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Statistics · Distributions

Multivariate Hypergeometric Distribution Calculator

Calculate the exact probability of a complete category composition drawn without replacement from a finite population.

Statistics · Distributions

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Private in-browser calculation · explicit assumptions
Discrete support uses separate whole-number outcomes; probability is carried by the individual masses.
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  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

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Understand the distribution

What the multivariate hypergeometric distribution calculator models

Assigning probability to separate outcomes. A discrete probability mass function assigns probability directly to each allowed count or category combination. All mutually exclusive masses across the full support sum to one.

Probability mass rule

P(X₁=x₁,…,Xₘ=xₘ)=∏C(Kᵢ,xᵢ)/C(N,n), where N=ΣKᵢ and n=Σxᵢ.

A probability mass is a probability at an allowed discrete outcome.

Interpretation and limits

Category draw counts are negatively related because sampling is without replacement and the total draw size is fixed.

Model boundary: Population and drawn-count lists must align as nonnegative whole numbers, and every draw is assumed uniformly random without replacement.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the multivariate hypergeometric distribution calculator works

P(X₁=x₁,…,Xₘ=xₘ)=∏C(Kᵢ,xᵢ)/C(N,n), where N=ΣKᵢ and n=Σxᵢ.

Category draw counts are negatively related because sampling is without replacement and the total draw size is fixed.

Worked example

Multivariate Hypergeometric Distribution example

Drawing counts 1,1 from category populations 3,2 has probability C(3,1)C(2,1)/C(5,2)=0.6.

P(X₁=x₁,…,Xₘ=xₘ)=∏C(Kᵢ,xᵢ)/C(N,n), where N=ΣKᵢ and n=Σxᵢ.

Supported inputs

Precision and limits

Model and design

Population and drawn-count lists must align as nonnegative whole numbers, and every draw is assumed uniformly random without replacement.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

Category draw counts are negatively related because sampling is without replacement and the total draw size is fixed.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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