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import chiSquaredDistributionTable from "./chi_squared_distribution_table";import mean from "./mean";
/** * The [χ2 (Chi-Squared) Goodness-of-Fit Test](http://en.wikipedia.org/wiki/Goodness_of_fit#Pearson.27s_chi-squared_test) * uses a measure of goodness of fit which is the sum of differences between observed and expected outcome frequencies * (that is, counts of observations), each squared and divided by the number of observations expected given the * hypothesized distribution. The resulting χ2 statistic, `chiSquared`, can be compared to the chi-squared distribution * to determine the goodness of fit. In order to determine the degrees of freedom of the chi-squared distribution, one * takes the total number of observed frequencies and subtracts the number of estimated parameters. The test statistic * follows, approximately, a chi-square distribution with (k − c) degrees of freedom where `k` is the number of non-empty * cells and `c` is the number of estimated parameters for the distribution. * * @param {Array<number>} data * @param {Function} distributionType a function that returns a point in a distribution: * for instance, binomial, bernoulli, or poisson * @param {number} significance * @returns {number} chi squared goodness of fit * @example * // Data from Poisson goodness-of-fit example 10-19 in William W. Hines & Douglas C. Montgomery, * // "Probability and Statistics in Engineering and Management Science", Wiley (1980). * var data1019 = [ *     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, *     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, *     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, *     2, 2, 2, 2, 2, 2, 2, 2, 2, *     3, 3, 3, 3 * ]; * ss.chiSquaredGoodnessOfFit(data1019, ss.poissonDistribution, 0.05); //= false */function chiSquaredGoodnessOfFit(data, distributionType, significance) {    // Estimate from the sample data, a weighted mean.    const inputMean = mean(data);    // Calculated value of the χ2 statistic.    let chiSquared = 0;    // Number of hypothesized distribution parameters estimated, expected to be supplied in the distribution test.    // Lose one degree of freedom for estimating `lambda` from the sample data.    const c = 1;    // The hypothesized distribution.    // Generate the hypothesized distribution.    const hypothesizedDistribution = distributionType(inputMean);    const observedFrequencies = [];    const expectedFrequencies = [];
    // Create an array holding a histogram from the sample data, of    // the form `{ value: numberOfOcurrences }`    for (let i = 0; i < data.length; i++) {        if (observedFrequencies[data[i]] === undefined) {            observedFrequencies[data[i]] = 0;        }        observedFrequencies[data[i]]++;    }
    // The histogram we created might be sparse - there might be gaps    // between values. So we iterate through the histogram, making    // sure that instead of undefined, gaps have 0 values.    for (let i = 0; i < observedFrequencies.length; i++) {        if (observedFrequencies[i] === undefined) {            observedFrequencies[i] = 0;        }    }
    // Create an array holding a histogram of expected data given the    // sample size and hypothesized distribution.    for (const k in hypothesizedDistribution) {        if (k in observedFrequencies) {            expectedFrequencies[+k] = hypothesizedDistribution[k] * data.length;        }    }
    // Working backward through the expected frequencies, collapse classes    // if less than three observations are expected for a class.    // This transformation is applied to the observed frequencies as well.    for (let k = expectedFrequencies.length - 1; k >= 0; k--) {        if (expectedFrequencies[k] < 3) {            expectedFrequencies[k - 1] += expectedFrequencies[k];            expectedFrequencies.pop();
            observedFrequencies[k - 1] += observedFrequencies[k];            observedFrequencies.pop();        }    }
    // Iterate through the squared differences between observed & expected    // frequencies, accumulating the `chiSquared` statistic.    for (let k = 0; k < observedFrequencies.length; k++) {        chiSquared +=            Math.pow(observedFrequencies[k] - expectedFrequencies[k], 2) /            expectedFrequencies[k];    }
    // Calculate degrees of freedom for this test and look it up in the    // `chiSquaredDistributionTable` in order to    // accept or reject the goodness-of-fit of the hypothesized distribution.    // Degrees of freedom, calculated as (number of class intervals -    // number of hypothesized distribution parameters estimated - 1)    const degreesOfFreedom = observedFrequencies.length - c - 1;    return (        chiSquaredDistributionTable[degreesOfFreedom][significance] < chiSquared    );}
export default chiSquaredGoodnessOfFit;