As of May 31, 2023, we have updated our Code of Conduct.

# Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

30 questions
Filter by
Sorted by
Tagged with
6k views

### What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?

If I am selecting 232 people from a pool of 363 people without replacement what is the probability of 2 of a list of 12 specific people being in that selection? This is a random draw for an ultra ...
3k views

### How to calculate a sample size for validating correct/incorrectness of records in a data table?

I have read through existing answers on CrossValidated (plus elsewhere online) and can't find what I'm looking for, but do please point me to existing sources if I've missed them. Let's say I have a ...
8k views

### What is the test statistic in Fisher's exact test?

For a 2 by 2 contingency table, some said Fisher's exact test uses the count $X_{1,1}$ in the (1,1) cell in the table as the test statistic, and under null hypothesis, $X_{1,1}$ will have a ...
1k views

### Estimating Size of a Set based on two Overlapping Subsets

I've searched everywhere for a similar question and many things come close but are not the same. I'm looking for a way to estimate the size of a set if two partially overlapping subsets are known (...
4k views

### Which are differences between the hypergeometric distribution and chi-square distribution

As the title suggest...I have a very basic question. I have a case with the following data: ...
7k views

### Geometric distribution without replacement

On an attempt to solve this problem I've managed to reduce it to finding the expected number of white balls picked until one black ball is observed (let's call that value $v$). Except that, unlike the ...
1k views

### How to compute confidence interval in a case with small sample size, small population size, and one very dominant class?

I have a situation that is analogous to someone starting with a bag of 150 red and blue marbles, and, sampling randomly without replacement, drawing 37 red marbles and 3 blue marbles. What is a ...
1k views

### Hypergeometric distribution when K is unknown

The probability to have $k$ white balls in a sample of size $n$ taken from an urn of $N$ balls with $K$ of them being white is equal to:  P(k|n,N,K) = \frac{{{n}\choose{k}}{{N-n}\choose{K-k}}}{{{N}\...
1 vote
4k views

### Hypergeometric test for enrichment analysis?

I am referring to a previously asked question on my case for gene enrichment analysis using hypergeometric distribution. Here is my modified question (many thanks to @Glen_b): I have a mixture of ...
160 views

### A variation of the Lady Tea Tasting problem [closed]

I am quite stuck on this question. My intuition would have been to say that we would prefer to pour milk first on heads, but I am not sure. The setting is: the Lady guesses "milk first" in 2/...
4k views

### How to apply multiple testing correction for gene list overlap using R

I have 2 studies looking at the patient response to the same drug. Study 1 found 10,000 genes expressed above the background and 500 of them are differentially expressed and referred to as the drug ... 12k views

### How to use hyper-geometric test

My professor wrote some things very quickly on the board and I had a very hard time interpreting what arguments are being made. I am trying to test the conclusion. I read this post but I'm still not ...
3k views

### Probability of drawing no red balls from 20 draws without replacement given finite sample

I understand this to be a binomial distribution: There are 100 balls in a bucket. 10 are red, 90 are blue. I select a ball at random and then replace it in the bucket, and I do this 20 times. I then ...
510 views

### Significance test across multiple simulated experiments

First time question on this site, so please bear with me, thank you: I have 6 coin-flip-type experiments for which I can calculate 6 binomial p-values. I would now like to calculate the significance ...
165 views

### How likely are various outcomes in a lottery with multiple prizes

This question is (I think) simpler than most posed here, but it's beyond my ability to solve. I'm trying to calculate the probability of various outcomes for a charter school lottery. There are ...
2k views

### Sum or mean of several related hypergeometric distributions

I have an odd problem which can be phrased in a general way, and a more specific way. I'm curious about the answers to both. Although, really, it's the k=0 case that I'm really interested in - ...
1k views

### Null and alternative hypothesis in a test using the hypergeometric distribution

I'm having doubts about some aspects of hypothesis testing, and I would appreciated if someone could please clarify / point me to some relevant literature or posts. The ones I could find so far didn't ...
89 views

### Characterize this discrete distribution

Suppose we have $k$ buckets, with an infinite number of balls in each bucket. The balls within one bucket are indistinguishable, those between buckets are. We assign to bucket $i$ a probability $p_i$ (...
65 views

### A GENERAL inequality for a bi-modal hypergeometric distribution

Say $X$ has a hypergeometric distribution with parameters $m$, $n$ and $k$, with $k\leq n<\frac12m$. I know that $X$ has a dual mode if and only if $d=\frac{(k+1)(n+1)}{m+2}$ is integer. In that ...
99 views

### An inequality for a bi-modal hypergeometric distribution

Say $X$ has a hypergeometric distribution with parameters $m$, $n$ and $k$, with $k\leq n<\frac12m$. I know that $X$ has a dual mode if and only if $d=\frac{(k+1)(n+1)}{m+2}$ is integer. In that ...
1k views

### multinomial distribution sampling

I was reading the Wikipedia example from the Multinomial Distribution article: In it they say: "Note: Since we’re assuming that the voting population is large, it is reasonable and permissible ...
986 views

### Is the beta-binomial distribution a conjugate prior for some distribution?

The beta distribution is conjugate prior for the binomial distribution. Is the beta-binomial distribution a conjugate prior for some sampling distribution?
1 vote
2k views

### Multivariate Hypergeometric Distribution with "or more" Successes

I understand how to calculate multivariate hypergeometric distributions. For example, if you have an urn with 2 red marbles, 4 white marbles, 8 blue marbles, and 12 orange marbles, the probability of ...
1 vote
2k views

### Which probability distributions are not exchangeable?

Are there any specific families of probability distribution which are not exchangeable by construction? I was thinking that the Hyper Geometric distribution would not be since it models random ...
244 views

### Probability of getting a run of r heads in n coin tosses where run ends at nth coin toss

Looking for a closed form solution. Here is the one of the approaches that a text book presents: Let $f_{n}$ be the probability of getting run of $r$ heads in $n$ coin flips where run ends at $n$ ...
20 views

### Vapnik-Chervonenkis dimension of hypergraph, given bound on number of hyperedges

in studying now about Vapnik-Chervonenkis dimension, and there is one question that I not able to solve. Let $\textrm{(X , R)}$ be a range space so that any hypergraph $\textrm{(V, F)}$ in it ...
200 views

### Calculating hypergeometric probability with approximations

I'm essentially trying to reproduce the dhyper function in R using !n ~ gamma(n+1). Why does this approach not work for large ...
553 views

### Confidence interval for number of successes in population in a hypergeometric distribution

I have a hypergeometric distribution with known $N$, $n$ and $k$ (following the notation on Wikipedia) and I'd like to calculate the confidence interval for $K$. I considered the Poisson ...