# Financial Mathematics, Statistics, and Data Foundations — fintech-algorithms

> 120 algorithms in 12 families, sliced out of the
> fintech-algorithms reference. Zero-dependency TypeScript: plain arrays and objects in,
> plain values out. This file covers D00 only.

D00 · 120 topics · 12 families · 120 verified
Install: npm install fintech-algorithms
Agent skill (install it rather than re-deriving this file): npx skills add IslamBaraka90/Fintech-Algorithms-Library
  what it is: https://docs.thefintechbuilder.com/guides/agent-skill/
Source: fintech-algorithms@0.12.0 · payload schema 2.0.0
Reference payload: https://docs.thefintechbuilder.com/reference/payload.json
Version endpoint: https://docs.thefintechbuilder.com/version.json
Domain page: https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/
Full index (471 topics across 16 domains): https://docs.thefintechbuilder.com/llms.txt

Verification tiers:
- verified — the worked example is the figure published in the algorithm's article, replayed
  and asserted by the test suite on every run. The arithmetic cannot drift without the build
  failing. Treat the numbers as reproducible.
- contract — the module loads, the entry point is callable and its declared signature matches
  the compiled code. The example is real captured output, but no independently published
  figure asserts it. Treat the shape as reliable and the numbers as unattested.
Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Each entry: name — signature — archetype — verification tier — docs URL
From the docs URL, mechanically:
  import subpath — swap the https://docs.thefintechbuilder.com/ prefix for fintech-algorithms/ and drop the trailing slash
  markdown page  — append index.md; same contract as the HTML page, a fraction of the bytes

## D00-F01 — Mathematical Language and Quantitative Reasoning
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/

- Variables, Constants, Expressions, and Equations — `variablesConstantsExpressionsAndEquations(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/variables-constants-expressions-and-equations/
- Functions, Domains, Ranges, and Graphs — `functionsDomainsRangesAndGraphs(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/functions-domains-ranges-and-graphs/
- Ratios, Proportions, Rates, and Percentages — `ratiosProportionsRatesAndPercentages(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/ratios-proportions-rates-and-percentages/
- Percentage Change, Percentage Points, and Basis Points — `percentageChangePercentagePointsAndBasisPoints(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
- Exponents, Roots, and Logarithms — `exponentsRootsAndLogarithms(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
- Summation, Products, and Index Notation — `summationProductsAndIndexNotation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
- Linear Equations and Systems — `linearEquationsAndSystems(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/linear-equations-and-systems/
- Inequalities, Bounds, and Constraints — `inequalitiesBoundsAndConstraints(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/inequalities-bounds-and-constraints/
- Units, Dimensions, Scale, and Normalization — `unitsDimensionsScaleAndNormalization(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/units-dimensions-scale-and-normalization/
- Rounding, Precision, Tolerance, and Significant Digits — `roundingPrecisionToleranceAndSignificantDigits(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/rounding-precision-tolerance-and-significant-digits/

## D00-F02 — Financial Arithmetic, Time Value, and Returns
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/

- Simple Interest — `simpleInterest(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/simple-interest/
- Compound Interest — `compoundInterest(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/compound-interest/
- Present Value and Future Value — `presentValueAndFutureValue(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/present-future-value/
- Discount Factors and Discount Rates — `discountFactorsAndDiscountRates(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
- Cash-Flow Timelines and Net Present Value — `cashFlowTimelinesAndNetPresentValue(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/cashflow-npv/
- Simple Return — `simpleReturn(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/simple-return/
- Log Return — `logReturn(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/log-return/
- Holding-Period and Cumulative Return — `holdingPeriodAndCumulativeReturn(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
- Arithmetic versus Geometric Average Return — `arithmeticVersusGeometricAverageReturn(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/arithmetic-geometric-return/
- Return Annualization and Deannualization — `returnAnnualizationAndDeannualization(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/annualization-deannualization/

