Description
For nonnegative safe-integer population, successes, and draws within population return minimum=max(0,draws-(population-successes)), maximum=min(draws,successes), and supportSize=maximum-minimum+1.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
For nonnegative safe-integer population, successes, and draws within population return minimum=max(0,draws-(population-successes)), maximum=min(draws,successes), and supportSize=maximum-minimum+1.
When to use this tool
Use Hypergeometric Support Endpoint Budget when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter population, successes, draws. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimum, maximum, supportSize. Use the output convention below.
For nonnegative safe-integer population, successes, and draws within population return minimum=max(0,draws-(population-successes)), maximum=min(draws,successes), and supportSize=maximum-minimum+1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| population | Population | Required. Safe integer; minimum 0. |
| successes | Successes | Required. Safe integer; minimum 0. |
| draws | Draws | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimum | Minimum | Required. Safe integer. |
| maximum | Maximum | Required. Safe integer. |
| supportSize | Support Size | Required. Safe integer. |
{
"input": {
"population": 10,
"successes": 4,
"draws": 8
},
"output": {
"minimum": 2,
"maximum": 4,
"supportSize": 3
}
}Limitations and assumptions
- This is the support of sampling without replacement, not a mass function. The all-zero population case is allowed and gives a singleton support at zero.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Beta Density Endpoint Power Test
Classify the Beta density at zero from its positive first shape parameter, holding the second shape positive.
- Discrete Tail Endpoint Inclusion Term
Return inclusiveTail=strictTail+endpointMass, requiring both inputs within zero through one and their sum no greater than one.