Sampling, Estimation, and Statistical Inference

10 algorithms in Financial Mathematics, Statistics, and Data Foundations · 10 with asserted arithmetic.

In this family#

1. Parameters, Statistics, Estimands, and Estimators verified

   Places the known population parameter from input.populationMean alongside the statistic computed from input.sample, and names which side is the estimand and which is the estimator.

   parametersStatisticsEstimandsAndEstimators(input)
2. Sampling Distributions verified

   Summarises the replicated estimates in input.estimates as a sampling distribution: where it centres, how wide it is, and how many replications produced it.

   samplingDistributions(input)
3. Estimator Bias, Consistency, Efficiency, and Robustness verified

   Scores an estimator against a known truth: the average error of the replicated estimates, their mean squared error, a robust median estimate, and whether the mean squared error clears mseBenchmark.

   estimatorBiasConsistencyEfficiencyAndRobustness(input)
4. Law of Large Numbers verified

   Walks the running mean of input.sample one observation at a time and reports how far it has drifted from input.populationMean by the end.

   lawOfLargeNumbers(input)
5. Central Limit Theorem verified

   Standardises the replicated estimates in input.estimates by subtracting populationMean and dividing by their spread, then checks how close the standardised values sit to zero.

   centralLimitTheorem(input)
6. Standard Error verified

   Reports the standard error of the mean for input.sample — its sample standard deviation divided by the square root of the observation count.

   standardError(input)
7. Confidence Intervals and Coverage verified

   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.

   confidenceIntervalsAndCoverage(input)
8. Null and Alternative Hypotheses verified

   States a two-sided test of the mean of input.sample against input.nullMean, and returns the z statistic with the reject-or-not decision taken at the fixed critical value 1.959963984540054.

   nullAndAlternativeHypotheses(input)
9. P-Values, Significance, Type I/II Errors, and Power verified

   Turns the two-sided z statistic for input.sample against input.nullMean into a p-value, compares it with alpha, and approximates the test's power at input.alternativeMean.

   pValuesSignificanceTypeIIiErrorsAndPower(input)
10. Effect Size, Practical Significance, and Multiple Comparisons verified

    Reports a standardised effect size for the gap between the mean of input.sample and input.nullMean, tests that gap against a practical threshold, and splits alpha across input.comparisons tests Bonferroni-style.

    effectSizePracticalSignificanceAndMultipleComparisons(input)

What they share#

Every topic here is a record-transform, so once you have called one the rest follow the same shape. Import paths differ only in the final segment:

import { parametersStatisticsEstimandsAndEstimators } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/parameters-statistics-estimands-and-estimators";
import { samplingDistributions } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/sampling-distributions";

Read them in the order above — the sequence is pedagogical, not alphabetical.

Where this sits#

Financial Mathematics, Statistics, and Data Foundations collects 120 algorithms across 12 families. For the concept behind this family rather than the call signatures, see the concept guides.