As a statistical consultant I frequently use boxplots. They're a great way to quickly visualize the distribution of a continuous… Read more
Category: Continuous distributions
Understanding Z-scores
The first time I took a statistics class I was mystified with z-scores. I understood how to find a z-score… 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
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
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
Deriving the exponential distribution
The exponential distribution looks harmless enough: $$ f(x) = \frac{1}{\theta}e^{-x/\theta}$$ It looks like someone just took the exponential function and… Read more
Investigating the chi-square test of independence
Survey a random sample of 500 men and ask if they have seen Star Wars more than twice. Survey 500… Read more
Explaining and simulating a chi-square distribution
Randomly select several values, say 10, from a standard Normal distribution. That’s a Normal distribution with a mean of 0… Read more