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A truncated distribution is one that is cut off at some value, either at the low or high end of the distribution, or both.
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Sufficiency and completeness of truncated distribution
[From Theory of Point Estimation (Lehmann and Casella, 1999, Exercise 6.37)]
Let $P=\{P_\theta:\theta \in \Theta\}$ be a family of probability
distributions and assume that $P_\theta$ has pdf $p_\the …