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

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3
votes
3answers
180 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. ...
4
votes
1answer
75 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 ...
3
votes
0answers
54 views

LinearModelFit gives bad fit for simple data set [closed]

I want to fit the rather simple data set: ...
0
votes
1answer
84 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 ...
2
votes
2answers
260 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 ...
-2
votes
1answer
101 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 ...
0
votes
0answers
58 views

FindFit giving many errors when given model produced by ParametricNDSolveValue

I am trying to use FindFit to determine 7 parameters using 7 differential equations based on data imported from Excel. A sample of the data is: ...
8
votes
2answers
121 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 ...
0
votes
2answers
73 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 ...
1
vote
0answers
158 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. ...
1
vote
1answer
98 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
1
vote
0answers
48 views

Problem with curve fit using integral [closed]

I need fitting a Langevin function on a experimental data, but one parameter must be firstly optimized by using a Lognormal distribution. The complete expression could be written as: The integrate ...
1
vote
2answers
127 views

stop rule for Nonlinearfit and best fit

I want to understand the rule under which the function Nonlinearfit stops to give the final result. I know that if the number of iterations exceeds ...
2
votes
1answer
65 views

Negative adjusted coefficients of determination - why?

I am trying to fit a polynomial function to some multi-dimensional data. However, I am getting a negative $R_{adj}^2$ as you can see: ...
1
vote
2answers
54 views

Find function to relate two lists of values

I know Mathematica has the FindFit function to determine the parameters of a known function that fits a sequence of points, but what if you do not know the relationship (linear, log, quadratic, etc)? ...
2
votes
2answers
108 views

Solving coupled ODEs with NDSolve to fit experimental data

I need to fit a multi-exponential data (Intensity x Time) using a model consisting of three differential equations. I want to find the parameters that gives the best fit to the experimental data. ...
2
votes
1answer
216 views

Non-linear curve fit problem

I am having a problem with making a fit to data in Mathematica, which may involve my understanding of the methods available. I am trying to fit the derivative of a Frota function (which is a Single ...
1
vote
3answers
190 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} }]; ...
4
votes
2answers
139 views

Problem with fit on a numerical function

My question is related to a previous one: Problem with simple fit, where I had a problem to fit a simple analytic function $\dfrac{a}{\sqrt{b^2-x^2}}$. The solution proposed in Problem with simple ...
4
votes
2answers
96 views

Problem with a simple Fit

I have defined two functions to fit $\dfrac{a}{\sqrt{x^2-b^2}}$ and $\dfrac{a}{\sqrt{b^2-x^2}}$. ...
0
votes
0answers
29 views

Save lists to re-open with Mathematica [duplicate]

I want to save a result of a computation in a file to re-open then in Mathematica in a new session. What is the most efficient and simple way to do this? To be specific, I am using ...
1
vote
0answers
45 views

Evaluation of likelihood very slow

I am trying to implement a simple statistical model for the first time in Mathematica. My model is made my one random variable which is the sum of background and signal. Background is an exponential ...
7
votes
0answers
122 views

FindFormula Control [closed]

FindFormula is great start on the path to full symbolic regression and I realize it's level of development is only experimental at this stage. But if I happen to ...
10
votes
1answer
294 views

Fittting data with combination of an unknown number of Gaussians

I have data that I want to fit with a constant plus a combination of Gaussians, with their actual number being one parameter of the fit (besides the average and the variance of every one of them). ...
0
votes
1answer
55 views

Extract coefficient from LinearModelFit [closed]

I want to know how to extract the coefficients from the result of LinearModelFit. The functions used to fit are complicated and being in different forms. For ...
6
votes
1answer
94 views

Extracting fit weights directly from a FittedModel object

Suppose I have the following data: ...
7
votes
3answers
195 views

Fitting data with interdependence

I have an issue, of which I'm not sure it can be solved, with or without Mathematica. I feel as if it should be possible, but I'm quite clueless as to how. Some introduction is required. I'm working ...
3
votes
2answers
181 views

Automatically detect higher slope in numerical data (within a certain range)

Suppose the dataset data is part of some simulations whose results should follow a certain model. Here is data and its ...
1
vote
1answer
146 views

