exercises for Tue Feb 7

1. On Tue Jan 31 I worked my way through certain important parts of Ch 2, and also discussed aspects of modelling and logLik-maximisation for the Egypt life-lengths dataset. Three things will be discussed next week, to complete the picture: (i) How to turn \hat\theta information and precision into \hat\mu information and precision, where \mu = \mu(\theta) is a function of the model parameter vector. This involves the *delta method*. (ii) Extending theory and methods from iid to regression models. (iii) The necessary theory behind the AIC and the model-robust AIC.

2. I've placed "com3c" on the website, doing 0.5 weib + 0.5 weib mixture for the Egypt dataset. Try it out, and do some modifications. Make sure you understand how the details work.

3. Exercises for Tue Feb 7:

(i) Make one more attempt at modelling the Egypt dataset, with n = 141 iid observations. Again, try to find models of parameter size 3 or 4, which beat the best of Gamma and Weibull. Include *Nils's three-parameter extended Gamma-Weibull model* of Exercise 7. *Note:* Do this with the life-lengths downscaled by division of 100, so that life-lengths are from 0 to 1. This is not absolutely necessary, but it turns out that the "nlm" algorithm more happily converges for different models when data are not as spread out as from 0 to 100.

(ii) Then do Exercise 2, which also requires basic understanding of Exercise 1. -- If we find time, we also do the first couple of points for Exercise 5.