In this post, I overview the optimal non-parametric approach to quantile confidence intervals. We will discuss the theoretical background as well as an efficient algorithm implemented in Python. Consider an ordered iid sample from a distribution , and let be the -th quantile, that is . Using our samples we want to build a possibly …
Continue reading “Correct Confidence Intervals for Quantiles”
Normality of data is important in statistics, so it is not a surprise that transforming data to look closer to a normal distribution can be beneficial in many ways. There are ways of finding the right transform, such as the popular Box-Cox method 1,2. In this post, I will share an elegant example on how …
Continue reading “On Importance of Log-Normality in Hypothesis Testing”
The post discusses normal approximations to the inverse gaussian distribution.
Beta distribution is ubiquitous in statistics, but particularly popular in real-world modeling. The beta-binomial model is perhaps the most known example, given the recent interest in Bayesian inference. But it was in use nearly 50 years ago, for example in toxicology. Unfortunately, computing probabilities from the density depends on intractable incomplete beta integrals. This creates …
