diff options
Diffstat (limited to 'numpy/random/mtrand.pyx')
| -rw-r--r-- | numpy/random/mtrand.pyx | 40 |
1 files changed, 26 insertions, 14 deletions
diff --git a/numpy/random/mtrand.pyx b/numpy/random/mtrand.pyx index 06e75a698..3e13503d0 100644 --- a/numpy/random/mtrand.pyx +++ b/numpy/random/mtrand.pyx @@ -1033,7 +1033,10 @@ cdef class RandomState: greater than or equal to low. The default value is 0. high : float or array_like of floats Upper boundary of the output interval. All values generated will be - less than or equal to high. The default value is 1.0. + less than or equal to high. The high limit may be included in the + returned array of floats due to floating-point rounding in the + equation ``low + (high-low) * random_sample()``. The default value + is 1.0. 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), @@ -2524,7 +2527,7 @@ cdef class RandomState: Raises ------ ValueError - If a < 1. + If a <= 0. See Also -------- @@ -3606,7 +3609,7 @@ cdef class RandomState: `a` > 1. The Zipf distribution (also known as the zeta distribution) is a - continuous probability distribution that satisfies Zipf's law: the + discrete probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table. @@ -3639,9 +3642,10 @@ cdef class RandomState: ----- The probability density for the Zipf distribution is - .. math:: p(x) = \\frac{x^{-a}}{\\zeta(a)}, + .. math:: p(k) = \\frac{k^{-a}}{\\zeta(a)}, - where :math:`\\zeta` is the Riemann Zeta function. + for integers :math:`k \geq 1`, where :math:`\\zeta` is the Riemann Zeta + function. It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely @@ -3657,21 +3661,29 @@ cdef class RandomState: -------- Draw samples from the distribution: - >>> a = 2. # parameter - >>> s = np.random.zipf(a, 1000) + >>> a = 4.0 + >>> n = 20000 + >>> s = np.random.zipf(a, n) Display the histogram of the samples, along with - the probability density function: + the expected histogram based on the probability + density function: >>> import matplotlib.pyplot as plt - >>> from scipy import special # doctest: +SKIP + >>> from scipy.special import zeta # doctest: +SKIP + + `bincount` provides a fast histogram for small integers. - Truncate s values at 50 so plot is interesting: + >>> count = np.bincount(s) + >>> k = np.arange(1, s.max() + 1) - >>> count, bins, ignored = plt.hist(s[s<50], 50, density=True) - >>> x = np.arange(1., 50.) - >>> y = x**(-a) / special.zetac(a) # doctest: +SKIP - >>> plt.plot(x, y/max(y), linewidth=2, color='r') # doctest: +SKIP + >>> plt.bar(k, count[1:], alpha=0.5, label='sample count') + >>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5, + ... label='expected count') # doctest: +SKIP + >>> plt.semilogy() + >>> plt.grid(alpha=0.4) + >>> plt.legend() + >>> plt.title(f'Zipf sample, a={a}, size={n}') >>> plt.show() """ |