Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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Can Bayesian methods be used to calculate the distribution of a candidate's true percentage of votes as a function of the # votes revealed?

Partly related to my earlier post: Null and alternative hypothesis in a test using the hypergeometric distribution I was watching the news yesterday evening; they covered the French presidential ...
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How to calculate significance with hypergeometric test on my data?

I have data of interactions between multiple nodes that are binned into either positive or negative. I want to do pairwise hypergeometric tests in R to get the significance of either positive or ...
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How do you calculate the expected value of a discrete distribution without replacement?

Say I have a set of 10 values I want to draw 3 values from, uniformly, without replacement. For instance: $$S = \{0,0,0,0,22.95,0,0,0,19.125,25.5\}$$ With replacement, this seems simple, you just add ...
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how does adding information change the probability of an event?

In a comedy TV programme, four men are sitting at the bar. The barman tells them: "Did you know that, statistically, one out of four men is having an affair?". The first man replies "...
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Drawing 0 green balls from an Urn with non-uniform probabilities

An urn contains $N_1$ red balls and $N_2$ green balls. Each ball has an associated weight. Each ball is drawn (without replacement) with a probability proportional to how much its weight contributes ...
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How to estimate the parameters of a hypergeomtric distribution?

I am looking for some guidance on how to estimate the parameters of a hyper-geometric distribution, based on a random sample. For example, if I generate a distribution as follows: ...
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What distribution does a ratio of successes to failures (with replacement) follow?

Suppose you realize $n$ draws—with no replacement—from a sample of $N$ marbles, in which I know there are $K$ white marbles and $N - K$ black marbles. The probability of getting $k \leq n$ white ...
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Comparing the probability of co-occurrence between two pairs of vectors

Say I have two binary vectors $x,y$ of length $N$, with $n_x, n_y$ the number of $1$'s in those vectors and $n_{xy}$ the number of $1$'s that co-occur in the same spot. The probability that $n_{xy}$ ...
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Are the reported odds to win Lotto Max on https://playalberta.ca/games/lotto-max incorrect?

The Alberta Lottery displays the odds to win various Lotto Max prizes on their website here . Each $5 wager contains 3 sets of 7 numbers. The winning numbers are drawn from a pool of 50, so the ...
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Least likely sample in Multivariate Hypergeometric distributions

Let $U=(U_1,U_2,\dots,U_c)$ being an urn with $U_i$ balls of color $i \in [1,c]$ and $\Omega(U)$ be the set of possible draws from urn $U$. For $D \in \Omega(U)$ the probability of drawing $D$ is ...
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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/...
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Combinatorics - calculating probability of choosing n people from m groups of k people

I am trying to calculate and understand the following question: I have 10 groups of 10 people each and am choosing 10 people at random. What is the probability that all 10 people I have chosen are ...
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Sampling identical sequences from two urns with unique colored balls

In very simple terms, my problem is as follows: given two urns, both with N balls where each ball has a unique color, I am interested in sampling sequences of N balls without replacement from each urn....
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Fixed margins in the fisher exact test

I'm working on my thesis and I've encountered a problem where Fisher's Exact Test proves helpful. I would however also like to understand what I'm exactly doing, rather than just plugging in numbers ...
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Is There a Conjugate Prior for a Multivariate Hypergeometric Likelihood?

I am working on a problem using a multivariate hypergeometric likelihood. The multivariate hypergeometric distribution does not belong to the exponential family of distributions, so (to my knowledge) ...
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Game design urn problem

I am designing a tabletop game and trying to conceptualise the probabilities involved. These can be expressed as an urn problem: Our urn contains seven counters, either green or red. We draw five and ...
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Test change in intersection between two sets of subsets

let's say I have a set A, and a set B, both subsets of C. To test whether A and B have statistically greater overlap, I can use the hypergeometric test. However, let's say I now have: $A_1, B_1 \in ...
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How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want?

Let there be 500 units of stock $s$ of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood $m$ of 5% that it is precisely the item that the customer ...
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Multivariate Hypergeometic Distribution with overlapping events

I have a deck of 52 playing cards and I play a game where I need a combination of specific card categories to make combos. For example: I draw 5 cards as a sample hand and I need exactly 1 Jack and 1 ...
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Hypergeometric distribution with no number of defect items information

So I am looking at the problem here: A hospital has received a shipment of 25 new X-ray machines. The hospital could lose its license for housing X-ray machines if the machines are not properly ...
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What is the best way to test of draws ( 10,000 unique possibilities) from multiple sample are random?

say I have 6 people drawing from their own box, each box contains 10,000 unique barcodes. Now at the end of the experiment each person has drawn roughly 10-20 barcodes. How do I test if the barcodes ...
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Intuition for hypergeometric variance?

I'm trying to learn the major facts about a bunch of probability distributions, hypergeometric included. I can use the commonalities between it and a binomial to my advantage for thinking through some ...
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Percent chance that two samples are different population (NPS)

Practical question (not a statistician), I want to make a PPT slide (amongst several) in a business discussion, related to comparing a new survey with an old one. Want to be able to say something to ...
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Draw two balls without replacement

Suppose we consider an urn with 3 red balls and 5 blue balls. We now draw two balls without replacement. If we draw a red, it is a success otherwise a failure. Let X=1 if we draw a red ball in the ...
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hypergeometric test for gene feature enrichment on population frequency data

I have a data frame that represents the frequency of gene features in the background population, and several sub populations. For each sub-population, I want to do an enrichment analysis in R with ...
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Head to Head Poker /w Special Rules

Is there a profitable strategy for this poker variant? If so, what is the most profitable strategy? Expressed as a percentage of your "special ante", how much would your strategy win on ...
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How to calculate $Var(X)$ for the union size?

