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'Power Law with singularity' regression - error

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130003] 'Power Law with singularity' regression - error
  • From: dpi <deepankur.thureja at hotmail.com>
  • Date: Sun, 3 Mar 2013 22:59:16 -0500 (EST)
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Hi,

I am testing the "Power Law with finite-time singularity" hypothesis for the World population growth for a project.

For that I was trying the following model:

    model = A + B*(c - x)^z;

And then the following curve fit method:

    FindFit[data, {model}, {A, B, c, z}, x]

But I always get the result:

    Power::indet: "Indeterminate expression 0.^0. encountered."
    FindFit::nrjnum: "The Jacobian is not a matrix of real numbers at {A,B,c,z} = {1.,1.,1.,1.}. "
    {A -> 1., B -> 1., c -> 1., z -> 1.}

If I do a normal Power law regression, FindFit works perfectly, but the title of the project being "Power Law with finite-time singularity" I need to have a singularity in the model and the main aim is to find when this singularity occurs.

Is there a way to use 'FindFit[]' to get the correct answer? Or Should I be using some other function?

I have seen other articles on this site concerning issues with FindFit, but none of them has helped me resolve this problem.

Thanks for the help!



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