kstats Benchmarks
March 22, 2026 · View on GitHub
JMH-based performance comparison between kstats and Apache Commons Math 3.
All benchmarks use kotlinx-benchmark with JMH under the hood.
Each benchmark method has a kstats* and commons* variant so the two libraries are measured under identical
conditions.
Environment
| Parameter | Value |
|---|---|
| JVM | OpenJDK 21.0.10 (Homebrew) |
| Architecture | Apple Silicon (aarch64) |
| JMH | 1.37 via kotlinx-benchmark |
| Warmup | 5 iterations x 3 s |
| Measurement | 5 iterations x 3 s |
| Mode | Average time (avgt) |
| Unit | microseconds per operation (μs/op) |
Running Benchmarks
# Full benchmark run (~40 min)
./gradlew :benchmark:benchmark
# Quick smoke test (~5 min)
./gradlew :benchmark:smokeBenchmark
Reports are written to benchmark/build/reports/benchmarks/main/<timestamp>/main.json in JMH-compatible JSON format.
Benchmark Profiles
| Profile | Warmup | Measurement | Iteration Time |
|---|---|---|---|
main | 5 iterations | 5 iterations | 3 s |
smoke | 2 iterations | 3 iterations | 1 s |
Available Benchmarks
Descriptive Statistics
| Class | Methods | Parameters |
|---|---|---|
DescriptiveStatsBenchmark | mean, variance, stdDev, geometricMean, median, skewness, kurtosis, describe | size: 100, 1K, 10K, 100K |
QuantileBenchmark | percentile50, percentile95, iqr | size: 1K, 10K, 100K |
Correlation & Regression
| Class | Methods | Parameters |
|---|---|---|
CorrelationBenchmark | pearson, spearman, kendallTau, linearRegression | size: 100, 1K, 10K |
CovarianceBenchmark | covariance | size: 100, 1K, 10K |
Hypothesis Tests
| Class | Methods | Parameters |
|---|---|---|
HypothesisTestBenchmark | oneSampleTTest, twoSampleTTest, oneWayAnova, chiSquared, mannWhitney, kolmogorovSmirnov | size: 100, 1K, 10K |
PairedTTestBenchmark | pairedTTest | size: 100, 1K, 10K |
ChiSquaredIndependenceBenchmark | chiSquaredIndependence | tableSize: 3, 10, 50 |
Probability Distributions
| Class | Distributions | Operations |
|---|---|---|
ContinuousDistributionBenchmark | Normal, Beta, Gamma, Chi-Squared, Student's t, Exponential | pdf, cdf, quantile |
DiscreteDistributionBenchmark | Binomial, Poisson | pmf, cdf |
FDistributionBenchmark | F | pdf, cdf, quantile |
CauchyBenchmark | Cauchy | pdf, cdf, quantile |
UniformContinuousBenchmark | Uniform | pdf, cdf, quantile |
WeibullBenchmark | Weibull | pdf, cdf, quantile |
LogNormalBenchmark | LogNormal | pdf, cdf, quantile |
GeometricBenchmark | Geometric | pmf, cdf, quantile |
HypergeometricBenchmark | Hypergeometric | pmf, cdf, quantile |
ZipfDistributionBenchmark | Zipf | pmf, cdf, quantile |
Results
Overall Comparison
Where kstats wins (>1.5x faster)
| Operation | Speedup |
|---|---|
| Zipf (pmf, cdf, quantile) | 6,700–47,000x |
| LogNormal quantile | 443x |
| Chi-Squared Independence (3x3) | 58x |
| Chi-Squared GOF | 39x |
| LogNormal pdf/cdf | 8–10x |
| ANOVA | 5.1x |
| Kurtosis | 4.2x |
| Geometric quantile | 3.4x |
| Weibull quantile | 3.0x |
| F distribution (pdf, cdf, quantile) | 1.7–2.5x |
| Normal CDF | 2.1x |
| Pearson correlation | 1.8x |
| Cauchy quantile | 1.7x |
| Geometric pmf | 1.6x |
| Linear regression | 1.6x |
| Covariance | 1.5x |
Where Commons Math wins (>1.5x faster)
| Operation | Speedup |
|---|---|
| Normal quantile | 14.0x |
| Describe (all stats) | 6.6x |
| Binomial pmf | 4.2x |
| Paired t-test | 4.0x |
| IQR | 3.6x |
| Hypergeometric (pmf, cdf) | 2.4–3.4x |
| Variance / StdDev | 2.2x |
| Skewness | 2.1x |
| One-sample t-test | 1.7x |
| Two-sample t-test | 1.6x |
Parity (within 1.5x)
Mean, Median, Percentile 50/95, Kolmogorov-Smirnov, Mann-Whitney U, Kendall Tau, Spearman, Beta, Gamma, Student's t, Exponential, Poisson, Uniform, Cauchy (pdf/cdf).
Descriptive Statistics
Other sizes
Key findings:
- kstats kurtosis is 4.2x faster — single-pass computation vs multi-pass in Commons
- kstats mean is 1.4x faster at scale (Neumaier compensated summation)
- Commons variance/stdDev is ~2x faster (simpler single-pass without compensation)
- Commons
describe()aggregation is ~7x faster (delegates to internalSummaryStatistics)
Quantile Benchmarks
Other sizes
Key findings:
- Percentile 50 and 95 are comparable
- Commons IQR is 3.6x faster (single-pass percentile estimation)
Correlation & Regression
Other sizes
Key findings:
- kstats Pearson correlation is 1.8x faster
- kstats covariance and linear regression are 1.4–1.5x faster
- Kendall Tau and Spearman are comparable (both O(n log n))
Hypothesis Tests
Other sizes
Key findings:
- kstats ANOVA is 5x faster — avoids per-group distribution object creation
- kstats chi-squared GOF is 39x faster — direct computation without object allocation
- Commons t-tests are 2–4x faster — highly optimized
TDistributionquantile lookup - Kolmogorov-Smirnov is essentially tied
Chi-Squared Independence
Key findings:
- kstats is 3.5–58x faster depending on table size — direct matrix computation vs object allocation overhead in Commons
Probability Distributions
Continuous
Discrete
Key findings:
- kstats Zipf is orders of magnitude faster — precomputed harmonic sums vs on-the-fly O(N) in Commons
- kstats LogNormal quantile is 443x faster — closed-form inverse vs iterative numerical solver
- kstats F, Normal CDF, Chi-Squared, Weibull quantile are 2–3x faster
- Commons Normal quantile, Binomial PMF, and Hypergeometric are faster (different algorithmic approaches)
- Most distribution operations are sub-microsecond in both libraries
Regenerating Charts
pip install -r benchmark/charts/requirements.txt
python benchmark/charts/generate_charts.py
Or with an explicit report path:
python benchmark/charts/generate_charts.py benchmark/build/reports/benchmarks/main/<timestamp>/main.json
Charts are saved to benchmark/charts/ as SVG files.