```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.> > > > JohnMy question is: why fit a curve at all?Why not do numerical integration of the histogram/pdf?
```