Download pro Fit 5.1 handbook - quantum

Frame............................................................................................................................ 32
Grid 32
Graph Styles................................................................................................................ 32
Graph coordinates and zooming ................................................................................. 34
8
Fitting.................................................................................................... 1
Mathematical background.....................................................................................................1
Distribution functions and data weights.........................................................................1
The mean square deviation: Chi-Squared...............................................................4
Zero X-errors ..................................................................................................................4
The “usual case”: Chi-squared and zero x-errors ...................................................4
Error analysis and confidence intervals ........................................................................5
Fitting algorithms................................................................................................................5
The Monte Carlo algorithm..........................................................................................6
The Levenberg-Marquardt algorithm.........................................................................6
Partial derivatives .....................................................................................................7
Estimation of parameter errors...............................................................................7
The Robust minimization algorithm............................................................................8
The Linear Regression algorithms.............................................................................9
The Polynomial fitting algorithm .............................................................................. 10
Goodness of fit................................................................................................................. 10
Literature and suggested reading ............................................................................... 10
The fitting process................................................................................................................ 11
General features ............................................................................................................. 11
Parameter limits.......................................................................................................... 11
Running a fit................................................................................................................. 12
Inspecting the progress of a fit ................................................................................. 14
Error analysis and confidence intervals................................................................. 14
Fitting results ............................................................................................................... 16
Using the various fitting algorithms ............................................................................. 16
Using the Levenberg-Marquardt algorithm ........................................................... 17
Using the Robust minimization algorithm .............................................................. 17
Using the Monte Carlo algorithm............................................................................. 17
Using the Linear Regression algorithm.................................................................. 18
Using the Polynomial fitting algorithm.................................................................... 19
Fitting multiple functions and x-values............................................................................. 19
Functions with multiple x-values.................................................................................. 19
Multiple functions with one x-value ............................................................................. 21
Multiple functions with multiple x-values.................................................................... 22
General hints for fitting ........................................................................................................ 24
Starting parameters........................................................................................................ 24
Redundancy of parameters........................................................................................... 24
The errors of the data set............................................................................................... 24
9
Defining functions and programs.......................................................... 1
Simple examples ....................................................................................................................2
Defining functions..............................................................................................................2
Defining programs.............................................................................................................5
Table of Contents
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