Description
Return geometric survival-tail ratio (1-p)^k with the k=0 empty-product convention.
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 geometric survival-tail ratio (1-p)^k with the k=0 empty-product convention.
When to use this tool
Use Geometric Tail 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 successProbability, additionalTrials. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read tailRatio. Use the output convention below.
Return tailRatio=(1-successProbability)^additionalTrials, requiring a valid probability and a nonnegative safe-integer additionalTrials.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| successProbability | Success Probability | Required. Finite number; minimum 0; maximum 1. |
| additionalTrials | Additional Trials | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| tailRatio | Tail Ratio | Required. Finite number. |
{
"input": {
"successProbability": 0.5,
"additionalTrials": 3
},
"output": {
"tailRatio": 0.125
}
}Limitations and assumptions
- This multiplies geometric survival across additional trials under a constant independent success probability. Zero additional trials returns one, including when successProbability is one.
- 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
- Discrete Tail Endpoint Inclusion Term
Return inclusiveTail=strictTail+endpointMass, requiring both inputs within zero through one and their sum no greater than one.
- Hypergeometric Adjacent Mass Ratio
Return the ratio of the next hypergeometric mass to the current mass at a supported count below the upper endpoint.