# Tagged Questions

Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution.

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### Uniform sampling from general simplex with a twist [closed]

This is part of a question I had asked elsewhere, and then some of the links redirected me to CS stack exchange. Given $a_1,\dots,a_D$ (all strictly positive), I want to draw points uniformly from ...
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### Uniform generation of random bipartite bi-regular graphs?

I want an algorithm that takes the following Input: $M,N,k,d$ positive integers such that $kM = dN$. and produces the following Output: Random bipartite graph, with $M$ vertices all of degree $k$ ...
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### How broken is LCG in the case of partial output?

Suppose we have a linear congruential generator defined by $X_{n+1} = (a X_n + c) \mod 2^n$ where $a, c, n$ are all known and we would like to determine the initial value $X_0$. However, if we can ...
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### Estimate distribution of a composite variable

Suppose I have N sets of numbers (10 numbers per set) {a1, ....., a10}. I form a sum by taking one number at random from each set. SUM = num from set 1 +......+ num from set N. If I do this a large ...
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### Generate a random graph with geometrical degree distribution

I'm working on graph generation, trying to implement the RT-nested-Smallworld network model described in this paper. We are talking about generating an undirected graph in a slightly different way ...
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### How to sample uniformly from a stream of elements, some of which are unsuited?

I get values $x_t$ in an online fashion and want to buy "good" ones, where "good" means that some measure $P(x_t) >T$. Consider the following simple algorithm. ...
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### Sampling perfect matching uniformly at random

Suppose I have a graph $G$ with $M(G)$ the (unknown) set of perfect matchings of $G$. Suppose this set is non-empty, then how difficult is it to sample uniformly at random from $M(G)$? What if I am ...
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### Best random permutation employing only one random number

The ideal random permutation algorithm of Fisher and Yates (Algorithm P in Knuth vol.2) for a sequence of $n$ objects requires $n-1$ random numbers. In some card games one first does a "cut" and ...
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### Algorithms for graph generation using given properties

There may be a large number of algorithms proposed for generating graphs satisfying some common properties (e.g., clustering coefficient, average shortest path length, degree distribution, etc). My ...
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### Stochastical algorithm

We have a stochastic random source. This gives the bit $0$ (or $1$) with probability $1/2$. We want to generate a uniform distribution on the set S = $\{0, 1,..., n-1\}$. Which algorithm gives with ...
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### Construction of binary random variable

We throw two coins in a row and thus get the event space $\{ZZ, WW, ZW, WZ\}$. Each of the 4 elementary events has a probability $1/4$. how can I construct 3 binary random variable $x_1$, $x_2$, $x_3$...
Suppose that we have a random generator that outputs numbers in the range $[0..R-1]$ with uniform distribution and we need to generate random numbers in the range $[0..N-1]$ with uniform distribution. ...