Module « numpy.random »

Fonction binomial - module numpy.random

Signature de la fonction binomial

Description

binomial.__doc__

        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)

        .. note::
            New code should use the ``binomial`` method of a ``default_rng()``
            instance instead; please see the :ref:`random-quick-start`.

        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.
        Generator.binomial: which should be used for new code.

        Notes
        -----
        The probability density 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.
               http://mathworld.wolfram.com/BinomialDistribution.html
        .. [5] Wikipedia, "Binomial distribution",
               https://en.wikipedia.org/wiki/Binomial_distribution

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

        >>> n, p = 10, .5  # number of trials, probability of each trial
        >>> s = np.random.binomial(n, p, 1000)
        # result of flipping a coin 10 times, tested 1000 times.

        A real world example. A company drills 9 wild-cat oil exploration
        wells, each with an estimated probability of success of 0.1. All nine
        wells fail. What is the probability of that happening?

        Let's do 20,000 trials of the model, and count the number that
        generate zero positive results.

        >>> sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.
        # answer = 0.38885, or 38%.