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Question: Fitting a parametric model function

Question:Fitting a parametric model function

Oliver K 1201 Maple
January 20 2010
0

Hi,

i want to fit the parameters of a function for a set of points in 2D, problem is, the function is not explicitly given as y=f(x), but in parametric form.

Example:

restart:with(Statistics):
N := 200:
U := Sample(Normal(0, 1), N):
X := <seq(cos(2*Pi*i/N)+U[i]/5, i = 1..N)>:
Y := <seq(sin(2*Pi*i/N)+U[i]/15, i = 1..N)>:
ScatterPlot(X, Y);

Lets say i want to fit a,b of the parametric model function [a*cos(t),b*sin(t)], t=0..2*Pi

And what if the model function is given implicitly, like F(x,y):=x^2/a+y^2/b=1 and parametrization is not allowed/possible ?

regards

 

 

 

 

 
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