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