Questions on the use of Mathematica to construct models for approximating empirical data.

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1
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1answer
82 views

Boundary parameter in Beta Distribution

I use EasyFit to find the probability distribution of my data. It turns out the data follows BetaDistribution with 0.54022,0.70601 shape parameters and 1.33,6.83 continuous boundary parameters I am ...
6
votes
2answers
217 views

Fitting does not work

I have a set of points, which is basically one minus a Lorentz curve. And the NonlinearModelFit ...
2
votes
1answer
98 views

Fitting a set of functions using same basis functions

I am trying to fit the functions in the plot below, but I need them to be fitted using the same basis functions. I want to interpolate between the functions by interpolating between their coefficients,...
6
votes
2answers
1k views

RSquared: LinearModelFit vs NonlinearModelFit

I'm trying to understand the differences between LinearModelFit and NonlinearModelFit. One thing I notice is that the ...
4
votes
1answer
1k views

Fitting piecewise functions

I have several large data sets which follow the following pattern: A position is measured, a force is applied until a new equilibrium is found. I'd like to find a fit for the position, at least at the ...
1
vote
1answer
81 views

Data fitted by two linear fits [duplicate]

can anybody help me please and tell me how to fit my set of points by two linear fits? It is always exactly two of them and are always linear and should cover all the data. The second line should ...
3
votes
1answer
53 views

Displacement around the x axis, how to change a function location

While plotting a function I want to change the location of x. I am doing a regression with the logistic function ...
0
votes
1answer
71 views

problems of Lorentizan fit with Nonlinear fit model [closed]

I tried to do a Lorentzian fit for a Spectroscopy data.I found that I have to actually give the precise value for this fit.[i do not like to call this as fit ,if that is the case]? Am I missing ...
0
votes
1answer
88 views

What´s wrong with my FindFit

I updated the data which is a table I deleted the first coordinate as it was the quote from the document. ...
0
votes
1answer
79 views

Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve, and then using FindFit. Therefore, I ...
1
vote
0answers
99 views

Fitting in Mathematica: Which function? [closed]

in other programs, there is a possibility to take a data set and to find the function which fits best. Is there also such a possibility in Mathematica? I only could find ...
2
votes
2answers
98 views

NonlinearModelFit gives imaginary numbers [duplicate]

I am having trouble using NonlinearModelFit to fit to data generated by the equation I am trying to fit to. ...
1
vote
1answer
96 views

Is there a built-in function implementing the minimum and maximum gradient?

Suppose I have a set of data. Mathematica has fitting functions to determine the line and corresponding equation to the best fit given any arbitrary set of data. But in experimental techniques, ...
1
vote
0answers
94 views

Fitting data using ParametricNDSolveValue and NonlinearModelFit [closed]

I'm trying to evaluate the kinetics of the chemical reaction. For that I need to fit my experimental data to the kinetic equation. These are my steps in Mathematica. ...
12
votes
2answers
1k views

Detecting an ellipse in a glaucoma photo

For glaucoma diagnosis it is common to determine a "cup to disk ratio" which compares the diameter of the optic disk (VDD) and optic cup (VCD). The optical disk is visible as a circular red feature (...
1
vote
0answers
73 views

Detecting and measuring an ellipse in a glaucoma photo? [duplicate]

I've tried the solutions given in How to find a circular object in the image glaucoma? to detect the ellipse, but the detection results are not quite what I wanted. In glaucoma we have a cup to disk ...
2
votes
1answer
161 views

Fitting to the system of equations with no analytical solution

I'm trying to fit linear combination of 2 functions to my experimental data set (it represents voltage of 2 photodiodes - Voc1 and Voc2 - connected in series under illumination - S) ...
4
votes
2answers
169 views

How to find analytical expresion for data from image

I need to find an analytical expression for the data collected from an image. I found a relevant topic on how to extract the data in here. But there are some differences in my question. I have this ...
2
votes
3answers
2k views
0
votes
0answers
48 views

Incorporating sophisticated constraints on the approximating function into NMinimize

Following the approach as given in the answer of Belisarius here I just wonder how one could incorporate some more sophisticated requirements on the approximating function. Suppose the approximating ...
7
votes
2answers
407 views

Maxwell fit in 2 dimensions

The histogram below shows the 2D-velocities v of a micrometer sized particle in a plasma measured from image to image (60 Hz) over 33,33 sec. I would like to fit ...
3
votes
1answer
148 views

Estimated Variance in LinearModelFit

Suppose that lmModel is a linear model which is fit using LinearModelFit. How come ...
4
votes
2answers
194 views

FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)

I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize. In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
3
votes
3answers
197 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
1
vote
0answers
59 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
6
votes
1answer
196 views

FindFormula can't deal with the population data from Wolfram server

Bug introduced in 10.2 and fixed in 10.3 In the documentation of FindFormula, the first application of it is to predict the population of Poland. ...
6
votes
1answer
246 views

