Description
Audit strict histogram edge monotonicity and minimum arity without silently sorting or removing equal/backwards edges; preserve signed adjacent differences.
A histogram uses ordered edges to partition numeric values into bins. This family assigns an interior boundary to the bin on its right and includes the final right edge in the last bin. Raw counts, sums of weights and probability density are different quantities; edges and observations must use consistent units.
Audit strict histogram edge monotonicity and minimum arity without silently sorting or removing equal/backwards edges; preserve signed adjacent differences.
When to use this tool
Use this tool to audit strict histogram edge monotonicity and minimum arity without silently sorting or removing equal/backwards edges; preserve signed adjacent differences.
How to use the tool and how it works
- Enter edges using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.valid, result.violations. Use the ordering, boundary rules and absence conditions described below.
Inspect adjacent edges and report nonpositive differences with their pair indexes. Return valid only for at least two edges and no such violations.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| edges | Finite strictly increasing bin edges; at least two for bin operations. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.valid | Whether at least two edges exist and every adjacent difference is positive. |
| result.violations | Adjacent edge pairs with a zero or negative difference. |
{
"input": {
"edges": [
0,
1,
1,
0
]
},
"output": {
"result": {
"valid": false,
"violations": [
{
"left": 1,
"right": 2,
"difference": 0
},
{
"left": 2,
"right": 3,
"difference": -1
}
]
}
}
}Limitations and assumptions
- An invalid ordering is a reported false result; nonfinite or wrongly typed inputs remain validation errors.
- Bin operations require at least two finite strictly increasing edges. Every bin is left-inclusive; right ends are exclusive except for the final right edge. The monotonicity audit reports violations instead of requiring valid ordering in advance.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Choose bin edges deliberately, then distinguish membership, count, weight and density calculations. Preserve underflow and overflow information instead of silently discarding observations outside the supplied range.
References
Similar or alternative tools
- Histogram Edge Width Center Table
Profile positive-width histogram intervals and arithmetic centers from explicit strictly ordered finite edges; no sample density, unit or distribution inference.
- Histogram Explicit Edge Count Table
Count explicit observations in supplied ordered histogram bins with final edge included, reporting outside count without clamping under/overflow into endpoint bins.