Appendix A — Technical background
This course requires fairly involved knowledge of statistics and probability. We’ll be introducing several new concepts through the semester, but we will provide refreshers of some basic concepts as a starting point for this course.
Software
In this class, we will use as our primary software. We expect you to be familiar with the tidyverse packages, and ggplot2 for visualization.
In this class, we will make extensive use of the survival package, as well as various specialized packages
Probability distributions
You are probably familiar with the normal (Gaussian) distribution and the binomial distribution. We’ll introduce some new distributions that will be used in the class
Exponential distribution
The exponential distribution has one parameter, usually denoted by \(\lambda > 0\) , which is also the mean of the distribution. If \(X\sim Exp(\lambda)\), then
\[ P(X > x) = e^{-\lambda x}\quad \text{for } x > 0 \]
Weibull distribution
The Weibull distribution is a generalization of the Exponential distribution. It is a two-parameter distribution, with the parameters called shape (\(\alpha\)) and scale ( \(\beta\) ). For this distribution,
\[ P(X > x ) = e^{-(x/\beta)^\alpha} \]
Notice that the Exponential distribution is a special case with \(\alpha = 1\) and \(\beta\) = \(1/\lambda\)