# Questions tagged [probability-limit-theorems]

For question about limit theorems of probability theory, like the law of large numbers, central limit theorem or the law of iterated logarithm.

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### Speed of convergence of empirical probability mass function

I was wondering about the following situation: Suppose we have a random variable $X$ taking values in the finite set $\{1,2,\ldots,k\}$. Let the probability mass function be denoted by $f$. Suppose we ...
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### Concentration of probability measures

Assume we have a vector $X$ consisting out of $N$ independent random variables $X_1, ..., X_N$. We determine ("measure") the value of "k" (say, for simplicity, the first $k$) of ...
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### Does the infinite limit probability of additive closure for pairs of elements from $(0, 1, 2 \cdots, n)$ not exist?

Suppose that we have a sequence of non-negative integers $S_n = (0, 1, 2 \cdots, n)$. At a given value of $n$ we can uniformly sample two elements of $S$ with replacement. We can check if adding those ...
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### Why is this estimator with ill-defined moments useful? And why is the Cauchy PV of its expectation integral a reasonable measure of center?

This question pertains to the paper (available online through JSTOR): M. H. QUENOUILLE, NOTES ON BIAS IN ESTIMATION, Biometrika, Volume 43, Issue 3-4, December 1956, Pages 353–360, https://doi.org/10....
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