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Results tagged with lower-bounds
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user 1131
3
votes
Accepted
Existence of copula bound pointwise strictly smaller than the Fréchet-Hoeffding upper bound
You can prove more. Let $F(u,v)$ be any $1$-Lipschitz function on $[0,1]^2$ such that $F(u,v)<\min(u,v)$ inside the square. Then there exists a copula $D(u,v)$ such that
$$
F(u,v)\le D(u,v)<\min(u,v)
…
- 61.9k
5
votes
Accepted
Lower bound on sum of independent heavy-tailed random variables
Certainly. All you need is $EX^2=+\infty$. Then the characteristic function $f_X(t)$ satisfies $\lim_{t\to 0}\frac{1-|f(t)|}{t^2}=+\infty$, so for every finite interval $I\subset \mathbb R$, we have $ …
- 61.9k