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Classe « Generator »

Méthode numpy.random.Generator.binomial

Signature de la méthode binomial

def binomial(self, n, p, size=None) 

Description

help(Generator.binomial)

        binomial(n, p, size=None)

        Draw samples from a binomial distribution.

        Samples are drawn from a binomial distribution with specified
        parameters, n trials and p probability of success where
        n an integer >= 0 and p is in the interval [0,1]. (n may be
        input as a float, but it is truncated to an integer in use)

        Parameters
        ----------
        n : int or array_like of ints
            Parameter of the distribution, >= 0. Floats are also accepted,
            but they will be truncated to integers.
        p : float or array_like of floats
            Parameter of the distribution, >= 0 and <=1.
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn.  If size is ``None`` (default),
            a single value is returned if ``n`` and ``p`` are both scalars.
            Otherwise, ``np.broadcast(n, p).size`` samples are drawn.

        Returns
        -------
        out : ndarray or scalar
            Drawn samples from the parameterized binomial distribution, where
            each sample is equal to the number of successes over the n trials.

        See Also
        --------
        scipy.stats.binom : probability density function, distribution or
            cumulative density function, etc.

        Notes
        -----
        The probability mass function (PMF) for the binomial distribution is

        .. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N},

        where :math:`n` is the number of trials, :math:`p` is the probability
        of success, and :math:`N` is the number of successes.

        When estimating the standard error of a proportion in a population by
        using a random sample, the normal distribution works well unless the
        product p*n <=5, where p = population proportion estimate, and n =
        number of samples, in which case the binomial distribution is used
        instead. For example, a sample of 15 people shows 4 who are left
        handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,
        so the binomial distribution should be used in this case.

        References
        ----------
        .. [1] Dalgaard, Peter, "Introductory Statistics with R",
               Springer-Verlag, 2002.
        .. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
               Fifth Edition, 2002.
        .. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden
               and Quigley, 1972.
        .. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A
               Wolfram Web Resource.
               https://mathworld.wolfram.com/BinomialDistribution.html
        .. [5] Wikipedia, "Binomial distribution",
               https://en.wikipedia.org/wiki/Binomial_distribution

        Examples
        --------
        Draw samples from the distribution:

        >>> rng = np.random.default_rng()
        >>> n, p, size = 10, .5, 10000  
        >>> s = rng.binomial(n, p, 10000)

        Assume a company drills 9 wild-cat oil exploration wells, each with
        an estimated probability of success of ``p=0.1``. All nine wells fail. 
        What is the probability of that happening?

        Over ``size = 20,000`` trials the probability of this happening 
        is on average:

        >>> n, p, size = 9, 0.1, 20000
        >>> np.sum(rng.binomial(n=n, p=p, size=size) == 0)/size
        0.39015  # may vary

        The following can be used to visualize a sample with ``n=100``, 
        ``p=0.4`` and the corresponding probability density function:

        >>> import matplotlib.pyplot as plt
        >>> from scipy.stats import binom
        >>> n, p, size = 100, 0.4, 10000
        >>> sample = rng.binomial(n, p, size=size)
        >>> count, bins, _ = plt.hist(sample, 30, density=True)
        >>> x = np.arange(n)
        >>> y = binom.pmf(x, n, p)
        >>> plt.plot(x, y, linewidth=2, color='r')

        

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