There's more detail on the chi square, t and F distributions in Chapter 9 of CT3. And more information about the chi square in Chapter 12.
To be honest, the chi-square, T and F distributions were all developed as part of statistical testing which you'll cover in chapters 11 and 12. They were simply given a name and the values were tabulated so they could be used to test hypotheses.
The gamma is a generalisation of an exponential distribution which can be used to model waiting times and claim amounts.
The beta distribution is a very general distribution that can create many different shapes and is used for modelling probabilities.
Can't recommend a text book but you can at least see the distributions on wolfram alpha.
All you need for the CT3 exam is to be able to calculate the probabilities for each distribution. For beta you just integrate it. For gamma you use the chi-square relationship and then use the chi-square tables. For chi-squar, t and F you just use their tables.
degrees of freedom will be explained in Chapter 12 of CT3.
there's nothing special or significant about this relationship - it's simply that when this holds we get the correct PDF.
Last edited: Jan 11, 2012
