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# Tag Info

## Hot answers tagged hypergeometric-distribution

12 votes
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### How do you calculate the expected value of a discrete distribution without replacement?

@BruceET's answer has some nice information, and simulations are often a good starting place for this sort of thing in practice. In this answer, I'll detail an exact approach, which demonstrates that ...
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9 votes
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7 votes
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### What is the difference between the Multivariate Hypergeometric distribution and the Noncentral Hypergeometric distribution?

Hypergeometric distribution describes the number of observed white balls $k$ out of $n$ draws without replacement from the urn containing $K$ white balls and $N-K$ black balls. Multivariate ...
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7 votes
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### How to use hyper-geometric test

You can look at wikipedia. The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of ...
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6 votes
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### Distribution like hypergeometric distribution, but with false replacements

Suppose an urn of $n$ balls begins with $s$ successes. What are the chances it will end up with $t$ successes ($0 \le t \le s$) after $d$ draws? Ignoring the trivial case $s=0$, this is a Markov ...
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6 votes

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4 votes
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### Multivariate distribution from drawing balls with elimination of previously picked colors from urn at each step

Whuber already answered your question in the comment by referring to this math.stackexchange.com thread, but for completeness let me expand his comment. Probability of drawing first ball of $i$-th ...
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4 votes
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### Hypergeometric distribution: less than ($P(X<k)$)

Since the hypergeometric is discrete with support over a set of non-negative integers, $P(X \lt k) = F(k - 1)$, where $F$ is the CDF of the hypergeometric distribution. The formula for the CDF is ...
• 8,864
4 votes

### Odds of winning multiple raffle prizes

Ignoring issues like how the tickets are clumped, which is hard to address without getting into empirical rather than purely mathematical matters, and the probability of this happening to any of the ...
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4 votes
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### Connection between Bayesian A/B testing and Fisher's exact test (specific example on Hydroxychloroquine trials)

Which "data generating story" corresponds to which test and why they're fundamentally different? Which "data generating story" and therefore modeling approach is more appropriate ...
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3 votes
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### Null distribution of fisher's exact test; where the nullity is used?

The hypergeometric results when randomly drawing without replacement from a collections of two kinds of objects. The classic example is drawing $n$ balls from a (well-mixed) urn containing $w$ white ...
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3 votes
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### Strategy to win a card game that follows Wallenius' noncentral hypergeometric distribution

Let there be $w$ win cards and $l$ loss cards. The chance of a win, with optimal play, is still just $w/(w+l)$. That's because at each stage you are making a choice between two (usually risky) ...
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3 votes
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### Best plausible estimate of parameter of hypergeometric distribution

Basically $$P(K=k|m=m,n=n,r=\tilde{r})$$ is the likelihood function, so you could as well conduct a grid search among any integers within the valid values for $r$ to maximize the likelihood. If ...
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3 votes
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### How to calculate this dependent probability (marbles without replacement)?

Let's generalize both questions so we don't have to solve them twice: Let there be $n\ge 0$ bins indexed $1,2,\ldots, n.$ Suppose there are $C\gt 0$ different colors of marbles and $0\le k\le n$ ...
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3 votes
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### UMP test for hypergeometric distribution

Here $X\sim \operatorname{HyperGeo}(N,D,n) .$ We need to find (if it exists) the UMP test of $\mathcal H_0: D\leq D_0$ vs $\mathcal H_1: D> D_0.$ What should be the approach to tackle such problem,...
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3 votes
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### Binomial distribution but only failures are replaced

At any given day $t$, the distribution of deaths in the remaining population of size $n_t$ is binomial with the probability $p$ and sample size $n_t$. There is no single distribution for all days, as ...
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3 votes

### Estimating parameters of hypergeometric distribution when population size is unknown

Just to echo @Ute 's answer, the maximum likelihood estimator can sometimes not exist even when there are multiple samples and none of the values of $n_1$ and $n_2$ are zero. Suppose we take 5 samples ...
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3 votes
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### Mark recapture with no knowledge of marked individuals

From first principles it is clear that the single observed hypergeometric sample of size $n$ out of which $k$ will be informative about little more than $p=K/N$. Both $N$ and $K$ will be nearly ...
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