Feature Comparison: @addmaple/stats vs jStat

This document compares the features available in @addmaple/stats versus jStat.

Summary

Category	Implemented	Missing	Total
Vector Statistics	35	0	35
Distributions	18	3	21
Statistical Tests	7	3	10
Matrix Operations	0	22	22
Linear Algebra	0	13	13
Other	0	82	82
Total	51	126	177

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✅ Implemented Features

Vector Statistics (26/29)

Basic Operations

• ✅ sum - Sum of array elements
• ✅ mean - Arithmetic mean
• ✅ min - Minimum value
• ✅ max - Maximum value
• ✅ product - Product of array elements
• ✅ range - Range (max - min)

Variance & Standard Deviation

• ✅ variance - Population variance
• ✅ sampleVariance - Sample variance (Bessel's correction)
• ✅ stdev - Population standard deviation
• ✅ sampleStdev - Sample standard deviation

Advanced Statistics

• ✅ median - Median value
• ✅ mode - Mode (most frequent value)
• ✅ geomean - Geometric mean
• ✅ skewness - Skewness (third moment)
• ✅ kurtosis - Kurtosis (fourth moment)
• ✅ coeffvar - Coefficient of variation
• ✅ deviation - Deviation from mean (array of deviations)
• ✅ meandev - Mean deviation (mean absolute deviation from mean)
• ✅ meddev - Median deviation (mean absolute deviation from median)
• ✅ pooledvariance - Pooled variance for two groups
• ✅ pooledstdev - Pooled standard deviation for two groups
• ✅ stanMoment - Standardized moment (k-th standardized moment)
• ✅ descriptiveStats - One-shot descriptive statistics snapshot (mean, stdev, quartiles, etc.)

Quantiles & Percentiles

• ✅ percentile - Percentile with linear interpolation
• ✅ percentiles - Vectorized helper for multiple percentiles at once
• ✅ percentileOfScore - Find percentile rank of a value
• ✅ quartiles - First, second (median), third quartiles
• ✅ iqr - Interquartile range
• ✅ quantiles - Multiple quantiles at once
• ✅ qscore - Quantile score (alias for percentileOfScore)
• ✅ qtest - Quantile test (check if value falls within quantile range)

Correlation

• ✅ covariance - Covariance between two arrays
• ✅ corrcoeff - Pearson correlation coefficient
• ✅ spearmancoeff - Spearman rank correlation coefficient

Transformations

• ✅ cumsum - Cumulative sum
• ✅ cumprod - Cumulative product
• ✅ diff - Differences between consecutive elements
• ✅ rank - Rank values (with tie handling)
• ✅ histogram - Histogram with auto or custom bins
• ✅ histogramBinning - Advanced binning strategies (auto rules, equal-frequency, fixed-width, custom)
• ✅ cumreduce - Cumulative reduction with custom reducer function

Statistical Tests

• ✅ anovaFScore / anovaTest - One-way ANOVA
• ✅ chiSquareTest - Chi-square test
• ✅ ttest - T-test
• ✅ ztest - Z-test
• ✅ regress - Linear regression
• ✅ normalci - Normal confidence interval
• ✅ tci - T-distribution confidence interval

Distributions (18/21)

• ✅ normal - Normal/Gaussian distribution (pdf, cdf, inv)
• ✅ gamma - Gamma distribution (pdf, cdf, inv)
• ✅ beta - Beta distribution (pdf, cdf, inv)
• ✅ fisherF - Fisher's F-distribution (pdf, cdf, inv)
• ✅ studentT - Student's t-distribution (pdf, cdf, inv)
• ✅ chiSquared - Chi-square distribution (pdf, cdf, inv)
• ✅ exponential - Exponential distribution (pdf, cdf, inv)
• ✅ poisson - Poisson distribution (pdf, cdf, inv)
• ✅ binomial - Binomial distribution (pdf, cdf, inv)
• ✅ uniform - Uniform distribution (pdf, cdf, inv)
• ✅ cauchy - Cauchy distribution (pdf, cdf, inv)
• ✅ laplace - Laplace distribution (pdf, cdf, inv)
• ✅ logNormal - Log-normal distribution (pdf, cdf, inv)
• ✅ weibull - Weibull distribution (pdf, cdf, inv)
• ✅ pareto - Pareto distribution (pdf, cdf, inv)
• ✅ triangular - Triangular distribution (pdf, cdf, inv)
• ✅ inverseGamma - Inverse gamma distribution (pdf, cdf, inv)
• ✅ negativeBinomial - Negative binomial distribution (pdf, cdf, inv)

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❌ Missing Features

Vector Statistics (0 missing)

All core vector statistics functions are now implemented!

Distributions (3 missing)

• ❌ kumaraswamy - Kumaraswamy distribution
• ❌ arcsine - Arcsine distribution
• ❌ noncentralt - Non-central t-distribution
• ❌ centralF - Central F-distribution (we have Fisher F, but not central F)

Statistical Tests (3 missing)

• ❌ ftest - F-test
• ❌ tukey - Tukey test
• ❌ tukeyhsd - Tukey HSD (Honestly Significant Difference)

Regression Utilities

• ❌ sse - Sum of squared errors
• ❌ ssr - Sum of squares regression
• ❌ sst - Total sum of squares
• ❌ sumsqerr - Sum of squared errors
• ❌ meansqerr - Mean squared error
• ❌ residuals - Regression residuals

Distribution Utilities

• ❌ zscore - Z-score
• ❌ tscore - T-score

Matrix Operations (22 missing)