## D00-F03 — Data, Variables, Samples, and Measurement
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/

- Observations, Entities, Variables, and Datasets — `observationsEntitiesVariablesAndDatasets(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/observations-entities-variables-and-datasets/
- Numeric, Categorical, Ordinal, and Binary Variables — `numericCategoricalOrdinalAndBinaryVariables(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/numeric-categorical-ordinal-and-binary-variables/
- Population, Sample, Census, and Sampling Frame — `populationSampleCensusAndSamplingFrame(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/population-sample-census-and-sampling-frame/
- Cross-Sectional, Time-Series, Panel, and Event Data — `crossSectionalTimeSeriesPanelAndEventData(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/cross-sectional-time-series-panel-and-event-data/
- Identifiers, Keys, Joins, and Data Grain — `identifiersKeysJoinsAndDataGrain(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/identifiers-keys-joins-and-data-grain/
- Timestamps, Time Zones, Calendars, and Observation Time — `timestampsTimeZonesCalendarsAndObservationTime(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/timestamps-time-zones-calendars-and-observation-time/
- Missing, Nonfinite, Censored, and Truncated Values — `missingNonfiniteCensoredAndTruncatedValues(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/missing-nonfinite-censored-and-truncated-values/
- Measurement Error, Resolution, Accuracy, and Precision — `measurementErrorResolutionAccuracyAndPrecision(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
- Revisions, Vintages, and Point-in-Time Availability — `revisionsVintagesAndPointInTimeAvailability(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/revisions-vintages-and-point-in-time-availability/
- Data Provenance, Lineage, Ownership, and Licensing — `dataProvenanceLineageOwnershipAndLicensing(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/data-provenance-lineage-ownership-and-licensing/

## D00-F04 — Location, Ranking, and Exploratory Summaries
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/

- Count, Sum, Minimum, Maximum, and Range — `countSumMinimumMaximumAndRange(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/count-sum-minimum-maximum-and-range/
- Arithmetic Mean — `arithmeticMean(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/arithmetic-mean/
- Weighted Mean — `weightedMean(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/weighted-mean/
- Median and Mode — `medianAndMode(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/median-and-mode/
- Trimmed and Winsorized Means — `trimmedAndWinsorizedMeans(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/trimmed-and-winsorized-means/
- Percentiles, Quantiles, and Quartiles — `percentilesQuantilesAndQuartiles(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
- Ranks, Ties, and Percentile Rank — `ranksTiesAndPercentileRank(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
- Frequency Tables and Relative Frequency — `frequencyTablesAndRelativeFrequency(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/frequency-tables-and-relative-frequency/
- Histograms and Empirical Distribution Functions — `histogramsAndEmpiricalDistributionFunctions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
- Five-Number Summary and Box Plot — `fiveNumberSummaryAndBoxPlot(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/five-number-summary-and-box-plot/

## D00-F05 — Dispersion, Shape, and Robust Statistics
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/

- Deviation, Absolute Deviation, and Squared Deviation — `deviationAbsoluteDeviationAndSquaredDeviation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/deviation-absolute-deviation-and-squared-deviation/
- Range and Interquartile Range — `rangeAndInterquartileRange(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/range-and-interquartile-range/
- Mean Absolute Deviation — `meanAbsoluteDeviation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/mean-absolute-deviation/
- Median Absolute Deviation — `medianAbsoluteDeviation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
- Population and Sample Variance — `populationAndSampleVariance(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/population-and-sample-variance/
- Population and Sample Standard Deviation — `populationAndSampleStandardDeviation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/population-and-sample-standard-deviation/
- Coefficient of Variation and Scale Comparability — `coefficientOfVariationAndScaleComparability(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/coefficient-of-variation-and-scale-comparability/
- Z-Score, Robust Z-Score, and Standardization — `zScoreRobustZScoreAndStandardization(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
- Skewness and Tail Asymmetry — `skewnessAndTailAsymmetry(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/skewness-and-tail-asymmetry/
- Kurtosis, Excess Kurtosis, and Tail Weight — `kurtosisExcessKurtosisAndTailWeight(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/kurtosis-excess-kurtosis-and-tail-weight/

## D00-F06 — Probability and Random Variables
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/

- Experiments, Outcomes, Sample Spaces, and Events — `experimentsOutcomesSampleSpacesAndEvents(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/experiments-outcomes-sample-spaces-and-events/
- Probability Rules, Complements, Unions, and Intersections — `probabilityRulesComplementsUnionsAndIntersections(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/probability-rules-complements-unions-and-intersections/
- Conditional Probability — `conditionalProbability(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
- Independence and Dependence — `independenceAndDependence(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/independence-and-dependence/
- Bayes' Theorem and Base Rates — `bayesTheoremAndBaseRates(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/bayes-theorem-and-base-rates/
- Discrete and Continuous Random Variables — `discreteAndContinuousRandomVariables(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
- Expected Value — `expectedValue(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/expected-value/
- Variance, Moments, and Moment-Generating Intuition — `varianceMomentsAndMomentGeneratingIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/variance-moments-and-moment-generating-intuition/
- Joint, Marginal, and Conditional Distributions — `jointMarginalAndConditionalDistributions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/joint-marginal-and-conditional-distributions/
- Covariance and Correlation of Random Variables — `covarianceAndCorrelationOfRandomVariables(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/covariance-and-correlation-of-random-variables/

