Description
Calculate raw upper-tail mass from every bin through the final bin, inclusive.
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.
Calculate raw upper-tail mass from every bin through the final bin, inclusive.
When to use this tool
Use inclusive upper-tail sums to inspect mass at or beyond each bin boundary without normalizing it.
How to use the tool and how it works
- Enter mass using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.inclusive, using the stated boundary, ordering, sign and absence conventions.
For each mass index j, sum all masses from j through the final bin, inclusive.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Nonnegative finite bin masses in bin order; paired edge lists require mass.length=edges.length-1. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.inclusive | Raw mass from each bin index through the final bin, including that index. |
{
"input": {
"mass": [
1,
3,
0
]
},
"output": {
"result": {
"inclusive": [
4,
3,
0
]
}
}
}Limitations and assumptions
- These are raw upper-tail masses, not normalized probabilities. No coordinate edges or interpolation within a bin are used.
- Masses are nonnegative finite counts or weights in bin order. Empty mass arrays are allowed. Floating-point arithmetic does not infer underlying observations or a population distribution.
- 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 Bin Probability Table
Convert supplied bin masses into fractions of total mass, returning nulls for zero total.
- Histogram Peak Tie Selector
Select every bin tied at the maximum supplied mass, retaining exact ties and empty-input evidence.