Basic Operations

• ❌ matrixmult - Matrix multiplication
• ❌ matrixsubtract - Matrix subtraction
• ❌ transpose - Matrix transpose
• ❌ inv - Matrix inverse
• ❌ det - Matrix determinant
• ❌ dot - Dot product

Matrix Creation

• ❌ identity - Identity matrix
• ❌ ones - Matrix of ones
• ❌ zeros - Matrix of zeros
• ❌ diag - Diagonal matrix
• ❌ antidiag - Anti-diagonal matrix

Matrix Access

• ❌ cols - Number of columns
• ❌ rows - Number of rows
• ❌ col - Get column
• ❌ row - Get row
• ❌ cola - Get column as array
• ❌ rowa - Get row as array
• ❌ slice - Matrix slice
• ❌ sliceAssign - Assign to matrix slice

Matrix Utilities

• ❌ copy - Copy matrix
• ❌ extend - Extend matrix
• ❌ dimensions - Matrix dimensions
• ❌ sumrow - Sum rows

Linear Algebra (13 missing)

• ❌ QR - QR decomposition
• ❌ SOR - Successive Over-Relaxation
• ❌ cholesky - Cholesky decomposition
• ❌ lu - LU decomposition
• ❌ gauss_elimination - Gaussian elimination
• ❌ gauss_jordan - Gauss-Jordan elimination
• ❌ gauss_jacobi - Gauss-Jacobi method
• ❌ gauss_seidel - Gauss-Seidel method
• ❌ householder - Householder transformation
• ❌ jacobi - Jacobi method
• ❌ lstsq - Least squares
• ❌ triaLowSolve - Solve lower triangular system
• ❌ triaUpSolve - Solve upper triangular system

Interpolation (3 missing)

• ❌ cubic_spline - Cubic spline interpolation
• ❌ lagrange - Lagrange interpolation
• ❌ hermite - Hermite interpolation

Numerical Methods (5 missing)

• ❌ gauss_quadrature - Gauss quadrature
• ❌ simpson - Simpson's rule
• ❌ romberg - Romberg integration
• ❌ richardson - Richardson extrapolation
• ❌ rungekutta - Runge-Kutta method

Matrix Builders (10 missing)

• ❌ builddxmatrix - Build design matrix
• ❌ buildjxmatrix - Build J matrix
• ❌ buildjymatrix - Build JY matrix
• ❌ buildxmatrix - Build X matrix
• ❌ buildymatrix - Build Y matrix
• ❌ jMatYBar - J matrix Y bar
• ❌ xtranspx - X transpose X
• ❌ xtranspxinv - (X transpose X) inverse
• ❌ aug - Augment matrix
• ❌ alter - Alter matrix

Combinatorics (5 missing)

• ❌ factorial - Factorial
• ❌ factorialln - Natural log of factorial
• ❌ combination - Combinations (n choose k)
• ❌ combinationln - Natural log of combinations
• ❌ permutation - Permutations

Special Functions (14 missing)

Gamma Functions

• ❌ gammafn - Gamma function
• ❌ gammaln - Natural log of gamma function
• ❌ gammap - Incomplete gamma function
• ❌ gammapinv - Inverse incomplete gamma function
• ❌ loggam - Log gamma function
• ❌ lowRegGamma - Lower regularized gamma function

Beta Functions

• ❌ betafn - Beta function
• ❌ betaln - Natural log of beta function
• ❌ betacf - Beta continued fraction
• ❌ ibeta - Incomplete beta function
• ❌ ibetainv - Inverse incomplete beta function

Error Functions

• ❌ erf - Error function
• ❌ erfc - Complementary error function
• ❌ erfcinv - Inverse complementary error function

Array Utilities (16 missing)

Element-wise Operations

• ❌ abs - Absolute value
• ❌ exp - Exponential
• ❌ log - Natural logarithm
• ❌ pow - Power
• ❌ add - Element-wise addition
• ❌ subtract - Element-wise subtraction
• ❌ multiply - Element-wise multiplication
• ❌ divide - Element-wise division

Array Creation & Manipulation

• ❌ map - Map function over array
• ❌ unique - Unique values
• ❌ arange - Array range
• ❌ seq - Sequence generation

Random Number Generation

• ❌ rand - Random numbers
• ❌ randn - Random normal distribution
• ❌ randg - Random gamma distribution
• ❌ setRandom - Set random seed

Other (4 missing)

• ❌ angle - Angle between vectors
• ❌ symmetric - Check if matrix is symmetric
• ❌ significant - Significant digits
• ❌ clear - Clear matrix/data

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Priority Recommendations

Medium Priority (Remaining Distributions)

1. Kumaraswamy Distribution - Useful for bounded random variables
2. Arcsine Distribution - Specialized distribution
3. Non-central t-distribution - Advanced statistical distribution

Low Priority (Remaining Features)

1. F-test - Additional statistical test
2. Tukey Tests (tukey, tukeyhsd) - Post-hoc analysis
3. Matrix Operations - If linear algebra is needed
4. Linear Algebra - For advanced statistical computing
5. Interpolation - For data smoothing/interpolation
6. Combinatorics - For probability calculations

Low Priority (Advanced Features)

1. Matrix Operations - If linear algebra is needed
2. Linear Algebra - For advanced statistical computing
3. Interpolation - For data smoothing/interpolation
4. Combinatorics - For probability calculations

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Notes

• Focus: @addmaple/stats focuses on high-performance vector statistics with SIMD optimizations
• Distributions: Currently supports 18 distributions with full pdf/cdf/inv support
• Matrix Operations: Not currently implemented (jStat has extensive matrix support)
• Performance: Implemented functions are significantly faster than jStat (see Performance Guide)

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Last updated: Based on jStat API comparison