# Questions tagged [discrete-distributions]

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### Maximum entropy discrete distributions with specified mean

Consider a discrete distribution on {1, ...,n}, with mean given as $m$, what is the maximum entropy distribution? I know it takes the form $p_{X}(k)=ar^{k}$ and is a geometric distribution when n is ...
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### Measure how good is the discrete approximation of continuous random process?

If continuous random random process approximated with discrete version - how to measure how good is the approximation? One possible way is to compute and compare the moments. But for some probability ...
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### How to prove or disprove that a complete sufficient statistic exists?

We have a discrete random variable which takes values with probabilities $p, q, p+q$ and $r$. I want to construct a complete sufficient statistic based on a single observation from this distribution, ...
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### What are the limmitations of reparametrization gradients for discrete random variables? (Gumbel-softmax)

We know that one approach for re-parametrizing gradients for variational inference is taking the Gumbel-softmax estimator proposed in [1] and [2]. In [3], that is a talk on SVI, D. Blei at around 29:...
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### Are discrete maximum entropy distributions uniquely determined by their energy function?

I read this somewhere but can't find a reference, I'd love to be pointed in the right direction. I'm specifically interested in discrete Boltzmann distributions with interactions at different orders, ...
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### guessing a number between 1 and 100

Person A chooses an integer between 1 and 100 at random, then B can guess that number in (at most) 7 attempts, i.e. $\log_2(100)+1=7$. What if now A chooses an integer from a distribution that is ...
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### Maximum-likelihood histogram from noisy data

Given a sequence of noisy observations $\{x_k\in\mathbb{R}\}$ and a set of thresholds $\{t_i\in\mathbb{R}\}$ we can bin the observations using the thresholds to create a histogram. However, since we ...
32 views

### Approximating a distribution with an integer histogram

Given a distribution $f:[0,a)\rightarrow\mathbb{R}$, is there a simple algorithm by which to find a sequence $\{h_i\in\mathbb{N_0}\}$ such that $f(x)$ is approximated by $h_{floor(x)}$ as a histogram ...
I need to compute the upped bound for the tail (survivor) probability $P(X \ge t)$ for the discrete Binomial random variable $X$. I could use Chernoff bounds, however according to this paper [1] the ...