w-distributions/src/studentt.mjs

merge to `w-statistic`

import cephes from 'cephes'

async function wStudenttDistribution(df) {

    //support browser
    await cephes.compiled

    function StudenttDistribution(df) {
        if (!(this instanceof StudenttDistribution)) {
            return new StudenttDistribution(df)
        }

        if (typeof df !== 'number') {
            //throw TypeError('mean must be a number')
            throw TypeError('df(degrees of freedom) must be a number')
        }
        if (df <= 0) {
            //throw RangeError('df must be a positive number')
            throw RangeError('df(degrees of freedom) must be a positive number')
        }

        this._df = df

        this._pdf_const = Math.exp(cephes.lgam((df + 1) / 2) - cephes.lgam(df / 2)) / Math.sqrt(this._df * Math.PI)
    }

    StudenttDistribution.prototype.pdf = function (x) {
        return this._pdf_const / Math.pow(1 + ((x * x) / this._df), (this._df + 1) / 2)
    }

    // Uses the idendenity specified in Abramowitz and Stegun 26.7.1 and
    // Abramowitz and Stegun 26.5.27.
    // F(x|df) = 1 - 0.5 * I_z (df/2, 1/2)
    //       z = df / (df + x^2)
    //     for   x > 0
    // Since the Student-t distribution is symetric:
    // F(x|df) = 0.5 * I_z (df/2, 1/2)
    //     for   x < 0
    StudenttDistribution.prototype.cdf = function (x) {
        const z = this._df / (this._df + x * x)
        const p = 0.5 * cephes.incbet(0.5 * this._df, 0.5, z)
        return (x <= 0) ? p : 1 - p
    }

    StudenttDistribution.prototype.inv = function (p) {
        if (p <= 0) return -Infinity
        if (p >= 1) return Infinity
        if (p === 0.5) return 0

        if (p > 0.25 && p < 0.75) {
            const phat = 1 - 2 * p
            const z = cephes.incbi(0.5, 0.5 * this._df, Math.abs(phat))
            const t = Math.sqrt(this._df * z / (1 - z))
            return (p < 0.5) ? -t : t
        }
        else {
            const phat = (p >= 0.5) ? 1 - p : p
            const z = cephes.incbi(0.5 * this._df, 0.5, 2 * phat)
            const t = Math.sqrt(this._df / z - this._df)
            return (p < 0.5) ? -t : t
        }
    }

    StudenttDistribution.prototype.median = function () {
        return 0
    }

    StudenttDistribution.prototype.mean = function () {
        return (this._df > 1) ? 0 : undefined
    }

    StudenttDistribution.prototype.variance = function () {
        if (this._df > 2) return this._df / (this._df - 2)
        else if (this._df > 1) return Infinity
        else return undefined
    }

    return StudenttDistribution(df)
}

export default wStudenttDistribution