Models of distribution functions F(x) and force of mortality µ(x)

In Lecture 1, the duration of life was introduced as a positive random variable T with some, in fact basically any, distribution function F(x). As soon as we do not require anything specific from F(x) we are facing an enormously rich choice from the class of all distribution functions on [0,∞). However, from practical analysis of data we know that some distribution functions are much more appropriate and relevant than others.