Description
Return one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails.
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 one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails.
When to use this tool
Use Empirical Cdf Single Observation Step 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 observation, evaluation, sampleSize, strict. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Return one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails. Require positive integer sample size.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observation | Observation | Required. Finite number. |
| evaluation | Evaluation | Required. Finite number. |
| sampleSize | Sample Size | Required. Safe integer; minimum 1. |
| strict | Strict | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | One term under the stated formula, not necessarily a complete statistic. | Required. Finite number. |
{
"input": {
"observation": 2,
"evaluation": 2,
"sampleSize": 4,
"strict": false
},
"output": {
"contribution": 0.25
}
}Limitations and assumptions
- This is one empirical-CDF contribution, not the complete CDF. The supplied sample size and observation membership are assumed, and the boundary flag controls equality explicitly.
- 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 One Tie Jump
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.
- Centered Sum Observation Update
Update count to count+1, mean by (value-mean)/(count+1), and m2 by the product of the old-mean and new-mean deviations.