Description
Compare aligned histogram masses using signed right-minus-left differences per bin and in total.
Histogram edges divide a numeric coordinate axis into ordered bins, while each bin mass represents a count or nonnegative weight. Probability mass is a fraction of the total; probability density additionally divides by bin width and therefore has inverse coordinate units. An edge plan alone contains no observations.
Compare aligned histogram masses using signed right-minus-left differences per bin and in total.
When to use this tool
Use signed bin differences to compare two already aligned histograms on an explicit shared edge plan.
How to use the tool and how it works
- Enter edges, left, right using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.difference, result.totalDifference, using the stated boundary, ordering, sign and absence conventions.
Validate left and right nonnegative mass arrays against one shared edge list. Subtract left from right bin by bin and sum the differences.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| edges | At least two finite strictly increasing coordinate edges. Their units define interval lengths and density units. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| left | Left nonnegative bin masses, exactly aligned to the shared edges. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| right | Right nonnegative bin masses, exactly aligned to the shared edges. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.difference | Signed right-minus-left mass for each aligned bin. |
| result.totalDifference | Sum of signed bin differences. |
{
"input": {
"edges": [
0,
1,
2
],
"left": [
1,
4
],
"right": [
3,
1
]
},
"output": {
"result": {
"difference": [
2,
-3
],
"totalDifference": -1
}
}
}Limitations and assumptions
- The signed convention is right-minus-left. Equal edges establish alignment but do not establish comparable sample exposure, weights or normalization.
- Edge lists contain at least two finite strictly increasing numbers. A mass array paired with edges has exactly one nonnegative finite mass per interval. Other mass-only operations accept empty arrays. Floating-point calculations do not imply exact decimal arithmetic or recover observations inside a bin.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric outputs must remain finite and within safe-integer magnitude. Original record indexes and cell coordinates are zero-based; stated half-open ranges exclude their end.
Alternative or Complementary methods
Keep edge definitions with mass arrays. Use common-boundary coarsening and whole-bin merging for aligned comparisons; use observation-level data when a calculation requires locations within bins.
References
Similar or alternative tools
- Histogram Common Edge Coarsening
Find exact common boundaries between two histogram edge plans with identical outer endpoints.
- Histogram Adjacent Bin Merge Plan
Merge adjacent whole histogram bins according to explicit retained boundary indexes.