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x/simplestatistics/src/sample_kurtosis.js

simple statistics for node & browser javascript
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import mean from "./mean.js";
/** * [Kurtosis](http://en.wikipedia.org/wiki/Kurtosis) is * a measure of the heaviness of a distribution's tails relative to its * variance. The kurtosis value can be positive or negative, or even undefined. * * Implementation is based on Fisher's excess kurtosis definition and uses * unbiased moment estimators. This is the version found in Excel and available * in several statistical packages, including SAS and SciPy. * * @param {Array<number>} x a sample of 4 or more data points * @returns {number} sample kurtosis * @throws {Error} if x has length less than 4 * @example * sampleKurtosis([1, 2, 2, 3, 5]); // => 1.4555765595463122 */function sampleKurtosis(x) { const n = x.length;
if (n < 4) { throw new Error("sampleKurtosis requires at least four data points"); }
const meanValue = mean(x); let tempValue; let secondCentralMoment = 0; let fourthCentralMoment = 0;
for (let i = 0; i < n; i++) { tempValue = x[i] - meanValue; secondCentralMoment += tempValue * tempValue; fourthCentralMoment += tempValue * tempValue * tempValue * tempValue; }
return ( ((n - 1) / ((n - 2) * (n - 3))) * ((n * (n + 1) * fourthCentralMoment) / (secondCentralMoment * secondCentralMoment) - 3 * (n - 1)) );}
export default sampleKurtosis;