Exercise 3.3

(a) Which moment-based coefficients could we use to test the Gaussian distribution hypothesis? Are there other ways to verify the normality of a sample?

(b) Are the following tests reliable to confirm the Gaussian distribution? If not, explain why.

(i) Jarque-Berra;

(ii) Revisited Jarque-Berra;

(iii) Lilliefors;

(iv) Cramer-von Mises.

(c) What are the advantage(s) of the test(s) identified in (b)?