
Lecture 3
The empirical distribution
function of duration of life
In demography, statistical problems begin where they always begin:
we do not know the true distribution function F of the duration of life;
but we have data, based on which we have to make inference about this
unknown F, test different hypotheses which we can formulate about F,
or estimate F and/or some of its parameters.
Suppose we have n independent, identically distributed durations
of life T
1
,T
2
,... ,T
n
, that is, n independent random variables, each with
the same distribution function F. Let us consider a function of a ran-
dom variable T and of a point x, defined as
I
{T <x}
=
(
1, if T