如何计算scipy中多项式的概率质量函数？

Question

有没有办法在python中使用numpy或scipy来计算多项式PMF？这里描述了PMF：https://en.wikipedia.org/wiki/Multinomial_distribution

scipy.stats.binom仅适用于二项式随机变量。

Answer 1

虽然it might be available in the future version (0.18 or up)已经在scipy中没有多项分布。

同时，你可以很容易地DIY它：

def logpmf(self, x, n, p):
    """Log of the multinomial probability mass function.
    Parameters
    ----------
    x : array_like
        Quantiles.
    n : int
        Number of trials
    p : array_like, shape (k,)
        Probabilities. These should sum to one. If they do not, then
        ``p[-1]`` is modified to account for the remaining probability so
        that ``sum(p) == 1``.
    Returns
    -------
    logpmf : float
        Log of the probability mass function evaluated at `x`. 
    """

    x = np.asarray(x)
    if p.shape[0] != x.shape[-1]:
        raise ValueError("x & p shapes do not match.")

    coef = gammaln(n + 1) - gammaln(x + 1.).sum(axis=-1)
    val = coef + np.sum(xlogy(x, p), axis=-1)

    # insist on that the support is a set of *integers*
    mask = np.logical_and.reduce(np.mod(x, 1) == 0, axis=-1)

    mask &= (x.sum(axis=-1) == n)
    out = np.where(mask, val, -np.inf)
    return out

此处gammaln为scipy.special.gammaln，xlogy为scipy.special.xlogy。如您所见，主要工作是确保非整数值的pmf为零。

Answer 2

scipy中没有提供Multiomial PMF功能。但是，您可以自己使用numpy.random.multinomial类来绘制样本。