Description
Divide a supplied coordinate interval into lengths inside, below and above the histogram domain.
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.
Divide a supplied coordinate interval into lengths inside, below and above the histogram domain.
When to use this tool
Use coordinate coverage lengths to compare an interval of interest with the histogram’s outer domain.
How to use the tool and how it works
- Enter edges, minimum, maximum using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.covered, result.below, result.above, using the stated boundary, ordering, sign and absence conventions.
Intersect [minimum,maximum] with the outer histogram domain [first edge,last edge]. Report intersection length plus the interval lengths below and above that domain.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. |
| minimum | Lower coordinate bound, at most maximum; logarithmic plans additionally require minimum>0 and maximum>minimum. | Finite numeric value satisfying the stated comparisons. |
| maximum | Upper coordinate bound on the same scale as minimum; strictly greater for a logarithmic plan. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.covered | Length of the supplied coordinate interval inside the edge domain. |
| result.below | Length of the supplied coordinate interval below the edge domain. |
| result.above | Length of the supplied coordinate interval above the edge domain. |
{
"input": {
"edges": [
0,
1,
2
],
"minimum": -1,
"maximum": 4
},
"output": {
"result": {
"covered": 2,
"below": 1,
"above": 2
}
}
}Limitations and assumptions
- Lengths have the same units as the edges. They describe coordinate coverage, not observed sample fractions; a zero-length interval contributes zero to all three budgets.
- 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 Sample Provenance Groups
Group original observation indexes into explicit histogram bins and retain outside-domain indexes.
- Histogram Common Edge Coarsening
Find exact common boundaries between two histogram edge plans with identical outer endpoints.