Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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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 ...
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UMP test for hypergeometric distribution

$P(X=x|N,D,n)=\frac{^DC_x \times ^{(N-D)}C_{(n-x)}}{^NC_n}$ Now, I was trying to test for $H_0:D\le D_0$ vs $H_1:D>D_0$ using likelihood ratio test. But to find the maximum likelihood estimate of $...
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Can biased samples be used to improve a confidence interval based on an unbiased sample?

Assume that an urn contains $N$ marbles some are red and some are white. The aim is to determine a confidence interval for the number of red marbles in the urn. This is done by drawing $n$ marbles ...
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Multivariate Hypergeometric distribution for non-exchangeable sequence

I have a problem that I think is similar to the Multivariate Hypergeometric distribution urn problem as described on Wikipedia. I have a dataset where each row is a trial. All trials have the same ...
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Do we assume independence among individual observations in a hypergeometric test?

Commonly, the hypergeometric test and Fisher's exact test are two main statistical approaches used when computing a gene set enrichment for a functional term (e.g., among the top 10 differentially ...
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Binomial Proportions when sampling without replacement not studied?

Question When doing surveys with a population, we obviously don't replace by design. Why is it then that the mathematics and statistics described in textbooks seems to be veering more on the side of ...
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Sample Size Determination for Hypergeometric Rare Event

Suppose that there are 10 smokers and 590 non-smokers in a room and let $X$ be a random variable that describes the number of smokers picked out, without replacement, in $n$ random draws. What methods ...
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How much error will there be if one models the multivariate hypergeometric distribution using a multinomial distribution?

See the title. I stumbled upon this answer which explains the approximation in more detail. One can approximate the multivariate hypergeometric distribution by using the multinomial distribution. ...
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Best way to check that categorical data have not been shuffled

Someone has done a survey, asking a list of $N$ people if they were married ($M$) or single ($S$). You get the result as a table with two columns, 'Name' (text, all unique values) and 'Status' (...
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Probability of getting k different colored balls from an urn with K different colors of balls, each color has the same number of balls

Let's say I have an urn with $n$ balls, with $K$ different colors of balls, where each color has the same number of balls: $\frac{n}{K}$. Given I reach into the urn and grab a ball (without ...
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What is correct way to calculate the expected overlap of protein sets in two related biological system

I have a question regarding the statistics of protein set differences in two biological samples. I have performed quantitative proteomics analyses on both WT and KO cells (derived from the WT cells by ...
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Does the hypergeometric distribution follow a Bernoulli process?

There is a comment in an online resource that I need help understanding: In a Bernoulli process, given that there are M successes among N trials, the number X of successes among the first n trials ...
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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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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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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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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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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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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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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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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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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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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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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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