression Library

A production library of 1,000 one-dimensional custom regression models for CurveExpert Professional, organised into 71 scientific, engineering, and statistical families.

The package contains:

• 500 general scientific and engineering models;
• 500 dedicated statistical models;
• one Python file per operational model;
• no more than five fitted parameters per model;
• data-dependent initialisation and multi-start screening;
• numerical safeguards for common domain and overflow problems;
• consistent model names, parameter names, and CurveExpert result displays.

CurveExpert Professional is separate software and is not distributed with this repository.

Why these are models

This repository provides custom regression models for CurveExpert Professional. Each model contains one or more free parameters that CurveExpert estimates from the supplied dataset. The fitting engine adjusts those parameters to minimise the difference between the model prediction and the observed response.

This differs from a fixed mathematical expression whose numerical coefficients are already known and which is only evaluated or plotted. Such an expression performs no parameter estimation and no regression against the dataset.

Characteristic	Regression models in this repository	Fixed mathematical expressions
Main purpose	Fit experimental or observed data	Evaluate a predefined expression
Free parameters	Present and estimated by CurveExpert	Absent
Dependence on data	Parameters are optimised from the dataset	No parameter fitting is performed
Typical result	Best-fit parameters, residuals, uncertainty, and fit statistics	Direct numerical values and plots
Included here	All 1,000 supplied files	None

Throughout this README, every installable CurveExpert item supplied by the library is referred to as a model.

Package contents

curveexpert_1000_models/
|-- INSTALL.bat
|-- README.md
|-- build_library.py
`-- models/
    `-- 1000 CurveExpert custom-model files

Requirements

• Windows
• CurveExpert Professional
• Python 3 only when rebuilding, validating, installing from source, listing families, or uninstalling through build_library.py

CurveExpert Professional is normally installed in:

C:\Program Files\CurveExpert Professional

The CurveExpert custom-model directory is:

%USERPROFILE%\.curveexpert\lib\2D\Custom

One-click installation

1. Close CurveExpert Professional.
2. Extract the repository or release archive to a writable folder.
3. Open the extracted curveexpert_1000_models folder.
4. Double-click INSTALL.bat.
5. Confirm that the installer reports 1,000 copied models.
6. Restart CurveExpert Professional.
7. Open a dataset.
8. Select Calculate -> Nonlinear Model Fit -> Custom.
9. Locate models whose names begin with EXT.

Important: the installer removes existing ext_*.py, ext_*.pyc, and ext_*.pyo files from the CurveExpert custom-model directory before copying this library. Back up any unrelated personal models that use the same filename prefix.

Manual installation

1. Close CurveExpert Professional.
2. Open the repository's models directory.
3. Copy all ext_*.py files to %USERPROFILE%\.curveexpert\lib\2D\Custom.
4. Remove stale ext_*.pyc and ext_*.pyo files from the destination.
5. Restart CurveExpert Professional.

Using the library

All models use one independent variable and one measured response.

For routine analysis:

1. Verify the input columns, units, decimal separators, missing values, duplicated observations, and weighting data.
2. Open Calculate -> Nonlinear Model Fit.
3. Expand the Custom group.
4. Select a limited set of relevant EXT models.
5. Run the fit and inspect the curve, residuals, standard error, parameter values, uncertainty, and extrapolation behaviour.

Do not select all 1,000 models for ordinary datasets. Choose candidate families according to the expected curve shape, valid input domain, scientific meaning, observation count, and intended prediction range.

