algebraic.dist R package

The R package algebraic.dist provides an algebra over distributions. It’s not fully-formed yet, but I plan on using it for a lot of my future work. For instance, I’ll move a lot of the code in algebraic.mle and likelihood.model to this package.

After that, I want to experiment with using the algebraic.dist to do the following:

• Compose distributions such that operations over distributions generate other known distributions.

  There are a lot of well-known compositions, such as the exponential distribution being the minimum of independent exponential distributions, or the sum of independent normal distributions being a normal distribution, but there is a very large space of possible compositions that are not as well-known or well-studied that I want to explore.

• Let people use an R expression to lazily compose functions of distributions. Simplifying a distribution expression will generate a most simple R expression that represents the same distribution.

Sometimes, this may result in a simple close-form distribution, like a multivariate normal distribution, but in other cases it may result in a (hopefully simpler) expression that composes multiple distributions and operations over them.

• With these R expressions that represent distributions, we can define more operations, like taking the limiting distribution of a sequence of distributions, say $\lim n \to \infty \frac{1}{n} \sum_{i=1}^n X_i$, which is of normal by the central limit theorem.

• Deduce various properties of these distributions, such as their moments, variances, etc. Sometimes, this may require numerical integration or Monte Carlo methods, but if the expression simplifies to a known distribution, then we can use the known properties of that distribution.

I have a lot of this code in place in C++, but I want to re-implement it in R so that it’s more accessible to others. I may also implement some of the more interesting compositions in C++ and expose them to R via Rcpp, but I’m not sure yet. I use a lot of templates and metaprogramming in C++, and I’m not sure how well that will translate to Rcpp.