## New answers tagged probability-distributions

0
votes

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### WLLN for bootstrap means of stationary ergodic processes?

Answered in comments above
It seems as though the answer should be yes. I would suggest writing $X_n$ as $Y_n+Z_n$ where $Y_n$ is $X_n$ if $|X_n|\le m(n)^{1/3}$ and 0 otherwise; similarly $Z_n$ is $...

- 21.7k

3
votes

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### Probabilistic Taylor theorem for concave functions

If $g^{(4)}\le0$, then
$$g(x)=\sum_{k=0}^3\frac{g^{(k)}(0)}{k!}\,x^k+\frac{x^4}4\,
\int_0^1g^{(4)}(sx)(1-s)^3\,ds
\le\sum_{k=0}^3\frac{g^{(k)}(0)}{k!}\,x^k$$
for real $x$.
Replacing here $x$ by $X-\mu$...

- 82.4k

3
votes

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### Behavior of F distribution quantile as degree of freedom varies

$\newcommand\al\alpha$If the $(1-\al)$-quantiles of $F_{n,m}$ were decreasing monotonically in $m$ for each $\al\in(0,1)$, the the corresponding cdf's -- say $G_{m,n}$ -- would be increasing pointwise ...

- 82.4k

0
votes

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### Does the (normalized) product of two independent binomial variables converges in distribution to a normal variable?

$\newcommand{\R}{\mathbb R}\newcommand\ep\epsilon\newcommand\tsi{\tilde\sigma}$Yes, of course. This follows by the multivariate (here, bivariate) so-called delta method.
Indeed, we may assume that
\...

- 82.4k

3
votes

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### Transforming two smooth densities to the same density

This is impossible if $f$ is injective, without further assumptions such as bijective, differentiable, etc. Let $Q_1,Q_2$ be probability measures on a measurable space $(\Omega, \mathcal{F})$, and ...

- 502

4
votes

Accepted

### CLT convergence rate for sum of uniforms (in TV distance)

$\newcommand\dee{\Delta_{\mathrm{TV}}}\newcommand{\vpi}{\varphi}$Let $f_n$ denote the pdf of
\begin{equation*}
S_n:=\sqrt{\frac3n} \sum_{i=1}^n X_i
\end{equation*}
and let $\vpi$ denote the ...

- 82.4k

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