Confidence Intervals and Coverage
Install and import#
npm install fintech-algorithmsimport { confidenceIntervalsAndCoverage } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/confidence-intervals-and-coverage";Signature#
confidenceIntervalsAndCoverage(input)Builds a two-sided interval around the mean of input.sample and reports whether populationMean falls inside it. The half-width always uses the fixed normal critical value 1.959963984540054; alpha is reported back but does not change the multiplier.
Parameters#
| Name | Type | Notes |
|---|---|---|
input | D00Input | One record. sample is the observed data, populationMean is the reference value coverage is checked against, and alpha sets the reported confidence level. estimates is validated for the whole family before dispatch.sample: non-empty list of finite numbers, at least two of them · estimates: non-empty list of finite numbers · alpha: strictly between 0 and 1 |
Returns#
D00Output
An object with lower and upper (the interval bounds), confidenceLevel (1 minus alpha) and containsReference (true when populationMean lies between the bounds).
Errors#
- When sample or estimates is missing, empty, or contains a non-finite number — both are parsed for every topic in the family, whether or not the topic uses them — throws RangeError
- When sample holds fewer than two observations — throws RangeError
- When alpha is not strictly between zero and one — throws RangeError
Complexity: time O(n + m),
space O(n + m).
Worked example#
verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.
Input#
{
"sample": [2, 3, 4, 3, 4],
"estimates": [3, 3.1, 3.2, 3.3, 3.4],
"populationMean": 3.2,
"alpha": 0.05,
"mseBenchmark": 0.1,
"nullMean": 3,
"alternativeMean": 3.5,
"practicalThreshold": 0.1,
"comparisons": 5
}Call#
confidenceIntervalsAndCoverage(input)Returns#
object with 2 fields: lower, upper
{
"lower": 2.4666486279434823,
"upper": 3.933351372056518
}Diagrams#
How it works#
This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.
References#
- Product and Process Comparisons — NIST/SEMATECH e-Handbook
- Confidence Intervals — NIST/SEMATECH e-Handbook
- Historical-example decision