This week’s resource post lists notes on probability approximations.

Do we even need probability approximations anymore? They’re not as necessary for numerical computation as they once were, but they remain vital for understanding the behavior of probability distributions and for theoretical calculations.

Textbooks often leave out details such as quantifying the error when discussion approximations. The following pages are notes I wrote to fill in some of these details when I was teaching.

- Error in the normal approximation to the binomial distribution
- Error in the normal approximation to the gamma distribution
- Error in the normal approximation to the Poisson distribution
- Error in the normal approximation to the t distribution
- Error in the Poisson approximation to the binomial distribution
- Error in the normal approximation to the beta distribution
- Camp-Paulson normal approximation to the binomial distribution
- Diagram of probability distribution relationships
- Relative error in normal approximations

See also blog posts tagged Probability and statistics and the Twitter account ProbFact.

**Last week**: Numerical computing resources

**Next week**: Miscellaneous math notes

The Box-Muller transform saved my butt on my second-ever consulting gig (in ’92). When all you have is a uniformly distributed RNG, transformations are the rule.

I was modelling the inter-arrival times of neutrons at a radiation detector within a nuclear reactor. The detector was monitored by a software system (also running within the simulation) that ran at a fixed cycle rate, so I had to smoothly transition back and forth between “time between neutrons” and “neutrons per cycle”. The goal was to prove the sensor + software system would react fast enough to safely scram the reactor under all physically possible transients.

It was the first software-based reactor safety system approved by the NRC (prior to then it was all analog).