Tuesday, 25 February 2014

Table of distributions

Here is a table of 5 discrete and 6 continuous distributions. It is supplied to second year students studying Statistics IB, as a reminder of things they are to know from Probability IA.

For each of distribution the table shows its usual notation, p.m.f. or p.d.f., mean, variance, and p.g.f. or m.g.f.

You will want to have at your fingertips most of the information in this table (or the method to by which to produce it). You might find it helpful to make your own table, using this one as a guide.

Some of these 11 distributions are not explicitly mentioned in the schedules for Probability IA. Rather they appear as examples of other things which are mentioned in the schedules. For example, the gamma distribution arises as an example of summing i.i.d. r.vs (in this case exponential r.vs). The multivariate normal provides an example of the p.d.f. of jointly distributed continuous r.vs. The beta distribution appears as an exercise on the joint distribution of order statistics of i.i.d. uniform r.vs. We have not mentioned in a lecture the negative binomial, but this is simply the sum of i.i.d. geometric r.vs. (as done in Examples sheet 3, #5).