New answers tagged probability-distributions
6
votes
Accepted
Why should we expect this odd behavior of negative binomial distributions?
This "odd behavior" is not peculiar to the negative binomial distribution.
A somewhat similar behavior is exhibited e.g. by the binomial distribution. For instance, here is the graph $\{(n,...
- 110k
3
votes
Accepted
Probabilty measures that are both discrete and continuous
A discrete probability distribution is one made up entirely of point masses; i.e. there is some set $S_1\subseteq S$ for which, for every $s\in S_1,$ the probability $P\{s\}$ assigned to the set $\{s\}...
- 11.4k
5
votes
Probabilty measures that are both discrete and continuous
Your notion of “has a density with respect to another measure” is essentially the notion of “absolute continuity”. Not all measures are absolutely continuous with respect to another, though one can ...
- 1,729
4
votes
Accepted
On Impossible events
This is a good question about practical simulation, but it needs
a bit of reinterpretation. This is what I understand to be
the question(s):
Q1. What is meant by saying that we are sampling finitely ...
- 3,914
2
votes
Some identities from graph theory and probability
These inequalities are not too bad. Note that the $t_{ij}$ are independent and mean zero by the fact hyperbolic tangent is an odd function and symmetry of the Gaussians. This implies the first ...
- 596
2
votes
Accepted
Concentration inequalities for random sampling without replacement
$\newcommand\E{\operatorname{E}}\newcommand\var{\operatorname{Var}}\newcommand\si{\sigma}$This will not work. E.g., if $N=10$, $\{c_1,\dots,c_{10}\}=\{-1, -1, -1, -1, -1, 1, 1, 1, 1, 1\}$, $n=5$, and $...
- 110k
5
votes
Accepted
Limit of distributions
$\newcommand{\R}{\mathbb R}$
Proposition 1: For
\begin{equation*}
s(x)\sim T(x)=\ln P(X>x) \tag{00}\label{00}
\end{equation*}
to hold (as $x\to\infty$), it is necessary and sufficient that
\...
- 110k
1
vote
What's the lower bound of the correlation coefficient?
$\newcommand\P{\operatorname P}\newcommand\E{\operatorname E}\newcommand\Var{\operatorname{Var}}\newcommand\Cov{\operatorname{Cov}}$As you noted, necessarily $\rho\ge0$, so that $0$ is a lower bound ...
- 110k
3
votes
Accepted
Form of minimax estimator
$\newcommand\P{\mathcal P}\newcommand\N{\mathbb N}\newcommand\de{\delta}$You wrote:
Hence I additionally assume that
$\mathcal{P}$ is permutation-invariant, in which case I conjecture that all of the ...
- 110k
1
vote
Accepted
Small deviations of real log-concave random variable
We have $f=e^g$, $g$ is concave, $\int f=1$, $\int x f(x)\,dx=0$, and $\int x^2 f(x)\,dx=1$. As you noted, then $f(0)\ge 1/8$ and hence
$$g(0)\ge-a,\tag{0}\label{0}$$
where $a:=\ln8$.
We have to show ...
- 110k
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