
Re: Numerical integration of polyfit coefficients
Posted:
Dec 12, 2013 2:48 PM


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?

