1.

Of the distributions mentioned in the random component of a GLM, give the density (including the range), the mean and the variance.

2.

Show that if X _i ~ gamma( ?, ? _i) with parameters ? = 1/ ? and ? _i = 1/( ? ? _i), all X _i have the same coefficient of variation, i = 1, , n. What is the skewness?

1.

? _i, ? _i; ? _i; ? _i; ? _i ? _i ? _i, ? _i ? _i, ? _i,(1 - ? _i). Cf. Table E.

2.

Coefficient of variation: s.d./mean = = skewness = .

1.

Verify (8.4), (8.16) and (8.17). Also verify if (8.11) describes the maximum of (8.13) under assumption (8.14).

2.

Show that the methods of Bailey-Simon, marginal totals and least squares, as well as the direct method, can all be written as methods of weighted marginal totals, where the following system is to be solved:

3.

Show that the additive model E[ X _ij] = ? _i + ? _j, of the least squares method coincides with the one of the marginal totals.

4.

Which requirement should the means and variances of Y _ij/( ? _i ? _j) fulfill in order to make (8.17) produce optimal estimates for ? _i?