Comparison of tests

The likelihood ratio, Wald and Lagrange multiplier tests.

With Python write a test trilogy application.

You are asked to simulate a set of data following a reduced centered normal distribution with Python.

We deduce its log likelihood.

We use a database containing $1000$ observations.

Two estimators mu and sigma $^2$

With Python find the gradient matrix.

Give the result of the LR$,$ Wald and LM test