Description
Compare two supplied CDF values at ordered arguments.
Probability calculations distinguish event mass, density likelihood, support membership and interval inclusion. Zero likelihood is not always proof of impossibility, and a known zero-probability category differs from an absent label. Independence, disjointness and supplied CDF values are assumptions or records, rather than properties established by local arithmetic.
Compare two supplied CDF values at ordered arguments.
When to use this tool
Use Two Cdf Values Monotonicity Residual when you already have lowerArgument, upperArgument, lowerCdf, upperCdf and need to compare two supplied CDF values at ordered arguments.
How to use the tool and how it works
- Enter lowerArgument, upperArgument, lowerCdf, upperCdf. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cdfIncrement, monotone. Inspect monotone before interpreting the associated values.
Require upperArgument>lowerArgument and both CDF values in [0,1]; return upperCdf-lowerCdf and upperCdf>=lowerCdf.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lowerArgument | Lower Argument | Required. Finite number. |
| upperArgument | Upper Argument | Required. Finite number. |
| lowerCdf | Lower Cdf | Required. Finite number; minimum 0; maximum 1. |
| upperCdf | Upper Cdf | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cdfIncrement | Upper supplied CDF minus lower supplied CDF; can be negative for inconsistent inputs. | Required. Finite number. |
| monotone | Monotone | Required. Boolean. |
{
"input": {
"lowerArgument": 2,
"upperArgument": 4,
"lowerCdf": 0.3,
"upperCdf": 0.8
},
"output": {
"cdfIncrement": 0.5,
"monotone": true
}
}Limitations and assumptions
- The CDF values may be inconsistent and give a negative increment; no distribution is fitted or evaluated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete joint model when independence or disjointness cannot be assumed. Evaluate a distribution on its actual support for CDF or likelihood questions, and keep absent categories distinct from explicitly listed zero-probability outcomes.
References
Similar or alternative tools
- Bernoulli Trial Signed Residual
Calculate a Bernoulli outcome's signed probability residual.
- Probability Interval Rounding Overlap
Check overlap of two closed probability intervals.