Lorentz2D Fit

Hello,

I'm trying to do a function that gives the volume under the 2D data wave. The shape of the data is lorentzian but on the curvefit menu I only have Gauss2D. Do you have an idea to make 2D lorentzian with correlated x and y coordinates.
The second problem is that of the initial guess parameters. Is it possible to have this option on user defined data ?

Thank you

Th.P.

This Wikipedia page has a description of a multivariate Lorentzian distribution (they call it Cauchy):

https://en.wikipedia.org/wiki/Cauchy_distribution#Multivariate_Cauchy_d…

Scroll down to the multivariate section. It says, "Note that in this example, even though there is no analogue to a covariance matrix, {\displaystyle x}x and {\displaystyle y}y are not statistically independent." So I don't know if that equation gives you what you need.

 

We have never tried to provide automatic guessing for user-defined fit functions. Those functions can be absolutely anything that has the form of an analytic function, so it's hard to know how we could do that. The auto-guessing for the built-in functions is the result of pains-taking hand coding specific to each of the fitting functions.

On the other hand, there may be a way for you to write something that guesses adequately for your particular function. If so, you can write a small function that automates the guessing and running of FuncFit for your situation.