Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

Filter by
Sorted by
Tagged with
1
vote
1answer
18 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 ...
1
vote
0answers
34 views

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 ...
1
vote
0answers
9 views

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 ...
1
vote
1answer
99 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 ...
4
votes
1answer
44 views

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 ...
0
votes
0answers
27 views

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 ...
3
votes
1answer
46 views

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 ...
0
votes
3answers
79 views

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 ...
1
vote
1answer
80 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 ...
3
votes
1answer
56 views

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 ...
0
votes
0answers
18 views

time complexity of sampling from multivariate hypergeometric distribuiton

numpy has an implementation and the doc is here. It says it is "roughly" equivalent to: ...
0
votes
0answers
23 views

Finding Unbiased Estimator for Good Elements (Hypergeometric Dist.)

So the question is we know "N" (population size), and we draw "n" from this population in a simple random sample. Let "X" be the number of Good elements in this simple ...
2
votes
1answer
108 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 ...
1
vote
1answer
41 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 $k$ = ...
3
votes
1answer
88 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 ...
3
votes
1answer
109 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,...
2
votes
1answer
56 views

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),\...
0
votes
1answer
37 views

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 ...
0
votes
0answers
8 views

Probability density function for possible intersections/conjunctions

Imagine the following scenario: There are n senators voting on two bills to be passed. A fraction of n voted to pass each bill respectively. For simplicity, let's assume n/2 senators voted for bill 1 ...
0
votes
1answer
109 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 ...
0
votes
1answer
33 views

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 ...
0
votes
0answers
20 views

What is ncp of negative hypergeometric distribution?

https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/fisher.test.R#L127 I see non-centrality parameter ncp on the above page. But I don't find ...
0
votes
1answer
152 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 ...
3
votes
1answer
57 views

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 ...
3
votes
1answer
19 views

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 ...
2
votes
1answer
93 views

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 ...
1
vote
1answer
75 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.
0
votes
1answer
206 views

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 $5$ ...
1
vote
0answers
50 views

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 ...
1
vote
1answer
41 views

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 (...
3
votes
0answers
82 views

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 ...
1
vote
0answers
14 views

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 ...
1
vote
0answers
85 views

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. ...
0
votes
0answers
19 views

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 ...
6
votes
1answer
367 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 ...
1
vote
2answers
42 views

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 ...
1
vote
0answers
37 views

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 ...
0
votes
0answers
242 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 ...
1
vote
0answers
38 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? ...
2
votes
1answer
111 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 ...
1
vote
2answers
68 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 ...
0
votes
1answer
39 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 ...
1
vote
1answer
573 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 ...
2
votes
1answer
59 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 ...
0
votes
0answers
95 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 ...
2
votes
0answers
22 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 ...
0
votes
1answer
27 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"....
1
vote
1answer
34 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 ...
2
votes
1answer
1k 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 ...
2
votes
0answers
98 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 ...