Let's say there is a set of $4$ bags $\{{a,b,c,d\}}$ containing balls of colors $\{{red,blue,green,orange,black\}}$. Balls are assigned to bags in an arrangement that allows a variable number of ...
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When is it justified to assume a hypergeometric distributions for power analysis and hypothesis testing

Suppose a car rental company historically only rented white cars, and they want to to test if red cars make customers more likely to pay for an upgrade, such as enabling satellite radio. (I am just ...
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Binomial vs hypergeometric finite sampling distribution

I was reading these notes:Finite Population Sampling with Application to the Hypergeometric Distribution and I have a question just about the first two pages. The first page, they derive the variance ...
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Exercise on MLE with hypergeometric distribution

I am struggling with the following exercise from Stapleton's book (it's exercise 7.4.1). A box contains eight eggs, of which an unknown number $R$ are rotten. You take a simple random sample of three ...
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Using hypergeometric test for presence/absence of different conditions

My dataset consists of 3 conditions, with different numbers of samples in each condition (30 in condition 1, 80 in condition 2, 50 in condition 3). I have measured the presence or absence of a gene in ...
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Drawing a random sample without replacement from data set

I have data generated by a RCT with a control and treatment group, each with n=300, so N=600. The observations are assumed to be i.i.d.. From that population, I'd like to draw 5 random observations ...
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Is this a Hypergeometric Distribution Problem?

There are $100$ people who bought a ticket for a raffle with $5$ prizes being offered. They randomly draw a name for the $5^{th}$ place prize, then they randomly draw a name for the $4^{th}$ place ...
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3 votes
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How to determine odds in a game similar to roulette

A game similar to Roulette has 360 slots. 20 of these slots are 'scoring' positions. Each slot will only accomodate 1 ball. If a number of balls are introduced (Say 3) What are the chances that any 1 ...
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Probability of drawing two differently colored balls in a partition of equally sized partitions

If I randomly distribute, say, 100 red and 10 blue balls onto a field of 10000 square meters (100*100 m), how would one calculate the chance of having at least one red and at least on blue in the same ...
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2 votes
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Comparing a random sample and a non random sample extracted from a finite population

I am not able to formulate a more descriptive title. I have a population of five million people, I code it with R programming language: pop <- 5e6 41% of them ...
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3 votes
1 answer
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How to interpret the univariate Fisher's noncentral hypergeometric density PMF?

This is my first time posting so I apologize in advance for any errors! I am struggling to understand the probability mass function (PMF) of the Fisher's noncentral hypergeometric distribution, which ...
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3 votes
1 answer
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Connection between Bayesian A/B testing and Fisher's exact test (specific example on Hydroxychloroquine trials)

I understand that there are multiple comparisons floating around between Fisher's Exact Test and Bayesian A/B Testing, here's an example. While I do understand these are fundamentally making different ...
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1 vote
1 answer
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Hypothesis testing for large N small k

I've got a set of differentially expressed biomarkers that I want to check for the significance of this observation. For a similar problem, I've seen the hypergeometric test being used, where $k$ = ...
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3 votes
1 answer
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How to calculate this dependent probability (marbles without replacement)?

I present the question in two steps: First: Let there be 100 bags. A person puts 5 marbles into 5 separate, randomly selected, bags. You are now to collect the contents of the bags, one by one. If you ...
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Correlation Coefficient for Hypergeometric-type Distribution

Problem Statement: A box contains $N_1$ white balls, $N_2$ black balls, and $N_3$ red balls $(N_1+N_2+N_3=N).$ A random sample of $n$ balls is selected from the box (without replacement). Let $Y_1,Y_2,...
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3 votes
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Hypergeometric distribution- problem with derivation

A random variable $K$ has hypergeometric distribution with parameters $N, m, n$, with probability mass function: $$ p_K(k)=\frac{\binom{m}{k}\binom{N-m}{n-k}}{\binom{N}{n}},\quad k\in\{\max(0,n+m-N),\...
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Which probability result is greater? Using hypergeometric distribution or binomial distribution?

Suppose I have $N$ samples, and 1/4 of them are bad. I draw $n$ samples $(n<N)$, and I want to know what's the probability that less than 1/3 are bad. I know it should use hypergeometric ...
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When to use hypergeometric vs binomial

I'm having some trouble understanding if I need to use a hypergeometric distribution. I have a set of components, a small proportion of which are faulty. I now want to know if a feature of that ...
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Hypergeometric-like test for ordinal/interval variables

The problem: Given an urn with $N$ balls of varying weights, with a mean (or median, in case of an ordinal variable) weight of $x$. The weights of all of the balls in the urn are known. If we were to ...
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Computing significance of overlap between two sets in Python

I am computing the significance of an overlap between two subgroups, each in two related datasets 1 and 2. For instance: Dataset1 total: 500 Dataset1 subgroup: 100 Dataset2 total: 300 Dataset2 ...
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1 answer
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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 ...
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3 votes
1 answer
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Probability of observing a number of special balls from a larger set

Suppose there is a collection of $n$ balls of which $m$ are special. What is the probability of drawing $k$ special balls, when $p$ balls are drawn? To give it a try I considered the following ...
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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 ...
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1 vote
1 answer
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Why does Fisher’s exact test use the hyper geometric distribution rather than the multi nomial distribution?

To understand hypergeometric and multinomial better, I’d like to know why fisher exact test used hypergeometric rather than multinomial distribution.
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