Quick family selection guide

Data behaviour or application	Suggested family groups
Power scaling or elasticity	Power and Scaling; Transformed Response and Elasticity
Exponential rise or decay	Exponential and Decay; Kinetic and Transient
Sigmoid, growth, or adoption	Sigmoidal and Growth; Asymmetric Sigmoids; Epidemic and Adoption Curves
Saturation or finite capacity	Saturation and Hyperbolic; Adsorption and Saturation; Hill and Dose Response
Single peak	Peak and Distribution; Chromatography and Separation; Optical Spectroscopy and Line Shapes
Multiple peaks	Multi-Peak Mixtures; Statistical Mixture Density Curves
Oscillation or resonance	Periodic and Oscillatory; Spectral and Wave Packets; Frequency Response and Resonance
Threshold or activation	Threshold and Activation; Smooth Transition and Piecewise
Probability density	Statistical Density Kernels; Statistical Skew and Heavy-Tail Curves
Cumulative probability or survival	Probability CDF and Survival; Statistical CDF and Survival Extensions
Hazard or cumulative hazard	Statistical Hazard and Cumulative Hazard
Quantile or rank	Statistical Quantile and Rank Curves
Extreme-value behaviour	Extreme Value and Heavy Tail; Statistical Extreme-Value Extensions
Count response or dispersion	Statistical Count Mean and Dispersion
Robust fitting models	Statistical Robust Influence and Weight Curves
Autocorrelation or covariance	Statistical Time-Series Correlation; Statistical Covariance Models
Spectral density	Statistical Spectral-Density Models
Variogram or geostatistics	Statistical Variogram Models
Smoothing or basis models	Statistical Kernel Models; Statistical Smoothing and Basis Curves
Reliability growth or renewal	Statistical Reliability Growth and Renewal

Model families

General scientific and engineering families — 500 models

1. Power and Scaling
2. Exponential and Decay
3. Logarithmic and Hybrid
4. Rational and Pade
5. Sigmoidal and Growth
6. Hill and Dose Response
7. Peak and Distribution
8. Adsorption and Saturation
9. Kinetic and Transient
10. Periodic and Oscillatory
11. Rheology and Transport
12. Smooth Transition and Piecewise
13. Polynomial and Basis Expansions
14. Inverse and Reciprocal
15. Saturation and Hyperbolic
16. Probability CDF and Survival
17. Extreme Value and Heavy Tail
18. Diffusion and Transport Profiles
19. Population and Ecological
20. Enzyme and Binding Kinetics
21. Reliability and Fatigue
22. Geotechnical and Hydraulic
23. Thermal and Reaction Engineering
24. Finance and Economic Growth
25. Spectral and Wave Packets
26. Asymmetric Sigmoids
27. Multi-Peak Mixtures
28. Threshold and Activation
29. Kernel and Basis Models
30. Orthogonal Polynomial Series
31. Transformed Response and Elasticity
32. Pharmacokinetic Profiles
33. Epidemic and Adoption Curves
34. Soil Water and Hydrology
35. Coastal and Ocean Engineering
36. Viscoelastic Relaxation and Creep
37. Electrochemical and Battery
38. Chromatography and Separation
39. Turbulence, Boundary Layer, and Flow
40. Fracture, Damage, and Creep
41. Optical Spectroscopy and Line Shapes
42. Learning, Performance, and Queueing
43. Atmospheric and Environmental
44. Particle Size and Mineral Processing
45. Neural Activation and Soft Nonlinearity
46. Frequency Response and Resonance

Dedicated statistical families — 500 models

47. Statistical Density Kernels
48. Statistical CDF and Survival Extensions
49. Statistical Hazard and Cumulative Hazard
50. Statistical Count Mean and Dispersion
51. Statistical GLM Inverse Links
52. Statistical Robust Influence and Weight Curves
53. Statistical Kernel Models
54. Statistical Skew and Heavy-Tail Curves
55. Statistical Mixture Density Curves
56. Statistical Order-Statistic Curves
57. Statistical Quantile and Rank Curves
58. Statistical Extreme-Value Extensions
59. Statistical Survival Cure and Frailty
60. Statistical Time-Series Correlation
61. Statistical Spectral-Density Models
62. Statistical Covariance Models
63. Statistical Variogram Models
64. Statistical Bayesian Prior Shapes
65. Statistical Entropy and Information Curves
66. Statistical Power and Operating-Characteristic Curves
67. Statistical Bounded-Response Models
68. Statistical Zero-Inflated and Hurdle Models
69. Statistical Smoothing and Basis Curves
70. Statistical Distribution Transformations
71. Statistical Reliability Growth and Renewal

Data preparation

Nonlinear regression is more stable when the independent variable, response, and main parameter scales are reasonably comparable.

