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

  Update after a fit
  Poisson distribution