Force of Mortality in Bathtub-Shaped Lifetimes

This tutorial will introduce Survival Analysis and its wide scope. Survival analysis is applicable to all fields that deal with time-dependent data: medicine, biology, engineering, marketing, finance, and many others. A data scientist in the role of a survival analyst is involved in questions concerning clinical trials, customer churn, time till violent death of Roman emperors, the failure rate of products or systems, and a practically infinite number of other situations that raise the question: "When will it happen, and what's its risk of failure or its chance of success?" After the introduction in chapter 1, we will explore a number of examples in chapter 2 -- and then complete the tutorial with bathtub-shaped lifetimes. To begin with: What is force of mortality? It is the conditional probability of death at a particular instant after having survived up to that instant. Also called the intensity of mortality or the instantaneous death rate in actuarial science. In fields that are less concerned about predicting the transition to the afterlife, it is better known as the hazard rate.