In generating a sample of n datapoints drawn from a normal/Gaussian distribution, how big on average the biggest datapoint is will depend on how large n is. I implement a variety of exact & approximate calculations from the literature in R to compare efficiency & accuracy.
Implementation of efficient random sampling of extreme order statistics (such as 1-in-10-billion) in R code using the beta transform trick, with a case study applying to the Jeanne Calment lifespan anomaly.
I implement random sampling from the extremes/order statistics of the Gompertz survival distribution, used to model human life expectancies, with the beta transformation trick and flexsurv/root-finding inversion. I then discuss the unusually robust lifespan record of Jeanne Calment, and show that records like hers (which surpass the runner-up’s lifespan by such a degree) are not usually produced by a Gompertz distribution, supporting the claim that her lifespan was indeed unusual even for the record holder.