I am confused by the identity function notation in a formula:

$f(y|\theta)= \theta\cdot e^{-\theta\cdot y}I_{(0, \infty)}(y)$

Could someone help me understand what $I_{(0, \infty)}(y)$ means in the formula?

Thank you so much in advance!


$I_{(0,\infty)}$ is the "indicator function" or "characteristic function" of the set $(0,\infty)$. It takes the value $1$ if its argument is in the set $(0,\infty)$ and $0$ otherwise. You might write $$I_{(0,\infty)}(y) = \begin{cases} 1&\text{if $0<y<\infty$}\\0 & \text{otherwise.}\end{cases}$$

  • $\begingroup$ Ahh! So does it mean I calculate the part before the indicator function, and plug the result to the indicator function, in order to decide I keep the result or make it 0? $\endgroup$ – Chenglu Sep 19 '18 at 22:52
  • $\begingroup$ Yes. Calculate the part in front of the indicator and multiply it by the value of the indicator. It does not matter which of the two quantities you work out first. $\endgroup$ – kimchi lover Sep 19 '18 at 22:54

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