See You Later, Indicator

(Mar 18, 2019)

A recurring feature in my previous blogs, such as this one on information, is the indicator process:

\[Y^*(x)=\begin{cases}1\quad\mbox{ if a person is alive at age \(x^-\)}\\0\quad\mbox{ otherwise}\end{cases}\]

where \(x^-\) means immediately before age \(x\) (never mind the asterisk for now).  When something keeps cropping up in any branch of mathematics or statistics, there are usually good reasons, and this is no exception.  Here are some:

  • It is a stochastic process, as a function of age \(x\). \(Y^*(x)\) tracks whether or not the life is alive in continuous time.  \(Y^*(x)\) has a familiar expected value: \({\rm E}[Y^*(x+t)|Y^*(x)=1]={}_tp_x\), the survival probability.
  • It leads to useful expectedů

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Tags: left-truncation, right-censoring, Poisson

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