### Right-Censoring Rules!

#### (Jan 23, 2019)

A fundamental assumption underlying most modern presentations of mortality modelling (see our new book) is that the future lifetime of a person now age $$x$$ can be represented as a non-negative random variable $$T_x$$.  The actuary's standard functions can then be defined in terms of the distribution of $$T_x$$, for example:

${}_tp_x = \Pr[ T_x > t ].$

In fact, all of classical life insurance mathematics follows from this assumption; see Dickson, Hardy and Waters (2013).  This is an example of a probabilistic model in action.  We specify a model in terms of one or more random variables and then calculate the probabilities of interesting events.

The inverse problem is the domain of statistics.  Given…