## D00-F07 — Probability Distributions and Simulation Basics
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/

- PMF, PDF, CDF, Survival, and Quantile Functions — `pmfPdfCdfSurvivalAndQuantileFunctions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/pmf-pdf-cdf-survival-and-quantile-functions/
- Bernoulli and Binomial Distributions — `bernoulliAndBinomialDistributions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/bernoulli-and-binomial-distributions/
- Poisson Distribution and Event Counts — `poissonDistributionAndEventCounts(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/poisson-distribution-and-event-counts/
- Uniform Distribution and Random Sampling — `uniformDistributionAndRandomSampling(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/uniform-distribution-and-random-sampling/
- Normal Distribution and Standard Normal — `normalDistributionAndStandardNormal(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/normal-distribution-and-standard-normal/
- Lognormal Distribution and Positive Quantities — `lognormalDistributionAndPositiveQuantities(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/lognormal-distribution-and-positive-quantities/
- Student-t Distribution and Heavy Tails — `studentTDistributionAndHeavyTails(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/student-t-distribution-and-heavy-tails/
- Exponential, Gamma, and Weibull Waiting-Time Models — `exponentialGammaAndWeibullWaitingTimeModels(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/exponential-gamma-and-weibull-waiting-time-models/
- Mixture Distributions, Multimodality, and Fat Tails — `mixtureDistributionsMultimodalityAndFatTails(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/mixture-distributions-multimodality-and-fat-tails/
- Random Sampling and Monte Carlo Intuition — `randomSamplingAndMonteCarloIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-distributions-and-simulation-basics/random-sampling-and-monte-carlo-intuition/

## D00-F08 — Sampling, Estimation, and Statistical Inference
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/

- Parameters, Statistics, Estimands, and Estimators — `parametersStatisticsEstimandsAndEstimators(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/parameters-statistics-estimands-and-estimators/
- Sampling Distributions — `samplingDistributions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/sampling-distributions/
- Estimator Bias, Consistency, Efficiency, and Robustness — `estimatorBiasConsistencyEfficiencyAndRobustness(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/estimator-bias-consistency-efficiency-and-robustness/
- Law of Large Numbers — `lawOfLargeNumbers(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/law-of-large-numbers/
- Central Limit Theorem — `centralLimitTheorem(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/central-limit-theorem/
- Standard Error — `standardError(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/standard-error/
- Confidence Intervals and Coverage — `confidenceIntervalsAndCoverage(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/confidence-intervals-and-coverage/
- Null and Alternative Hypotheses — `nullAndAlternativeHypotheses(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/null-and-alternative-hypotheses/
- P-Values, Significance, Type I/II Errors, and Power — `pValuesSignificanceTypeIIiErrorsAndPower(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/p-values-significance-type-i-ii-errors-and-power/
- Effect Size, Practical Significance, and Multiple Comparisons — `effectSizePracticalSignificanceAndMultipleComparisons(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/sampling-estimation-and-statistical-inference/effect-size-practical-significance-and-multiple-comparisons/

## D00-F09 — Dependence, Regression, and Model Foundations
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/

- Scatter Plots, Association, and Nonlinear Patterns — `scatterPlotsAssociationAndNonlinearPatterns(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/scatter-plots-association-and-nonlinear-patterns/
- Sample Covariance Calculation and Interpretation — `sampleCovarianceCalculationAndInterpretation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/sample-covariance-calculation-and-interpretation/
- Pearson Correlation Calculation and Interpretation — `pearsonCorrelationCalculationAndInterpretation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/pearson-correlation-calculation-and-interpretation/
- Spearman Rank Correlation and Kendall Tau — `spearmanRankCorrelationAndKendallTau(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/spearman-rank-correlation-and-kendall-tau/
- Correlation, Causation, Confounding, and Spurious Relationships — `correlationCausationConfoundingAndSpuriousRelationships(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
- Simple Ordinary Least Squares Regression — `simpleOrdinaryLeastSquaresRegression(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/simple-ordinary-least-squares-regression/
- Intercepts, Slopes, Coefficients, and Predictions — `interceptsSlopesCoefficientsAndPredictions(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/intercepts-slopes-coefficients-and-predictions/
- Residuals, MAE, MSE, and RMSE — `residualsMaeMseAndRmse(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/residuals-mae-mse-and-rmse/
- R-Squared and Adjusted R-Squared — `rSquaredAndAdjustedRSquared(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/r-squared-and-adjusted-r-squared/
- Regression Assumptions, Heteroskedasticity, and Multicollinearity — `regressionAssumptionsHeteroskedasticityAndMulticollinearity(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/regression-assumptions-heteroskedasticity-and-multicollinearity/

