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Results tagged with probability-distributions
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user 111097
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.
7
votes
1
answer
726
views
Reference request: discretisation of probability measures on $\mathbb R^d$
Given a probability measures $\mu$ on $\mathbb R^d$ with finite first movement, i.e.
$$\int_{\mathbb R^d}|x|\mu(dx)~~<~~+\infty.$$
My concern is to approximate $\mu$ some $\mu_n$ that is countably o …
- 345
1
vote
0
answers
69
views
Reference request on numerical integration
Let $\rho:\mathbb R^d\to\mathbb R_+$ be a density function with finite first moment, i.e.
$$\int_{\mathbb R^d}~ \rho(x)dx~=~1 \quad \mbox{ and }\quad \int_{\mathbb R^d}~ |x|\rho(x)dx<+\infty.$$
For …
- 345
0
votes
Question about Wasserstein metric
I've a solution but it's not perfectly satisfying. Assume that
$$V~~~:=~~~\int |x|^pd\mu(x)~+~\int |x|^pd\nu(x)~~~<~~~+\infty$$
for some fixed $p>1$. It follows from Thought 1 that, there exists $f …
- 345
8
votes
3
answers
916
views
Question about Wasserstein metric
Let $\mu$ and $\nu$ be two probability measures on $\mathbb R^n$ with finite first moment. Denote by $d:=W_1(\mu,\nu)$, where $W_1(\cdot,\cdot)$ stands for the Wasserstein distance of order $1$.
My …
- 345