All Questions
5 questions
1
vote
0
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86
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How to find $\mathbb{E} \left[\frac{\bar{\mu}}{\bar{\sigma}^2}\right]$?
I asked the same question on math stacks: MathStacks:, and some user suggest to ask it here for better insight. So this question has found interest in many research problems, but there have been no ...
- 11
1
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0
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79
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Bounds on distance between two independently variables drawn from the same distribution
Suppose $X_1$ and $X_2$ are iid from an arbitrary distribution with variance $\sigma^2$. How can we derive an upper bound for:
$$P(|X_1-X_2|\ge\delta)$$
One simple idea is Chebyshev's Inequality, ...
- 51
1
vote
2
answers
545
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Two distributions, same mean, different variance: Stochastic dominance for deviation from mean?
Say you have two (bounded) random variables, $X$ and $Y$, on the same discrete probability space, such that $E(X)=E(Y)$ but $Var(X) < Var(Y)$. Do I know that, for any $k \geq 0$,
$$
\text{Prob}(|X-...
- 33
2
votes
0
answers
130
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Existence of estimator that reaches Cramer-Rao bound
There is a well known classical result called Cramer-Rao bound:
https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound
Particularly, it is a lower bound for a variance of any unbiased estimate. ...
- 121
4
votes
0
answers
101
views
Index of dispersion with approximate distribution
I have an unknown discrete probability distribution $D$ ($D$ is a probability mass function), defined on an interval $[a,b]$ ($a>0$) and an estimation $\hat{D}$ such that, for all $t\in[a,b]$,
$$(...
- 213