Information of Sample from Given Distribution

Theorem

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

The information $I$ is given by:

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

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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.