When doing linear modelling, we make certain assumptions about the data. One such assumption is uniform variance. The fancy word… Read more
The variance of a maximum likelihood estimator
Maximum likelihood is one of those topics in mathematical statistics that takes a while to wrap your head around. At… Read more
The power function
Power is the probability of rejecting a null hypothesis when the alternative is true. Say your null hypothesis is \(… Read more
Understanding qq-plots
qq-plot is short for quantile-by-quantile plot. You plot one quantile against another and you see if their coordinate pairs form… Read more
Evidence of the truth of the Central Limit Theorem
The Central Limit Theorem is really amazing if you think about it. It says that the sum of a large… Read more
Explaining and simulating an F distribution
I remember feeling very uncomfortable with the F distribution when I started learning statistics. It comes up when you’re learning… Read more
Independence vs. Mutually Exclusive
I used to tutor undergrad students in statistics when I was in grad school. One question that almost every student… Read more
The moment generating function of the gamma
The moment-generating function of the gamma distribution is \( M(t) = (1-\theta t)^{-\alpha}\). Such a friendly little guy. Not what… Read more
Deriving the gamma distribution
Let’s take a look at the gamma distribution: $$ f(x) = \frac{1}{\Gamma(\alpha)\theta^{\alpha}}x^{\alpha-1}e^{-x/\theta}$$ I don’t know about you, but I think… Read more
The forgetful exponential distribution
The exponential distribution has the quirky property of having no memory. Before we wade into the math and see why,… Read more