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Results tagged with probability-distributions
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user 979
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
2
votes
0
answers
144
views
Monotone coupling between "two-sided Gumbel" distributions
I am interested in finding a monotone coupling between two random variables. Let $\alpha_1>\alpha_2$, $b<a$. Define the following two (non-normalized) densities on the whole real line:
\begin{align*}
…
- 1,765
10
votes
1
answer
260
views
q-versions of the geometric distribution and their names
I'm trying to set straight various $q$-deformations of the standard geometric distribution.
The geometric distribution on $\left\{ 0,1,\ldots \right\}$ is well-known, it has
$$
\mu_1(X=j)=(1-p)p^j,\q …
- 1,765
3
votes
0
answers
291
views
Exchangeable or iid random variables and linear conditioning
Let $X_1,\ldots ,X_N$ be independent identically distributed random variables (or, more generally, exchangeable random variables,
but let's assume independence for simplicity). Then
$$
E(X_i\mid X_1+ …
- 1,765