Beta distribution for exam P?

Question

I had a quick question regarding the beta distribution and exam P for actuaries.

From the recommended books that I have seem, beta distribution does not seem like it is likely to show up on the P exam. However, some of the example problems that I am working on actually uses this to solve some problems which makes me feel a bit puzzled.

Do Beta distribution show up often in actuarial science? In the future I am sure that I will be taking other higher level exams, so I was wondering if it actually be worth it to study extensively right now. My plan is to take the P exam on September.

Answer 1

Yes, the beta (or better, the transformed beta) shows up in actuarial research. An example is this paper: http://www.casact.org/pubs/forum/03wforum/03wf629c.pdf or this book: http://www.amazon.com/gp/product/0615133568/

The transformed beta gives you a very flexible form that allows you to model events with fat tails. The beta in the unit interval may not be very used but in Bayesian analysis it can be used to model high level uncertainty: say you have a Bernoulli random variable (heads or tails) but you are unsure about the probability of heads, p - you can use a beta to model the prior distribution of p.

You should also ask this at cross validated (the stats site, there are lots of practitioners there). https://stats.stackexchange.com/

Answer 2

I can't speak directly to the use of the Beta in actuarial science but I can say that the Beta is tremendously useful for probabilistic modeling in general. Whenever you need to cover the support in the interval $[0,1]$ the Beta is your "go-to" distribution because of its flexibility. For example, the special case Beta(1,1) is the Uniform(0,1) distribution but, depending on the parameters, it can be unimodal monotonic, unimodal with positive and negative first derivatives, or bimodal. Plus, it appears all the time in order statistic derivations.

If I were you I'd make friends with the Beta distribution as soon as possible.

Answer 3

Many times when doing Bayesian Analysis which coming quite popular you will have a uniform prior and beta posterior after you gathered data. An example you may use it for is if you want a distribution of Basketball Players free throws percentages you after gathered data it would be fitting to have some sort of beta distribution.

Answer 4

I've gone through the material of the first four actuarial exams.

A scaled version of the beta distribution, known to some as the "modified de Moirve's law" comes up in the fourth actuarial exam (exam MLC, Models for Life Contingencies). A Google search should help in helping you find more information on why it is used.