Recommended checks:

• use more observations than fitted parameters;
• remove or investigate invalid and missing values;
• verify duplicated observations and measurement limits;
• scale variables that span many orders of magnitude;
• retain sufficient data across transitions, peaks, thresholds, and tails;
• include enough cycles for periodic models;
• ensure that the selected model is valid over the input range;
• treat extrapolation beyond the observed range with caution.

A numerical convergence result does not prove that a model is unique, identifiable, physically meaningful, or suitable for prediction.

Numerical design

The operational model files include:

• finite input-array conversion;
• protected logarithms, roots, divisions, powers, and inverse mathematical operations;
• bounded exponential and hyperbolic evaluations;
• input-domain preparation for positive, non-negative, bounded, and greater-than-one variables;
• data-dependent location, scale, baseline, amplitude, and rate estimates;
• deterministic screening of multiple starting candidates;
• local numerical refinement of the selected initial parameter vector;
• finite-result checks;
• a maximum of five fitted parameters per model.

These protections improve numerical robustness but cannot make an unsuitable model scientifically valid.

Statistical interpretation

CurveExpert performs curve fitting. Statistical-shaped models should be supplied with suitable processed data.

Model type	Appropriate input
Density	Density estimates or normalised histogram ordinates
Cumulative distribution	Empirical cumulative probability against ordered values
Survival	Estimated survival probability against time or exposure
Hazard	Estimated hazard against time
Quantile	Probability or plotting position against observed quantiles
Covariance or autocorrelation	Lag against an empirical dependence estimate
Spectral density	Frequency against an estimated spectrum
Variogram	Separation distance against empirical semivariance

Fitting one of these curves by least squares is not a replacement for a complete likelihood-based, censored-data, time-series, or geostatistical analysis when such methods are required.

Source commands

Run these commands from the repository directory:

py -3 build_library.py all
py -3 build_library.py build
py -3 build_library.py validate
py -3 build_library.py readme
py -3 build_library.py install
py -3 build_library.py list
py -3 build_library.py uninstall

Typical purposes:

Command	Purpose
all	Build and validate the complete library
build	Generate operational model files
validate	Check the generated library
readme	Regenerate repository documentation
install	Install models in the CurveExpert user library
list	List available model families
uninstall	Remove this library's installed models

Troubleshooting

Models are not visible

• Confirm that the files exist in %USERPROFILE%\.curveexpert\lib\2D\Custom.
• Restart CurveExpert Professional after installation.
• Confirm that the dataset has one independent variable.
• Inspect the CurveExpert Messages pane for import errors.

A fit does not converge

• Check the valid input domain.
• Scale the input and response data.
• Select a simpler related model.
• Reduce the number of candidate models.
• Check whether the available observations can identify every fitted parameter.
• Inspect duplicated points, outliers, censoring, and instrument limits.

A fitted result is implausible

• Check parameter signs, magnitudes, units, and uncertainty.
• Inspect residual patterns and extrapolation.
• Compare the result with known physical or statistical limits.
• Reject models that fit numerically but have no valid interpretation for the dataset.

Uninstallation

Run:

py -3 build_library.py uninstall

Alternatively, close CurveExpert Professional and remove this library's ext_*.py, ext_*.pyc, and ext_*.pyo files from:

%USERPROFILE%\.curveexpert\lib\2D\Custom

Library summary

• Families: 71
• Models: 1,000
• General scientific and engineering models: 500
• Dedicated statistical models: 500
• Independent variables per model: 1
• Maximum fitted parameters per model: 5