Category Archives: statistics

Maximum likelihood, moments, and the mean of a Poisson

If we observe data coming from a distribution with known form but unknown parameters, estimating those parameters is our primary aim. If the distribution is uniform on $[0,\theta]$ with $\theta$ unknown, we already looked at two methods to estimate $\theta$ given $n$ i.i.d. observations $x_1,\dots,x_n$: Maximum likelihood, which maximizes the likelihood function and gives $\max\{ […]

A very quick tour of R

This post is a quick introduction to the R. I learnt R when I was an undergrad and I still use it from time to time. It was one of the first major programs I compiled from source as well. What is R? It is simply the best statistical computing environment in use today. Better […]

P-values and goodness-of-fit normality testing

In statistical hypothesis testing, the computed p-value is the probability of getting a result "as extreme" as the given data under the null hypothesis. Here, "as extreme" means relative to a test-statistic, which has some distribution under the null hypothesis. In the natural sciences, an experiment is performed. A statistical test is used whose null […]