Does anyone know what the following distribution is, please? I can tell it is discrete and $\theta$ is somehow a probability. Thank you!
$$\mathbb P_X(x; \theta) = (x-1) \theta^2 (1-\theta)^{x-2}, \ \ x=2,3,\ldots; \ \ 0 < \theta < 1.$$
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Sign up to join this communityDoes anyone know what the following distribution is, please? I can tell it is discrete and $\theta$ is somehow a probability. Thank you!
$$\mathbb P_X(x; \theta) = (x-1) \theta^2 (1-\theta)^{x-2}, \ \ x=2,3,\ldots; \ \ 0 < \theta < 1.$$
It's a negative binomial (the number of trials form) with $p=1-\theta$ and $r=2$
http://en.wikipedia.org/wiki/Negative_binomial#Alternative_formulations
$\Pr(X = x) = {x-1 \choose x-r} (1-p)^r p^{x-r} \quad\text{for }x = r, r+1, r+2, \dots, $