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Questions tagged [hypergeometric]

A discrete distribution used to model sampling without replacement.

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20 views

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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1answer
100 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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51 views

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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12 views

Central Limit Theorem and hypergeometric distribution

We have a game V, which is about pulling 3 cards repeatedly from a deck of 52 cards. For each card with a picture (12 of 52 cards are with a picture) then we win 100 USD of money for each card. We ...
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1answer
26 views

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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1answer
76 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 ...
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1answer
27 views

Probability distribution for draws with conditional replacement? (or how many matches does it take to beat Yugi The Destiny?)

While trying to figure out an old video game, I seem to have stumbled upon a problem that's halfway between a binomial distribution problem and a hyper-geometric distribution problem. With the hopes ...
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15 views

Enrichment analysis--what does this psi mean?

Here is a figure taken from this bioinformatics paper. It's describing the "Deviation of the cumulative distribution from uniform of the scaled ranks", but it doesn't explicitly tell me about what $D(...
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96 views

Hypergeometric Confidence Intervals

I need to create a confidence interval for the mean and variance of hypergeometric distribution of random numbers in R. Does anybody know how I can do this?
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45 views

Finding p-value of similarity between 2 networks

So, I want to calculate p-value of a case if possible. Suppose I have: set A with 1,295 elements set B with 493 elements number of same element between set A and B (intersection) is 478 From each ...
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18 views

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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1answer
19 views

Background selection in hypergeometric test using diferent cell types

I have to select the background for an hypergeometric test that I have to perform. The problem is as follow: I have a list of genes differentially expressed in cell B between "control vs treatment"....
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1answer
30 views

Probablity that at least n selections from one sample exist in another

Have a probability question I'm not sure how to solve. Hopefully this makes sense: 1) Lets say we have a population of 1000 unique books. 2) First, we take a random sample (without replacement) of ...
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26 views

Distribution for selecting marbles from an urn, but some marbles can't be removed, and checkpoints on success

I'm doing some research to see if there is a distribution I can use to match a somewhat complicated problem, which is as follows: 158 numbers are to be selected at random in the range of 0 to 8191. ...
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1answer
146 views

How to decide on whether it is a hypergeometric or a multinomial?

I am a bit confused whether I should use a hypergeometric or a multinomial distribution when I encounter a questions having more than two X_i and I kinda remember that for multinomial distribution the ...
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59 views

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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88 views

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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1answer
74 views

Confidence interval for sample size for urn problem (sampling without replacement)

I have a finite population (H) of animals with a known number of GPS collars (C). If I take a random sample of (M) animals, the probability of a given number (X) of GPS collars being in the sample is ...
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34 views

Probability of finding a rejection in a sample

What is the probability that I find a rejection in 20 samples inspected if the total population is 234 and there are 11 rejections?
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274 views

MGF of the multivariate hypergeometric distribution

Does the multivariate hypergeometric distribution, for sampling without replacement from multiple objects, have a known form for the moment generating function?
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120 views

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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1answer
59 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 $n$ ...
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391 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 ...
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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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235 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 ...
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174 views

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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1answer
40 views

What is probability of this event? [closed]

Sorry for my English at first. I have 20 balls with numbers from 1 to 20. First I write on paper two different numbers from 1 to 20 and than pick randomly 10 balls (without return). What is ...
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1answer
309 views

Odds of winning multiple raffle prizes

A few weeks ago, my wife and I went to a fundraising banquet. We bought 12 raffle tickets, of what I estimate was about 4,000 sold. There were about 30 prizes drawn (tickets pulled randomly from a big ...
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1answer
53 views

Best plausible estimate of parameter of hypergeometric distribution

Consider the Urn problem where a hypothetical urn contains a finite number of $m$ balls, $r$ of which are black and $m-r$ are white. We take a random sample without replacement of $n$ balls and ...
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1answer
54 views

Strategy to win a card game that follows Wallenius' noncentral hypergeometric distribution

Let's say that you have a two valued deck of N = 53 cards. Win and lose are the only values and we know that #win = 26 and #lose = 27. To play, we pay 1 unit of value. We draw one card at a time, but ...
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266 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 ...
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2answers
99 views

Distribution like hypergeometric distribution, but with false replacements

I'm trying to find probabilities for a scenario that works exactly like hypergeometric distribution, except that every time you make a draw, you replace it with a "failure"-object. So eventually you'd ...
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29 views

Probability that two different size lists, drawn from the same pool, will have common members

Two companies are marketing their similar products to a limited pool of 400,000 eligible customers. Company A has 2500 customers total. Company B has 150 customers total. Upon examination of the ...
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562 views

How to modify Fisher's exact test if sample size if larger than 20?

I have a 2x2 contingency table with the following values: $$A = 20, B = 10, C = 200, D = 300$$ As you can see, the sample size is much larger than $20$, the recommended sample size if one were to use ...
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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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1answer
3k 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 ...
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1answer
95 views

What is the repetition distribution of Pulling balls out of two bags?

I have two bags each with $m$ balls. In the first bag I have $n_1$ blue balls. In the second bag I have $n_2$ blue balls. The target is to pull out a total of k blue balls from both bags ($m>n_1&...
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1answer
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What is the repetition distribution of Pulling balls out of a bag?

I have m balls in a bag, n of them are blue. The target is to pull out k blue balls. (m>n>k) Once I pull out a ball I don't put it back. I want find out the distribution of the number of times I need ...
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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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1answer
168 views

Modify hypergeometric test?

I have a problem with the fundamentals of hypergeometric distribution for gene enrichment analysis. Here is the problem: I have a set of genes (population size 1500), a mixture of various genes ...
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1answer
537 views

Use Fisher's Exact Test or a Hypergeometric Test?

I'm looking to test for set enrichment and I'm wondering whether a fisher's exact test or hypergeometric test is more appropriate (and, if there isn't a straightforward answer, what the relative ...
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217 views

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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1answer
93 views

What can I infer from “no evidence” in a hypergeometric distribution sample

I have a population of 320 marbles--they are all supposed to be white, but I can't be certain. If I set a "resolution threshold"--say 5%, then I am hypothesizing there may be up to 16 black marbles. ...
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1answer
425 views

min and max of hypergeometric random variable X

I am a bit confused by the min and max values of hypergeometric random variable. Suppose that we have a bag with b blue marbles and r red marbles. we choose k marbles at random (without replacement) ...
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1answer
482 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}\...
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1answer
24 views

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 ...
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256 views

Hypergeometric distribution and Fisher's exact test

I have looked around but I cannot seem to find a conclusive answer. Does the Hypergeometric distribution assume that the probability of selecting a defective item at any point is equal to that of ...
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1answer
57 views

Multivariate distribution from drawing balls with elimination of previously picked colors from urn at each step

Consider an urn with n balls of k colors ( labelled 1 through k ) where n >= k. You get to draw j times (j <= k) with the following action between draws. Each time you draw a ball belonging to a ...
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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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1answer
42 views

Analyzing a chemistry experiment - Sampling without replacement

I've been reviewing the results of an interesting chemistry experiment a colleague of mine was conducting, and she sought some help analyzing the results. Would you be able to help, please? The ...