Description
Check whether a supplied value belongs to one categorical probability bin, with an explicit final-bin endpoint rule.
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.
Check whether a supplied value belongs to one categorical probability bin, with an explicit final-bin endpoint rule.
When to use this tool
Use Categorical Resampling One Bin 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 uniform, lower, upper, last. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read selected. Inspect selected before interpreting the associated values.
Require uniform, lower, and upper within zero through one with lower<=upper. Select when uniform>=lower and either uniform<upper or last=true with uniform=upper=1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| uniform | Supplied draw-like value in [0,1]; no randomness is generated. | Required. Finite number; minimum 0; maximum 1. |
| lower | Lower | Required. Finite number; minimum 0; maximum 1. |
| upper | Upper | Required. Finite number; minimum 0; maximum 1. |
| last | Include uniform=upper=1 on this bin when true. | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| selected | Zero-based index of the selected category. | Required. Boolean. |
{
"input": {
"uniform": 0.5,
"lower": 0,
"upper": 0.5,
"last": false
},
"output": {
"selected": false
}
}Limitations and assumptions
- This checks one supplied half-open bin, with a last-bin exception at one. It does not draw randomness, validate a full partition, or reject a zero-width last bin at 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
- 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.