Statistics Library Skill

120+ statistical calculations in a single library - TradingView Featured Scripts inspired

Overview

Comprehensive statistics library providing 120+ calculations for quantitative analysis, risk metrics, and strategy optimization. Based on TradingView's featured statistical libraries with K.I.T. enhancements.

Categories

1. Descriptive Statistics (20+)

Function	Description
mean()	Arithmetic mean
median()	Median value
mode()	Most frequent value
variance()	Population variance
stdev()	Standard deviation
skewness()	Distribution asymmetry
kurtosis()	Distribution tail heaviness
range()	Max - Min
iqr()	Interquartile range
percentile()	Nth percentile
zscore()	Standardized score
mad()	Mean absolute deviation
cv()	Coefficient of variation
sem()	Standard error of mean
gmean()	Geometric mean
hmean()	Harmonic mean
wmean()	Weighted mean
trimean()	Tukey trimean
winsorize()	Winsorized mean
entropy()	Shannon entropy

2. Risk Metrics (25+)

Function	Description
sharpe()	Sharpe ratio
sortino()	Sortino ratio (downside)
calmar()	Calmar ratio
treynor()	Treynor ratio
omega()	Omega ratio
sterling()	Sterling ratio
burke()	Burke ratio
ulcer()	Ulcer index
pain()	Pain index
var()	Value at Risk
cvar()	Conditional VaR (Expected Shortfall)
maxDrawdown()	Maximum drawdown
avgDrawdown()	Average drawdown
recoveryTime()	Time to recover from DD
kellyFraction()	Kelly criterion position sizing
profitFactor()	Gross profit / Gross loss
expectancy()	Expected value per trade
sqn()	System Quality Number
lakeRatio()	Lake ratio
gainPain()	Gain to pain ratio
tail()	Tail ratio
commonSense()	Common sense ratio
cpc()	CPC index
kRatio()	K-ratio
martin()	Martin ratio

3. Correlation & Regression (20+)

Function	Description
pearson()	Pearson correlation
spearman()	Spearman rank correlation
kendall()	Kendall tau correlation
beta()	Market beta
alpha()	Jensen's alpha
r2()	R-squared
adjR2()	Adjusted R-squared
covariance()	Covariance
autocorr()	Autocorrelation
crosscorr()	Cross-correlation
linearReg()	Linear regression
polyReg()	Polynomial regression
expReg()	Exponential regression
logReg()	Logarithmic regression
powerReg()	Power regression
residuals()	Regression residuals
durbin()	Durbin-Watson statistic
vif()	Variance inflation factor
partialCorr()	Partial correlation
semiCorr()	Semi-correlation

4. Time Series (25+)

Function	Description
sma()	Simple moving average
ema()	Exponential moving average
wma()	Weighted moving average
hma()	Hull moving average
vwma()	Volume-weighted MA
dema()	Double EMA
tema()	Triple EMA
alma()	Arnaud Legoux MA
kama()	Kaufman adaptive MA
mcgd()	McGinley dynamic
linreg()	Linear regression value
diff()	First difference
pctChange()	Percent change
logReturn()	Logarithmic returns
momentum()	Price momentum
roc()	Rate of change
atr()	Average true range
tr()	True range
highest()	Highest value
lowest()	Lowest value
stoch()	Stochastic oscillator
rsi()	Relative strength index
cci()	Commodity channel index
adx()	Average directional index
aroon()	Aroon indicator

5. Distribution & Probability (15+)

Function	Description
normalPdf()	Normal probability density
normalCdf()	Normal cumulative distribution
normalInv()	Inverse normal
tPdf()	Student's t PDF
tCdf()	Student's t CDF
chiSqPdf()	Chi-squared PDF
chiSqCdf()	Chi-squared CDF
fPdf()	F-distribution PDF
fCdf()	F-distribution CDF
binomPmf()	Binomial PMF
binomCdf()	Binomial CDF
poissonPmf()	Poisson PMF
poissonCdf()	Poisson CDF
expPdf()	Exponential PDF
expCdf()	Exponential CDF

6. Hypothesis Testing (15+)

Function	Description
tTest()	Student's t-test
zTest()	Z-test
chiSqTest()	Chi-squared test
fTest()	F-test
anova()	Analysis of variance
mannWhitney()	Mann-Whitney U test
wilcoxon()	Wilcoxon signed-rank
kruskal()	Kruskal-Wallis test
levene()	Levene's test
shapiro()	Shapiro-Wilk normality
jarqueBera()	Jarque-Bera normality
adf()	Augmented Dickey-Fuller
kpss()	KPSS stationarity
granger()	Granger causality
cointegration()	Cointegration test

Usage

import stats from '@kit/statistics-library';

// Calculate Sharpe ratio
const sharpe = stats.sharpe(returns, riskFreeRate);

// Get full risk report
const riskReport = stats.riskReport(equity, {
  riskFreeRate: 0.02,
  benchmark: 'SPY',
  confidence: 0.95
});

// Correlation matrix
const corrMatrix = stats.correlationMatrix([btc, eth, sol, avax]);

// Regression analysis
const reg = stats.linearReg(x, y, {
  includeStats: true,
  forecast: 10
});

Commands

• kit stats calc <function> <data> - Calculate statistic
• kit stats risk <equity> - Full risk report
• kit stats corr <symbols> - Correlation matrix
• kit stats test <hypothesis> <data> - Run hypothesis test
• kit stats export <format> - Export calculations

Performance

• Vectorized: Operations use SIMD where available
• Streaming: Handle infinite data streams
• Cached: Memoized calculations
• GPU: Optional GPU acceleration for large datasets