Description
Return the ratio of the next hypergeometric mass to the current mass at a supported count below the upper endpoint.
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.
Return the ratio of the next hypergeometric mass to the current mass at a supported count below the upper endpoint.
When to use this tool
Use Hypergeometric Adjacent Mass Ratio 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, count. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio. Use the output convention below.
For population from one through one million and valid integer successes, draws, and supported count, require count below the upper support endpoint. Return ratio=((successes-count)*(draws-count))/((count+1)*(population-successes-draws+count+1)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| population | Population | Required. Safe integer; minimum 1; maximum 1000000. |
| successes | Successes | Required. Safe integer; minimum 0. |
| draws | Draws | Required. Safe integer; minimum 0. |
| count | Count under the stated event or record definition. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Ratio in the direction and unit convention stated in the formula. | Required. Finite number. |
{
"input": {
"population": 10,
"successes": 4,
"draws": 3,
"count": 1
},
"output": {
"ratio": 0.6
}
}Limitations and assumptions
- The ratio is P(X=count+1)/P(X=count) for sampling without replacement. The top endpoint is rejected rather than given a zero-next-mass convention.
- 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
- Binomial Mass Mode Tie Boundary
Return lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.
- Censored Event Boundary Mass
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.