# Questions tagged [bounds]

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### Sampling a proposed value with a limited range target when running MCMC [duplicate]

I want to do an MCMC algorithm and need to sample a proposed value from a proposed distribution. In the Metropolis algorithm, people usually use a normal distribution as proposal. But if the prior ...
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### Is a range of values from an exponential distribution still exponentially distributed?

I have to generate numbers of two different exponential distribution ($e_1, e_2$) with parameters respectively $\lambda_1$ and $\lambda_2 = k \lambda_1$, with $0<k<1$. But I also want to ...
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### Understanding the concept of “Bounded in probability”

My statistics book defines the concept of "bounded in probability" in the followng way: ..But doesn't this mean that any sequence of R.V.'s that does not include any R.V.'s with a pdf with infinite ...
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### Bounds on variance and mean of maximum of difference of independent random variables

Suppose $X_1,\dotsc,X_n$ are independent but not necessarily identical random variables. $$Y = \max_{1\le i,j\le n}(X_i-X_j)$$ What upper and lower bounds can be derived for expectation and variance ...
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### Upper bound on KL divergence

Is there a maximum (unique?) to the KL divergence between discrete distributions p & q, with the restriction that q is a proper probability distribution? I know KL is unbounded from above when q ...
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### Correlation bounds for uniformly distributed matrix?

For a uniformly or Guassian distributed $M\times N$ matrix. Is there any analytical expression in terms of $M$ and $N$ to estimate the maximum and minimum bounds of correlation between the columns of ...
### Tail bounds for F-distribution (not using $\chi^2$ bounds)
Are there any sharp tail bounds for an $F_{p,q}$ distribution? That is, if $X \sim F_{p,q}$, then for a $t_1,t_2 > 0$, what are the sharpest $\delta_1$ and $\delta_2$ known such that P(X > ...
Given a random variable $X$ with CDF $F(X)$, mean $E(X)=0$, and variance $Var(X) =\sigma^2$, I would like to bound the tail conditional expectation where $X$ is in the tail with probability $1-p$: \$E(...