Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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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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91 views

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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30 views

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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64 views

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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96 views

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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94 views

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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208 views

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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Studies on a special case of the hypergeometric distribution

-Hi, The hypergeomtric distribution is one that is generally intractable to much in depth analysis (i.e. a closed form expression for the median is not known). However, I am working on a problem where ...
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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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82 views

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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time complexity of sampling from multivariate hypergeometric distribuiton

numpy has an implementation and the doc is here. It says it is "roughly" equivalent to: ...
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142 views

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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50 views

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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108 views

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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163 views

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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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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157 views

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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276 views

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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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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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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88 views

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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Confusion over multinomial and multivariate- hypergeometric distributions

You, your parents, your sister, go to visit grandma for her birthday. Grandma made a cake for the party. If she puts $20$ raisins in the cake at random in the cake, and she divides the cake into $5$ ...
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What is the probability of 5 anomalies appearing in a batch of 100, from a data set of 1000 examples and 10 anomalies?

I am trying to work out the expected value of the following example: A data set contains 1000 examples in total. 10 examples can be considered anomalous. I am randomly drawing 100 examples to form a ...
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mutual information for testing set enrichment?

I've created a process that associates members of two sets, specifically codes from the International Classification of Diseases (ICD) hierarchy and the semantically richer Monarch Disease Ontology (...
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What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?

Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
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why is the margin (total number of sample) important when deciding between hypergeometric and Fisher's exact test

My impression is that both of hypergeometric and Fisher's exact test are similar in calculating the significance of contingency table. The main difference is whether or not you know the margin (if you ...
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Different formulas for two-sided mid $p$-value ($2\times2$ table setting)

I'm interested in testing independence of two binary variables in a $2\times 2$ table: i.e. $H_0: \theta=1$ against the two-sided alternative $H_1:\theta\neq 1$, where $\theta$ is the odds-ratio. ...
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Expected value for a sequence of group samplings from a fixed population

Suppose I've 100 apples where 25 of them are bad and the remaining 75 are good. I draw apples 20-by-20 from this group of apples. That is, I draw the first set of 20 apples from 100 apples, second ...
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540 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 ...
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How can I calculate the continuous cumulitive density function for a hypergeometric distribution?

I have a sample from a large population where it is possible to select either a 1 or a 5. I want to find the probability that the average in any sample is greater than 4.76, and I want to chart the ...
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Devising an acceptance sampling plan for False Negative Rate

I need to evaluate a binary classifier that classifies inputs in positives and negatives. Since all predicted positives (PP) are assessed, I have complete data on the true positives (TP) and the false ...
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293 views

Quantile (Inverse Cumulative Density) Function for Hypergeometric Distribution

The hypergeometric distribution arises from sampling without replacement. The similar binomial sampling distribution assumes replacement. Hypergeometric distributions are commonly used in quality ...
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Variance of a hypergeometric distribution

I'm trying to answer the following question from Ross's book: A pond contains 100 fish, of which 30 are carp. If 20 fish are caught, what are the mean and variance of the number of carp among the 20? ...
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114 views

Question regarding MLE

I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get. The question is ...
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Hypergeometric Probability with a twist

A manufacture receives a lot of 200 parts from vendor. The lot will be unacceptable : If more than five (>5) parts are defective. The manufacturer will select randomly K parts from the lot ...
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What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the ...
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662 views

SOA Conditional probability question [closed]

I can't get this correct. Could you please provide a hint to aproach this problem? How do i get the probability of that loss? "A state is starting a lottery game. To enter this lottery, a player ...