Description
Standardize one supplied cosmological bin residual by a supplied deviation.
Cosmological quantities depend on scale factor, redshift, distance definition and the dimensionless Hubble parameter h. Proper and comoving distances differ at a specified epoch, and h-scaled units differ from the dimensional Hubble constant. A scalar rescaling or model contribution preserves supplied conventions without fitting a cosmology or inferring an observed distance.
Standardize one supplied cosmological bin residual by a supplied deviation.
When to use this tool
Use Cosmology Likelihood Bin Residual when you already have observedBin, predictedBin, suppliedStandardDeviation and need to standardize one supplied cosmological bin residual by a supplied deviation.
How to use the tool and how it works
- Enter observedBin, predictedBin, suppliedStandardDeviation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read standardizedResidual. Use the output convention below.
Require suppliedStandardDeviation positive/finite; return (observedBin-predictedBin)/SD.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observedBin | Observed Bin | Required. Finite number. |
| predictedBin | Predicted Bin | Required. Finite number. |
| suppliedStandardDeviation | Supplied Standard Deviation | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| standardizedResidual | Standardized Residual | Required. Finite number. |
{
"input": {
"observedBin": 12,
"predictedBin": 10,
"suppliedStandardDeviation": 2
},
"output": {
"standardizedResidual": 1
}
}Limitations and assumptions
- No variance or bin is estimated. This is one standardized residual, not a likelihood, chi-square, independent-bin model or complete covariance treatment.
- 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 cosmological model and its parameter, epoch and unit definitions for a physical inference. Review redshift, distance, lensing and spectrum conventions before combining these local terms; they do not perform line-of-sight integration, parameter estimation or uncertainty analysis.
References
Similar or alternative tools
- Cosmology Density Closure Residual
Calculate a supplied density-parameter sum and target residual.
- Cosmology Distance Physical Comoving Label
Crosswalk supplied same-epoch physical and comoving lengths using a scale factor.