Normal distribution
Assume that each data point, yk
, has an error that is
independently random and distributed as a normal distribution, that is,
where σ2
is the variance, and
f(xk,p)
is the expression that we want to fit.
The goal is to minimize the χ2
function:
where the weights are defined as: w≡1/σ2
.
Consider the Taylor expansion of χ2
:
Define the arrays ,
and
:
Linearize and the problem reduces to solving the matrix equation
Chi-square and weights
Hint for physicists
Degrees of freedom