Description
Return lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.
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 lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.
When to use this tool
Use Binomial Mass Mode Tie Boundary 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 trials, probability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lowerMode, upperMode, tied. Inspect tied before interpreting the associated values.
Set a=(trials+1)*probability for integer trials from zero through one million. Return lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| trials | Trials | Required. Safe integer; minimum 0; maximum 1000000. |
| probability | Dimensionless probability from zero through one. | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lowerMode | Lower Mode | Required. Safe integer. |
| upperMode | Upper Mode | Required. Safe integer. |
| tied | Tied | Required. Boolean. |
{
"input": {
"trials": 3,
"probability": 0.5
},
"output": {
"lowerMode": 1,
"upperMode": 2,
"tied": true
}
}Limitations and assumptions
- Ties use exact floating-point integer detection. This returns binomial modal counts under the supplied fixed probability, not their masses or a fitted probability.
- 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
- Censored Event Boundary Mass
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.
- Categorical Resampling One Bin Boundary
Check whether a supplied value belongs to one categorical probability bin, with an explicit final-bin endpoint rule.