Description
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.
A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.
When to use this tool
Use Empirical Cdf One Tie Jump when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.
How to use the tool and how it works
- Enter less, tied, count. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftLimit, rightLimit, jump. Use the output convention below.
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| less | Less | Required. Safe integer; minimum 0. |
| tied | Tied | Required. Safe integer; minimum 0. |
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftLimit | Left Limit | Required. Finite number. |
| rightLimit | Right Limit | Required. Finite number. |
| jump | Jump | Required. Finite number. |
{
"input": {
"less": 3,
"tied": 2,
"count": 10
},
"output": {
"leftLimit": 0.3,
"rightLimit": 0.5,
"jump": 0.2
}
}Limitations and assumptions
- Less and tied are supplied counts at a particular evaluation value. The tool does not sort observations, find ties, or select an empirical-CDF continuity convention beyond these terms.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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 complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.
References
Similar or alternative tools
- Empirical Cdf Single Observation Step
Return one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails.
- Median Tie Middle Gap
Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.