Class NormalDist

Lib/statistics.py:1228–1448

Normal distribution of a random variable

## Normal Distribution #####################################################

class NormalDist:
    "Normal distribution of a random variable"
    # https://en.wikipedia.org/wiki/Normal_distribution
    # https://en.wikipedia.org/wiki/Variance#Properties

    __slots__ = {
        '_mu': 'Arithmetic mean of a normal distribution',
        '_sigma': 'Standard deviation of a normal distribution',
    }

    def __init__(self, mu=0.0, sigma=1.0):
        "NormalDist where mu is the mean and sigma is the standard deviation."
        if sigma < 0.0:
            raise StatisticsError('sigma must be non-negative')
        self._mu = float(mu)
        self._sigma = float(sigma)

    @classmethod
    def from_samples(cls, data):
        "Make a normal distribution instance from sample data."
        return cls(*_mean_stdev(data))

    def samples(self, n, *, seed=None):
        "Generate *n* samples for a given mean and standard deviation."
        rnd = random.random if seed is None else random.Random(seed).random
        inv_cdf = _normal_dist_inv_cdf
        mu = self._mu
        sigma = self._sigma
        return [inv_cdf(rnd(), mu, sigma) for _ in repeat(None, n)]

    def pdf(self, x):
        "Probability density function.  P(x <= X < x+dx) / dx"
        variance = self._sigma * self._sigma
        if not variance:
            raise StatisticsError('pdf() not defined when sigma is zero')
        diff = x - self._mu
        return exp(diff * diff / (-2.0 * variance)) / sqrt(tau * variance)

    def cdf(self, x):
        "Cumulative distribution function.  P(X <= x)"
        if not self._sigma:
            raise StatisticsError('cdf() not defined when sigma is zero')
        return 0.5 * erfc((self._mu - x) / (self._sigma * _SQRT2))

    def inv_cdf(self, p):
        """Inverse cumulative distribution function.  x : P(X <= x) = p

        Finds the value of the random variable such that the probability of
        the variable being less than or equal to that value equals the given
        probability.

        This function is also called the percent point function or quantile
        function.
        """
        if p <= 0.0 or p >= 1.0:
            raise StatisticsError('p must be in the range 0.0 < p < 1.0')
        return _normal_dist_inv_cdf(p, self._mu, self._sigma)