standard distributions

Joram Soch managed to get a short note arXived about the Normal cdf Φ by exhibiting an analytical version, nothing less!!! By which he means a power series representation of that cdf. This is an analytical [if known] function in the complex calculus sense but I wonder at the point of the (re)derivation. (I do realise that something’s wrong on the Internet is not breaking news!)

Somewhat tangentially, this reminds me of a paper I read recently where the Geometric Geo(p) distribution was represented as the sum of two independent variates, namely a Binomial B(p/(1+p)) variate and a Geometric 2G(p²) variate. A formula that can be iterated for arbitrarily long, meaning that a Geometric variate is an infinite sum of [powers of two] weighted Bernoulli variates. I like this representation very much (although it may well have been know for quite a while). However I fail to see how to take advantage of it for simulation purposes. Unless the number of terms in the sum can be determined first. And even then it would be less efficient than simulating a single Geometric…