What is a Student's t-Distribution?

Despite the ubiquity of the t-distribution in classrooms, it often simply with only with one piece of advice: "use the \( t \)-distribution for small sample sizes and the normal distribution (a \(Z \) distribution) for larger ones". Supposedly, according to every introductory statistics class, a t-distribution is supposed to work better because of of mythical fatter tails.

Let us deconstruct this ubiquitous distribution a little bit, and hopefully learn what these mythical fat tails do. 

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Existence Precedes Essence


Welcome to my blog. This is an exploratory and expiremental space for the publication of my ideas. I am not sure what will arise here, and so I will not attempt to already characterize it. Enjoy.