# Derivation of the censoring likelihood function? [duplicate]

The (right-) censoring of likelihood function is defined as:

$$L(\theta) = \prod_{i=1}^m f(x_i;\theta) \cdot \prod_{i=m+1}^n P_{\theta}(X_j>a)$$

where observations $x_i$, $i=1,...,m$ have known values and for $m+1,...,n$ the values are unknown.

I would like to know, how has this been derived? I.e. why is this the definition for censoring?

• @BCLC If the observation $x_i$ (its value) is higher than $a$ then it's not observed (it's censored). Therefore there's the probability of $P_{\theta}(X_j>a)$, in other words, the probability of an unobserved observation. – mavavilj Mar 19 '16 at 16:44

What is the probability of this occurring if the chance $p$ of rolling a six is constant for each roll?
$$P[X_1=4, X_2 \ge 9] = \left[ \left( 1-p \right)^3 p \right] \left[ \left( 1-p \right)^8 \right]$$