Date: Dec 12, 2013 2:48 PM
Author: Derek Goring
Subject: Re: Numerical integration of polyfit coefficients
On Friday, December 13, 2013 7:59:28 AM UTC+13, John D'Errico wrote:

> "Rajin " <patelr37@aston.ac.uk> wrote in message <l8ctcd$jrp$1@newscl01ah.mathworks.com>...

>

> > Hello,

>

> >

>

> > I have the coefficients of a polynomial of order 12 given to me using polyfit (it was fitted to model a probability density function). I now need to use the given polynomial f(x), multiply it by x^2, and integrate it over a given boundary.

>

> >

>

> > I have tried using the integral function: integral(fun,xmin,xmax), where:

>

> > fun = @(x) poly2sym(f) and f is the coefficients given by polyfit, but this doesn't work.

>

> >

>

> > Any ideas? Apologies if this seems trivial, I have tried everything!

>

> >

>

> > Thanks in advance,

>

> > Rajin

>

>

>

> Why use a mack truck to carry a pea to Boston?

>

>

>

> % Assume that p12 is a 12th degree polynomial.

>

> P12 = rand(1,13);

>

>

>

> % Multiply by x^2, to get a 14th degree polynomial

>

> % Remember, these are just the coefficients of the polynomial.

>

> P14 = [P12,0,0];

>

>

>

> % integrate

>

> Pint = [P14./(15:-1:1),0];

>

>

>

> Having done this, use of a 12th degree polynomial like

>

> this is a numerical obscenity. I don't really care who gave

>

> you the polynomial.

>

>

>

> Polynomials are a terrible way to fit distribution functions

>

> in general. Think of it like this: The PDF of these functions

>

> must go to zero at +/- inf. In fact, all of the derivatives

>

> go to zero too. No polynomial has this behavior.

>

>

>

> What tends to happen is the polynomial fits the data

>

> points used in the fit, but then it does execrable, nasty

>

> things between the points. This is a common behavior

>

> of high order polynomials, but it is especially true for

>

> this kind of model.

>

>

>

> So I'd go back to your source, and suggest use of a

>

> better model. A spline is often a good idea. For example

>

> there are very nice shape preserving splines to be found.

>

>

>

> John

My question is: why fit a curve at all?

Why not do numerical integration of the histogram/pdf?