Linear Fit of multidimensional data

I am trying to find linear decomposition of vector B (of arbitrary dimension $n$) in the form : $B = \alpha_{1} C_{1} + \alpha_{2} C_{2} + ...$ where $C_{i}$ are known vectors (of dimension $n$) ...
2
votes
2answers
238 views

Finding the FWHM of a NonlinearModelFit gaussian [duplicate]

I have a NonlinearModelFit in a very large program, f1 = NonlinearModelFit[d1, a Exp[-(b (x - c1))^2] + yoff, {a, b}, x] Which is used in my program to produce ...
19
votes
2answers
390 views

Sensitivity of NonlinearModelFit to model

I have come across a circumstance where NonlinearModelFit is very sensitive to the model used. I am aware that NonlinearModelFit ...
7
votes
3answers
171 views

Make NonlinearModelFit return continuous function

Suppose I want to fit the dataset ...
4
votes
0answers
167 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
3
votes
2answers
148 views

Estimate parameters of AR1 process

I am trying to estimate the parameters of a series $Z_t=W_t^\beta$, where W_t follows an AR1 process with mean 2, $\rho=0.9$ and $\sigma=0.1$: $W_t = \rho W_{t-1} + (1-\rho) \bar{W} + \epsilon_t$ ...
2
votes
1answer
158 views

Why does FindFit work and NonlinearModelFit does not?

I have a somewhat complicated function that I have defined. ...
4
votes
2answers
100 views

How to use Evaluation Monitor in conjunction with NonlineaModelFit?

I am trying to find out how many function, gradient and hessian evaluations are made when i run NonlinearModelFit for example in this case ...
0
votes
1answer
136 views

How to speed up NonlinearModelFit applied on a NDSolve solution?

I'm trying to perform fittings of a model defined through a system of ODEs to data consisting of time courses of a measured quantity. As described in a previous question, the system of ODEs is as ...
2
votes
1answer
195 views

Fitting one set of data with two function

I have a set of data (42 points): ...
2
votes
1answer
101 views

Fails to apply NonlinearModelFit on a numerically evaluated model defined as a system of ODEs

I call for your help with because I'm getting troubles to fit a model defined through a system of ODEs. The system of ODEs is as follows: ...
5
votes
1answer
228 views

How are p-values in fittings estimated?

I am trying to understand how p-values retrieved in a ParameterTable estimated but I couldn't find any specific information in the documentation about this. For instance, considering ...
1
vote
0answers
111 views

NonlinearModelFit::nrnum error [closed]

I'm trying to fit data (including some small negative numbers at both extremes) to a normal distribution. ...
-1
votes
1answer
71 views

Pulling variable out of NonlinearModelFit [closed]

I have a fit, Dynamic[f1 = NonlinearModelFit[d1, a Exp[-(b (x - c1))^2] + yoff, {a, b}, x]] Where I need to be able to access ...
3
votes
2answers
553 views

Gauss Fit to List of 2D Points

I've been trying to find a solution to what I think is a common problem. I have a list of Data like ...
6
votes
1answer
177 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. ...
0
votes
0answers
72 views

Modify measured values to improve NonlinearModelFit results

Problem: Measured data points have a random distribution of DC offsets (either +/- 0.65 mV), that came from an incorrect setting on the 24-bit ADC we were using. Essentially for each measured voltage ...
1
vote
1answer
115 views

Problem fitting when some data is missing

I have a problem fitting a function to data, where I only have the falling and rising edges of the data, with the peak having been capped and was wondering if you have some tips. The data should have ...
34
votes
3answers
764 views

What is behind experimental function: FindFormula?

In version 10.2 there is a new experimental function: FindFormula[]. I suspect that a genetic programming algorithm (symbolic regression) is behind this new ...
3
votes
0answers
101 views

How to find the best fit for given input data? [closed]

I have the following data: ...
2
votes
1answer
108 views

Still more problems with Fitting, please help

I'm in a little over my head here and I'm fully aware of it, so I'm hoping for some help. I've been assigned to a project where I am given data: http://www.pastebin.ca/3061136 (Example Data) I ...
2
votes
3answers
344 views

Fitting and plotting Weibull distribution

How can I find the best fitted 2-parameter Weibull's distribution (PDF) to describe my data? How can i plot my data and estimated distribution all in one graph? How can I show/compare results of ...