ABSTRACT
One common type of simple null hypothesis involves i.i.d. com ponents with densities of some well-known standard form. As examples, according to H0, the densities of , . . . , Yn might be standard normal, Poisson of known mean, or uniform over (0, 2n). This last example is of particular interest in connexion with data on directions around a circle, the null hypothesis being that the n directions are independently randomly distributed over the circle. An example of a simple null hypothesis involving non-independent random variables is with binary observations, the null hypothesis being that the values are generated by a two-state Markov chain with known transition matrix.
