Questions tagged [hypergeometric-distribution]
A discrete distribution used to model sampling without replacement.
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How to construct confidence limits based on small stratified samples of finite populations?
Imagine a business wishes to audit its transactions. It has a database summarizing the transactions, which constitute a sampling frame for the population. It would be time-consuming and expensive to ...
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Hypergeometric: how do I construct a credibility interval around K (population successes) in R?
I have a problem for which I believe I should use the hypergeometric distribution, but I can't figure out how to do it in R.
Say I have a bag of marbles with known number ($N$) of marbles, but the ...
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Using the hypergeometric distribution for skipping events in transcriptome sequencing
My question is inspired by this post. However, its a bit more complicated than that to explain. I hope I succeed.
I work with RNA-Seq data on alternative splicing in plants. For this discussion, lets ...
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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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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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want to calculate significance of pairwise sharing between lists. Standard hypergeometric test seems inappropriate
I want to calculate if the percentage of sharing of strings (genes in this case) between lists is significantly more than expected by chance for multiple pairwise comparisons between lists of strings. ...
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Combination of Z-scores and hypergeometric distribution?
I am trying to apply an analysis I've seen in a publication to our data, but I ran into problems when it came down to the specifics. The publication is open-access an can be found here for reference. ...
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Test of strict difference in independent binomial probabilities
Suppose $X,Y$ are two independent binomial random variables with parameters $n_1,p_1$ and $n_2,p_2$ respectively. Suppose one wanted to test the hypothesis $p_1>p_2$. Conditional on $X+Y=s$, ...
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Can I use Bayes Theorem to find a conditional distribution rather than conditional probability?
I might be going about this the wrong way, but I'm trying to develop an understanding of a particular conditional value, say $P(CustomerBuysFries | CustomerBuysHamburger) = P(F|H)$. Ultimately, I want ...
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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 $p_i$ (...
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Is there an efficient algorithm for sampling from the negative hypergeometric distribution?
I'm writing a small statistics library currently. One of the algorithms I'm implementing has two variants: one that samples the hypergeometric distribution and one that samples the negative ...
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Distribution of the size of overlap between two random samples with duplicates?
Similar to this question, I want to know if the overlap between two samples is significant. However, my items are not unique; I have $c$ distinct colors of items, there are $m_i$ items of color $i: (...
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Sample from multiple urns - when to stop?
I have a problem that hasn't yet been addressed, although follows similar lines of reasoning here and here. My problem is as follows:
I have $N$ urns, each with a different number of black and white ...
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Pseudocounts and Hypergeometric Distribution
How can I add pseudocounts to hypergeometric distribution to calculate p-values.
By Pseudocounts I mean: A pseudocount is an amount (not generally an integer, despite its name) added to the number of ...
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CDF of multivariate hypergeometric distribution
I am trying to find the CDF of the multivariate hypergeometric distribution, but was unable to come across any sources. Could someone point me in the right direction?
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Chance that sample contains more individuals from one group than from another
Question:
18 men and 12 women have agreed to participate in a randomized
controlled experiment. A simple random sample of 15 of these 30 people
is chosen as the treatment group; the others form the ...
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Barnard's Exact Test (Boschloo's variant) when distribution is hypergeometric
Let's say, we have a standard $2 \times 2$ contingency table and because of low sample size we're about to use some type of Exact Test, e.g. Fisher's Exact Test (FET) or Barnard's Exact Test.
It's ...
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Urn with balls of two colours with a priori probability of each ball
If we have a urn with $N$ balls of two colours ($D$ red and $N-D$ black balls respectively), then probability of having $k$ red out of $n$ balls drawn at once without replacement follows the ...
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Multivariate hypergeometric confidence intervals
Suppose you have an urn filled with money. You know there are $N$ total bills, and that each is either a \$1, \$10, or \$100. You draw $n$ bills without replacement from the urn, and wish to construct,...
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Combined hypergeometric distribution of exclusive sets
Given the following:
a set of numbers, 1 to 20
four sets of five numbers from the set above (each number used once)
a draw of five different numbers from the first set
How would I determine the ...
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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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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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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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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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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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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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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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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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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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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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Multivariate hypergeometric distribution: Multiple bins
My question concerns a variant of the classic urn problem for the case of more than 2 types (colours).
Given a single urn with $N$ balls of 3 distinct colours (say, red ($R$), green (G) and blue ($B$...
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Hypergeometric testing
I have a large container with
21505 toys, **14,038 action figures (5,397 brands)** and 7,467 barbies (1 brand).
Sample:
...
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2x2 contigency table hyper-geometric test
I'm having trouble using the hyper-geometric test on a 2x2 contingency table. I have listed the null hypothesis below.
Assuming the null hypothesis is: $$P = \frac{A}{A+B} = \frac{C}{C+D}$$
From here,...
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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 ...
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Fisher's exact test for multidimensional contingency tables
I have a dataset that has 6000 instances, each with 8 boolean values.
...
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Tests for independence in ragged arrays / bipartite matchings
Let $(Y_i, K_i)$, $i=1,\dotsc,N$ be pairs of observations drawn from discrete labels $L$ and discrete clusters IDs $C$.
For example $Y$ could be individual birds, $L$ could be a set of species and $...
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Binomial modelling, testing and Bonferroni
I am currently trying to validate an implementation that is supposed to randomly assign a certain number of tags to users who enter a platform. The variable of interest here for me is the sum of all ...
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Sampling from hypergeometric distribution
Suppose there are 1 million balls in the urn. And 1% of those are red, the rest are black. I sample 1000 balls from the urn, and I want to know what's the cumulative probability of getting at least 10 ...
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Hypergeometric problem - balls of two colors drawn from box
There are 55 balls in the box, of which are 25 red and the rest is black. We draw randomly 8 balls from the box. What is the probability that among the selected balls will be a) exactly 2 black balls, ...
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Hypergeometric dist. with three balls
We have 13 black balls, 3 red balls and 16 white balls.
We want to calculate the probability for getting 16 balls where we want only
the white and red balls i.e. zero black balls.
We draw without ...
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Non-integer Arguments for R's phyper Function
In the code below, why does phyper return a result for non-integer arguments? I would expect it to complain bitterly in the same fashion dhyper did.
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Incorporating uncertainty in hypergeometric probability test
Wikipedia's page on determining the hypergeometric probability describes the variables in the following way:
N is the population size,
K is the number of success states in the population,
n ...
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Test statistic and C.I. for population proportion
I'm doing a test statistic and C.I. for population proportion. Can someone explain to me what are assumptions coming from hypergeometrical distribution directly to normal distribution?
As I understand,...
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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 ...
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Test to find expected outcome
I have a list of genes and I tested if these genes are associated with a disease by using the genome-wide association summary statistics dataset. Chi-square statistics was used and after performing ...
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multivariate hypergeometric test in R
I have 10 multiple choice questions, each question has 4 answers and all answers are same for each question. Lets say choice D is the correct answer for all questions, but 35% of the answers were ...
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Likelihood of all hypergeometric parameters conditional on all others
How to derive the likelihood function of other parameters of the hypergeometric distribution conditional on the others?
Why is the $L(N|y)$ equivalent to $P(Y=y)$?
I mean This seems too evident. I'm ...
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