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Deepbox
19intermediate

Statistics

Descriptive statistics, percentiles and correlation on small samples. For hypothesis tests see example 43.

What you will learn

  • Use deepbox/ndarray for tensor, stack.
  • Use deepbox/stats for mean, median, std, variance, skewness, kurtosis, percentile, pearsonr, corrcoef.
  • Descriptive statistics, percentiles and correlation on small samples. For hypothesis tests see example 43.

Source

index.ts
/** * Example 19: Statistics * * Descriptive statistics, percentiles and correlation on small samples. * The statistics functions return tensors, and item() turns a one-element * tensor into a number. See example 43 for hypothesis tests. */ import { stack, tensor } from "deepbox/ndarray";import {  corrcoef,  kurtosis,  mean,  median,  pearsonr,  percentile,  skewness,  std,  variance,} from "deepbox/stats"; console.log("=== Statistics ===\n"); // Sample dataconst data = tensor([23, 25, 28, 30, 32, 35, 38, 40, 42, 45, 48, 50, 55, 60, 65]); console.log("Dataset:");console.log(`${data.toString()}\n`); // Descriptive statisticsconsole.log("Descriptive Statistics:");console.log("-".repeat(50)); const meanVal = Number(mean(data).item());const medianVal = Number(median(data).item());const stdVal = Number(std(data).item());const varVal = Number(variance(data).item());const skewVal = Number(skewness(data).item());const kurtVal = Number(kurtosis(data).item()); console.log(`Mean:     ${meanVal.toFixed(2)}`);console.log(`Median:   ${medianVal.toFixed(2)}`);console.log(`Std Dev:  ${stdVal.toFixed(2)}`);console.log(`Variance: ${varVal.toFixed(2)}`);console.log(`Skewness: ${skewVal.toFixed(4)}`);console.log(`Kurtosis: ${kurtVal.toFixed(4)} (excess kurtosis, 0 for a normal distribution)\n`); // std and variance divide by n by default (the population value, like NumPy).// Pass ddof: 1 for the sample value (like pandas).const sampleStd = Number(std(data, { ddof: 1 }).item());console.log(`Sample Std Dev (ddof = 1): ${sampleStd.toFixed(2)}\n`); // Percentilesconsole.log("Percentiles:");console.log("-".repeat(50)); const p25 = Number(percentile(data, 25).item());const p50 = Number(percentile(data, 50).item());const p75 = Number(percentile(data, 75).item()); console.log(`25th percentile (Q1): ${p25.toFixed(2)}`);console.log(`50th percentile (Q2): ${p50.toFixed(2)}`);console.log(`75th percentile (Q3): ${p75.toFixed(2)}\n`); // Several percentiles at once return one tensor.console.log(`Quartiles in one call: ${percentile(data, [25, 50, 75]).toString()}\n`); // Correlation analysisconsole.log("Correlation Analysis:");console.log("-".repeat(50)); const x = tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);const y = tensor([2.1, 4.2, 5.8, 8.1, 10.3, 11.9, 14.2, 16.1, 17.8, 20.2]); // pearsonr returns [coefficient, p-value]. The default test is two-sided.const [r, pTwoSided] = pearsonr(x, y);console.log(`Pearson correlation: ${r.toFixed(4)} (p = ${pTwoSided.toExponential(2)})`); // Test one direction only: the alternative is that the correlation is greater than zero.const [, pGreater] = pearsonr(x, y, { alternative: "greater" });console.log(`One-sided p-value (alternative "greater"): ${pGreater.toExponential(2)}`); // corrcoef on a matrix: rows are observations and columns are variables.// stack(..., 1) joins three vectors as the columns x, y and z, where z falls as x rises.const z = tensor([9, 8, 8.5, 6, 5.5, 5, 3, 3.5, 1, 0.5]);const observations = stack([x, y, z], 1);console.log(`\nCorrelation Matrix (columns x, y, z, shape [${observations.shape}]):`);console.log(corrcoef(observations).toString());

Output

Console output
Console output only.