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

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11
votes
2answers
801 views

Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
6
votes
3answers
2k views

Finding the linear regression of data and plotting it

This is for a physics report that I have to hand in. I have a list of two-dimensional data points that approximately form a linear line. I want to: calculate the best linear fit. put both data ...
2
votes
1answer
337 views

non-linear trend reduction using thresholds

Doing some mappings of the earth magnetic field results in the left-hand figure below (which consists of 181 profiles): To improve this I tried a non-linear trend reduction using, for example, ...
4
votes
5answers
2k views

How to plot Fit functions?

If I do something like this f[x_]:=x^2 Plot[f[x],{x,1,10}] Mathematica plots the function $f(x)=x^2$, as expected. However, ...
0
votes
3answers
362 views

Creating simple procedure for The Least-Square $m^\text{th}$ Degree Polynomials

I am CS major, taking Computational Numerical Analysis course. Instructor gave us freedom of choice, we were allowed to use anything or any computer language we picked, I picked Mathematica.This is my ...
15
votes
1answer
931 views

Compact Rational Function Fitting

I have some data from a study that I am trying to fit with a rational function of arbitrary form: $y(x) = \frac{\sum_{i=n}^m A_ix^{i/q}}{\sum_{j=o}^p B_jx^{j/r}}$ where $i$, $j$, $k$, $l$, $m$, $n$, ...
2
votes
0answers
201 views

How to predict some constant number of values with NeuralNetworks

Example: << NeuralNetworks` data = {Sin[#]} & /@ Range[0, 4 Pi, 0.5]; learn = data[[1 ;; 15]]; Now, lets fit our neural network: ...
4
votes
1answer
496 views

Why FindFit could not exactly fulfill condition?

I tried to fit some data with boundary conditions, but FindFit just could not work. Does anyone know the reason? Details: The function to be fitted is ...
8
votes
3answers
869 views

Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
19
votes
2answers
1k views

Finding the area, algebraic curve and jaggedness of an arbitrary shape

I start with a photograph of a shape (physically made by the flow of a liquid into another), of which I can extract the border, manually or using Mathematica's feature detect feature : Using the ...
13
votes
3answers
1k views

Finding a fit to a multi-dimensioned function

I have a model function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, and a bunch of data points for which I'd like Mathematica to fit for me. Unfortunately FindFit ...
10
votes
2answers
311 views

Unexpected differences with various uses of NormFunction

I would expect all of the following to give the same answer (2.12467) but only half of them give this answer. The others seem to be using the default ...
4
votes
3answers
599 views

Output of NonlinearModelFit differs from the correct result

I'm having a bad time dealing with the NonlinearModelFit in Mathematica 8, since the result given is a bit imprecise. An example is given on potential regression, ...
2
votes
2answers
263 views

Non-linear trend reduction with missing data

How can I reduce a non-linear trend of some data series if there are parts of "no data", represented by the value 99999? For example: ...
5
votes
2answers
316 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
18
votes
3answers
2k views

Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...
16
votes
2answers
1k views

FindFit returns Infinity::indet error when data contains {0,0}

Let's consider the following data: data = Table[{q, 2*q^2}, {q, 0, 2}]; and then, do a very simple fitting to this data: ...
15
votes
3answers
2k views

Fitting fractional complex data with NonlinearModelfit

I've difficulites with the NonlinearModelFit function. In principle Mathematica should be able to deal with complex data. E.g. if I define the following table ...
19
votes
4answers
2k views

Mathematica envelope for the bottom of a plot, a generic function

I have the following set-up: xaxis = Table[x, {x, 0, 10, 0.01}]; yaxis = Table [Sin[x] + Abs[RandomReal[{-1, 1}]], {x, 0, 10, 0.01}]; ListLinePlot[Transpose[{ xaxis, yaxis}]] My ...
17
votes
5answers
5k views

Problem with NonlinearModelFit

I'm having trouble with a non-linear fit: fit = NonlinearModelFit[data, y0 + A Sin[\[Pi] (x - xc)/w], {y0, xc, A, w}, x] where ...
12
votes
2answers
583 views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
13
votes
4answers
4k views

Using FindFit to fit $a\,b^t$: how to avoid introducing complex numbers?

I'd like to find a model $f(t)=a\,b^t$ which matches the following data ...
30
votes
4answers
5k views

Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
5
votes
0answers
623 views

Analytical model fitting

I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear. We have a variable $$ ...