SOME POPULAR DISTRIBUTIONS
Note that I won’t describe the distributions thoroughly here. All of this information is readily available in much more detail on the Internet or in standard statistics books. This section is really for reference in later chapters. Although it’s not necessary to memorize the formulas for these distributions, you should try to remember the kinds of data that they can be used to model.
The Uniform Distribution
This is the simplest of all distributions. It has a finite maximum and minimum, and assigns the same probability to every number in the interval. So the probability of observing X is just 1/(maximum - minimum). Some people even use the word “random” to mean uniform distributed.
The T-distribution is a so-called “heavy-tailed” approximation to a Gaussian distribution (with mean = 0 and standard deviation = 1). This means that it looks a lot like the normal distribution, except that the probability in the tails of the distribution (the parts of the distribution far away from the peak or mode) doesn’t decay as fast as in the Gaussian. The similarity of the T-distribution to the Gaussian (with mean = 0 and standard deviation = 1) is controlled by the only parameter of the distribution, which is called the “degrees of freedom” or df for short. When df = 1 or 2, the tails of the T-distribution are quite a bit heavier than the Gaussian, so the probability of getting observations far away from the mean is large. When df is around 30, the T-distribution starts to look a lot like a Gaussian. Of course, only when df = infinity is the T-distribution exactly equal to the Gaussian distribution.
The formula for the T-distribution is a bit complicated, so I won’t reproduce it here.