I was wondering how to use Maxima to integrate a Normal Distribution
Function
(1.0/sqrt(2.0*PI))*exp(-0.5*x*x),
under the Clenshaw-Curtis or Chebyshev Integration Schema, WITHOUT any
weight function.
I'm using the above example to get used to Maxima in order to tackle a more
protracted problem..
Namely, ideally I want to integrate a Chebyshev Fit for a set of points of a
histogram distribution. i.e. calculate P( x <= b ), given that I already
have the Chebyshev curve (and coefficients) that interpolates the data.
There seems to be 2 approaches (a) compute the moments of the fitted curve
and calculate the integral (b) Follow the suggestions albeit unclear in
Numerical Recipies in C pp 196 - Clenshaw-Curtis Quatrature - paragraph 1.
I'd like to use Maxima to benchmark my implementation. Any ideas on how I
might solve this second problem in Maxima - namely integrating Chebyshev
fitted PDFs ? Any if anybody has any pointers wrt it's implementation, I'd
very much appreciate it.
Kind regards,
Alan