## D00-F10 — Financial Time-Series Foundations
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/

- Time Order, Frequency, Regularity, and Financial Calendars — `timeOrderFrequencyRegularityAndFinancialCalendars(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/time-order-frequency-regularity-and-financial-calendars/
- Levels, Changes, Differences, and Returns — `levelsChangesDifferencesAndReturns(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/levels-changes-differences-and-returns/
- Lags, Leads, and Temporal Dependence — `lagsLeadsAndTemporalDependence(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/lags-leads-and-temporal-dependence/
- Rolling and Expanding Windows — `rollingAndExpandingWindows(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/rolling-and-expanding-windows/
- Resampling, Aggregation, and Time Alignment — `resamplingAggregationAndTimeAlignment(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/resampling-aggregation-and-time-alignment/
- Trend, Seasonality, Cycles, and Remainder — `trendSeasonalityCyclesAndRemainder(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/trend-seasonality-cycles-and-remainder/
- Autocovariance and Autocorrelation — `autocovarianceAndAutocorrelation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/autocovariance-and-autocorrelation/
- Stationarity and Differencing Intuition — `stationarityAndDifferencingIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/stationarity-and-differencing-intuition/
- Smoothing, Baselines, and Naive Forecasts — `smoothingBaselinesAndNaiveForecasts(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/smoothing-baselines-and-naive-forecasts/
- Look-Ahead Leakage and Time-Aware Data Splits — `lookAheadLeakageAndTimeAwareDataSplits(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-time-series-foundations/look-ahead-leakage-and-time-aware-data-splits/

## D00-F11 — Financial Risk and Performance Statistics
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/

- Volatility and Annualized Volatility — `volatilityAndAnnualizedVolatility(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/volatility-and-annualized-volatility/
- Downside Deviation and Target Shortfall — `downsideDeviationAndTargetShortfall(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/downside-deviation-and-target-shortfall/
- Drawdown and Maximum Drawdown — `drawdownAndMaximumDrawdown(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/drawdown-and-maximum-drawdown/
- Loss Distributions and Loss Quantiles — `lossDistributionsAndLossQuantiles(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/loss-distributions-and-loss-quantiles/
- Value at Risk Intuition — `valueAtRiskIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/value-at-risk-intuition/
- Expected Shortfall Intuition — `expectedShortfallIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/expected-shortfall-intuition/
- Beta and Market-Relative Risk — `betaAndMarketRelativeRisk(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/beta-and-market-relative-risk/
- Sharpe, Sortino, and Information Ratio Intuition — `sharpeSortinoAndInformationRatioIntuition(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/sharpe-sortino-and-information-ratio-intuition/
- Active Return and Tracking Error — `activeReturnAndTrackingError(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/active-return-and-tracking-error/
- Covariance Matrices, Portfolio Variance, and Diversification — `covarianceMatricesPortfolioVarianceAndDiversification(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/covariance-matrices-portfolio-variance-and-diversification/

## D00-F12 — Statistical Computing and Reproducibility
https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/

- Floating-Point Representation, Overflow, and Underflow — `floatingPointRepresentationOverflowAndUnderflow(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/floating-point-representation-overflow-and-underflow/
- Stable Summation and Mean Calculation — `stableSummationAndMeanCalculation(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation/
- Stable Online Variance and Welford's Algorithm — `stableOnlineVarianceAndWelfordsAlgorithm(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/stable-online-variance-and-welford-s-algorithm/
- Batch, Rolling, and Streaming Statistic Equivalence — `batchRollingAndStreamingStatisticEquivalence(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/batch-rolling-and-streaming-statistic-equivalence/
- Missing, Infinite, Invalid, and Unsupported-State Policies — `missingInfiniteInvalidAndUnsupportedStatePolicies(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/missing-infinite-invalid-and-unsupported-state-policies/
- Pseudorandom Numbers, Seeds, and Reproducibility — `pseudorandomNumbersSeedsAndReproducibility(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/pseudorandom-numbers-seeds-and-reproducibility/
- Vectorization, Index Alignment, and Shape Safety — `vectorizationIndexAlignmentAndShapeSafety(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/vectorization-index-alignment-and-shape-safety/
- Leakage-Free Fitting, Scaling, and Preprocessing — `leakageFreeFittingScalingAndPreprocessing(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/leakage-free-fitting-scaling-and-preprocessing/
- Fixtures, Numerical Tolerances, and Property Tests — `fixturesNumericalTolerancesAndPropertyTests(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
- Reproducible Analysis, Metadata, and Audit Trails — `reproducibleAnalysisMetadataAndAuditTrails(input)` — record-transform — verified — https://docs.thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/reproducible-analysis-metadata-and-audit-trails/