# Questions tagged [distribution-tails]

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### How do we proof that Gaussian Tails is interesting area

I have a programming problem that i solve using Gaussian Distribution. The problem is outlier detection. I use the uncertainty of the data, calculated from the classifier confidence, based on the ...
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### If $X$ is a nonnegative $\sigma$-subGaussian random variable with $P(X=0)\ge p$, what is a good upper bound for $P(X \ge h)$?

Let $X$ be a nonnegative random variable and let $\sigma \in [0,\infty)$ and $p \in (0,1)$ such that (1) $P(X=0) \ge p$ (2) $Var(X) \le \sigma^2$ For $h \ge 0$, define $c_X(h):=P(X \ge h)$. The ...
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### concentration of function of Chi squared random variables

Let $X, Y$ be iid Chi-squared random variables with parameter $k$ and consider, \begin{align*} Z = \frac{X-Y}{X+Y}. \end{align*} I am after bounds for the tail: $\mathbb{P}[ |Z| > t ]$. I know the ...
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### Parameters of product of scalar sub-gaussian independent random variables

I know that the product of two sub-gaussian random variables is a sub-exponential random variable and it's easy to show that. What I want is to find parameters of resulting sub-exponential R.V. namely ...
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### Comparing Tail Probabilities of Sum of Dominated Random Variables

I have been thinking about the following problem for quite a while, but did not get much progress of how to approach it: Assume that $X$, $Y$ are independent random variables with N(0, 1) ...
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### Tail bound for integral product of two functions

(I am reformulating this question which did not get much attention) Suppose I have a well defined probability density function $f$ over $(0,\infty)$. I would like to find an upper bound for the tail ...
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### Regular tails of a probability distribution

In a text I read, the distribution of a random variable $X$ has so-called regular tails, if the following property holds: The distribution of $X$ belongs without centering to the domain of attraction ...
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### Tail bound on difference of shifted binomials (generalization)

I have a post Tail bound on difference of shifted binomials answered before and now I want to consider I slightly generalization of it which can't be solved using the methods in the previous thread. ...
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### Tail bound on difference of shifted binomials

I would like to derive an upper bound on $\mathsf{Pr}\{(\frac{X}{n}-\frac{1}{2})^2 \leq (\frac{Y}{n}-\frac{1}{2})^2\}$ where $X,Y$ are independent and $X\sim$ Bin($n,p$) where $p\neq \frac{1}{2}$, and ...
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### a probability bound related to conditional 1-subgaussian variables

I am taking an intermediate probability course and this problem is assigned as a challenge (no ready solution). It goes like this: $\{z_i\}_{i=1}^{N}$ is a conditional 1-subGaussian sequence. $d$ is ...
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### whats is the Chernoff bound for an uniform distribution variable

Let $X$ be an uniform random variable between $[0,K]$. I want to find an upper bound for a state that $X> \alpha$. So I have used blow Chernoff bound: \begin{align*} \mathbb{P}(X\ge \alpha)&\...
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### Tail bound for the maximum of a reduced-rank Gaussian random vector

Suppose that $X_i, i=1,...,n$ are Gaussian random variables, each with mean equal to $0$ and variance equal to $1$. However, suppose that their covariance matrix is reduced rank (assume that such a ...
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### Large deviation upper bound for Chi-squared random variable

Let $X \sim \chi^2_n$ random variable. I am looking for a large deviation upper bound for $X$. The answer here, says that Since you said that you're looking for an upper bound, it should also be ...
This question came up a little while ago but unfortunately was put on hold. However, I found it intriguing as I had never come across a question like this before. There are $2$ groups of $30$ people ...