deno.land / x / simplestatistics@v7.8.3 / src / sample_skewness.js
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253import mean from "./mean.js";
/** * [Skewness](http://en.wikipedia.org/wiki/Skewness) is * a measure of the extent to which a probability distribution of a * real-valued random variable "leans" to one side of the mean. * The skewness value can be positive or negative, or even undefined. * * Implementation is based on the adjusted Fisher-Pearson standardized * moment coefficient, which is the version found in Excel and several * statistical packages including Minitab, SAS and SPSS. * * @since 4.1.0 * @param {Array<number>} x a sample of 3 or more data points * @returns {number} sample skewness * @throws {Error} if x has length less than 3 * @example * sampleSkewness([2, 4, 6, 3, 1]); // => 0.590128656384365 */function sampleSkewness(x) { if (x.length < 3) { throw new Error("sampleSkewness requires at least three data points"); }
const meanValue = mean(x); let tempValue; let sumSquaredDeviations = 0; let sumCubedDeviations = 0;
for (let i = 0; i < x.length; i++) { tempValue = x[i] - meanValue; sumSquaredDeviations += tempValue * tempValue; sumCubedDeviations += tempValue * tempValue * tempValue; }
// this is Bessels' Correction: an adjustment made to sample statistics // that allows for the reduced degree of freedom entailed in calculating // values from samples rather than complete populations. const besselsCorrection = x.length - 1;
// Find the mean value of that list const theSampleStandardDeviation = Math.sqrt( sumSquaredDeviations / besselsCorrection );
const n = x.length; const cubedS = Math.pow(theSampleStandardDeviation, 3);
return (n * sumCubedDeviations) / ((n - 1) * (n - 2) * cubedS);}
export default sampleSkewness;
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