Default algorithm in NonlinearModelFit

Does anyone know the default algorithm used in NonlinearModelFit? The documentation gives several possible algorithms, but I can't figure out what it uses if you do not specify the algorithm. Thanks.
23
votes
4answers
1k views

Generating an “average curve” from a dense set of “semicontinuous curves” which clear trends

This question is related to a previous one of mine: Partitioning a superset of coordinates into subsets that generate continuous curves, where the challenge was to partition a data set into two ...
6
votes
2answers
4k views

NonlinearModelFit Problem

I have some problems with the NonlinearModelFit: NonlinearModelFit[data, A (1 + Cos[a x]) + B (1 + Cos[b x]) + c , {A, B, a, b, c}, x] The model should fit my ...
1
vote
1answer
110 views

FindFit algorithm?

Does anyone know how to program a mathematica algorithm that does the same thing that FindFit does? Is there documentation of it somewhere? I assume it is a least ...
14
votes
2answers
1k views

What is the difference between FindFit and NonlinearModelFit

I cannot get the difference between these two fitting functions in Mathematica. I even read in MMA that the result of these two are the same.
0
votes
0answers
33 views

EstimatedBackground function on Mathematica 9

Is there a way to replicate the EstimatedBackground function on Mathematica 9?
5
votes
3answers
252 views

Removing background from peak function

Let's say I have a a very large list of data in the format {{n,f[n]}} so something like {{1,600},{2,700},{3,1100}...} and if this data is plotted, then it will look like a sum of Gaussian functions+a ...
0
votes
0answers
62 views

Using the results of FindPeak in FindFit

Using FindPeak on some datapoints, I have found the positions and values of likely Gaussian peaks which form the data. The format is ...
1
vote
1answer
106 views

Using List/Histogram Data As A Weighted Function?

I have a list of data points that I would like to use as a weighted function. The data represents the number of particles within a bin of a particle distribution. Ultimately I would like to multiply ...
4
votes
1answer
78 views

Proper command to fit a distribution with data incomplete in a known way

Here is my scenario: got some data that I have to fit to a specific parametric family of probability distributions (cannot be changed). Data consist of several bunches of integers between, say, 0 and ...
1
vote
0answers
160 views

NonLinearFit running too slowly when the model contains an integral [closed]

I am new to Mathematica and am learning to use it. I have come up with the following situation where I have to fit the data. ...
3
votes
0answers
61 views
11
votes
1answer
221 views

How can the Theil-Sen estimator be made to work on larger datasets?

The Theil-Sen estimator finds the slope and intercept of a line passing through a set of points by calculating the median slope and median intercept of the set of lines passing through all possible ...
19
votes
4answers
2k views

Implementation of smoothing splines function

I have some problems in writing a module for spline smoothing. Actually, I have been trying for about two weeks. My listing is here: ...
2
votes
2answers
330 views

Help with NonLinearModelFit

I have a question about fitting data with a model. I have a quite complicated model, based on Arctans, modified Bessel functions, etc, that I want to fit to my data, a table of couples (minimal ...
0
votes
1answer
96 views

Meaning of << >> in Mathematica [duplicate]

I used NonlinearModelFit to fit some data and although Mathematica thinks it has got the result, the answer is enclosed in these double angular brackets. What does it mean? More importantly, I cannot ...
1
vote
1answer
186 views

Efficiency problem with least square algorithm (Error in both variables)

I was informing myself about the least square algorithms with errors in x and y. I found this post and the top answer wasn't ...
-2
votes
1answer
115 views

A piecewise function with way too many pieces

I'm currently calculating a periodic square wave current function to feed into a particle accelerator. It's a square wave that ramps up to a certain frequency and then drops back to the base frequency ...
8
votes
2answers
123 views

Behaviour of RegionDistance with Ellipse?

The data is: data = {{13, 60}, {36, 35}, {70, 29}, {106, 41}, {118, 72}, {94, 94}, {49, 99}, {24, 85}}; When I try to find a fit circle,So my method is work ...
34
votes
5answers
3k views

Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
0
votes
2answers
79 views

Fit a polynomial/curve to an NIntegrate result

I want to NIntegrate a function which also contains some parameter. In the end, I would like to plot the result as a function of one of these parameters. The thing ...
2
votes
2answers
180 views

BSpline or other curve through arbitrary ordered sequence of two-dimensional points

How does one create a BSplineCurve or other smooth curve passing through each point in an ordered list, where the curve may be non-simple, i.e., can double-back ...
1
vote
1answer
103 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
1
vote
3answers
203 views

Fit dataset with customized discontinuous distribution

I have the following parametric CDF: F[x_, λ_, β_, γ_] = Piecewise[{ {0, x < 0}, {1 - (1 - β) E^(-x λ), 0 <= x < γ }, {1, x >= γ} }]; ...