I came across this problem with the Rayleigh distribution where this notation was used:
$f(x|\theta) = \displaystyle\frac{x}{\theta^2}\exp(-\displaystyle\frac{x^2}{2\theta^2})1_{[0,\infty)}(x)$
What does the notation $1_{[0,\infty)}(x)$ mean?
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Sign up to join this communityIt is likely the indicator function, which in this case is defined by
$$ 1_{[0,\infty)}(x) = \begin{cases} 1 & \text{if}\ x\in[0,\infty), \\ 0 & \text{otherwise}. \end{cases} $$
$1_A$ is an indicator function. $1_A(x) = 1$ if $x\in A$ and $1_A(x) = 0$ otherwise.