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A distribution is a mathematical description of probabilities or frequencies.

4 votes

Is $\overline{X}_n = \frac{X_1 + X_2 + \cdots + X_n}{n}$ an estimator of the mean in general...

Let $X_1, X_2, \dots$ be a sequence of independent and identically distributed random variables (and such that $\mathbb{E}[|X_i|] < \infty$). Any statistic $f(X_1, X_2, \dots, X_n)$ can be an estimato …
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15 votes

Is it possible to apply KL divergence between discrete and continuous distribution?

If $P$ and $Q$ are distributions on some space $\mathbb{X}$, then both $P$ and $Q$ have densities $f$, $g$ with respect to $\mu = P+Q$ and $$ D_{KL}(P,Q) = \int_{\mathbb{X}} f \log\frac{f}{g}d\mu. $$ …
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