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/** * This function calculates the Wilcoxon rank sum statistic for the first sample * with respect to the second. The Wilcoxon rank sum test is a non-parametric * alternative to the t-test which is equivalent to the * [Mann-Whitney U test](https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test). * The statistic is calculated by pooling all the observations together, ranking them, * and then summing the ranks associated with one of the samples. If this rank sum is * sufficiently large or small we reject the hypothesis that the two samples come * from the same distribution in favor of the alternative that one is shifted with * respect to the other. * * @param {Array<number>} sampleX a sample as an array of numbers * @param {Array<number>} sampleY a sample as an array of numbers * @returns {number} rank sum for sampleX * * @example * wilcoxonRankSum([1, 4, 8], [9, 12, 15]); // => 6 */function wilcoxonRankSum(sampleX, sampleY) {    if (!sampleX.length || !sampleY.length) {        throw new Error("Neither sample can be empty");    }
    const pooledSamples = sampleX        .map((x) => ({ label: "x", value: x }))        .concat(sampleY.map((y) => ({ label: "y", value: y })))        .sort((a, b) => a.value - b.value);
    for (let rank = 0; rank < pooledSamples.length; rank++) {        pooledSamples[rank].rank = rank;    }
    let tiedRanks = [pooledSamples[0].rank];    for (let i = 1; i < pooledSamples.length; i++) {        if (pooledSamples[i].value === pooledSamples[i - 1].value) {            tiedRanks.push(pooledSamples[i].rank);            if (i === pooledSamples.length - 1) {                replaceRanksInPlace(pooledSamples, tiedRanks);            }        } else if (tiedRanks.length > 1) {            replaceRanksInPlace(pooledSamples, tiedRanks);        } else {            tiedRanks = [pooledSamples[i].rank];        }    }
    function replaceRanksInPlace(pooledSamples, tiedRanks) {        const average = (tiedRanks[0] + tiedRanks[tiedRanks.length - 1]) / 2;        for (let i = 0; i < tiedRanks.length; i++) {            pooledSamples[tiedRanks[i]].rank = average;        }    }
    let rankSum = 0;
    for (let i = 0; i < pooledSamples.length; i++) {        const sample = pooledSamples[i];        if (sample.label === "x") {            rankSum += sample.rank + 1;        }    }
    return rankSum;}
export default wilcoxonRankSum;