Information of Sample from Given Distribution under Regularity Conditions

Theorem

Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta}$.

Let it be assumed that certain regularity conditions apply.

Let it also be assumed that the extremes do not depend on $\theta$.

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The information $I$ is given by:

$I = -n \map E {\dfrac {\partial^2 \ln f} {\partial \theta^2} }$

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): information: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): information: 2.