diff options
| -rw-r--r-- | numpy/random/_generator.pyx | 13 | ||||
| -rw-r--r-- | numpy/random/mtrand.pyx | 13 |
2 files changed, 14 insertions, 12 deletions
diff --git a/numpy/random/_generator.pyx b/numpy/random/_generator.pyx index c103f42aa..1e65be3f1 100644 --- a/numpy/random/_generator.pyx +++ b/numpy/random/_generator.pyx @@ -3107,7 +3107,7 @@ cdef class Generator: `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. @@ -3135,9 +3135,10 @@ cdef class Generator: ----- 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 ``k`` >= 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 @@ -3167,10 +3168,10 @@ cdef class Generator: `bincount` provides a fast histogram for small integers. >>> count = np.bincount(s) - >>> x = np.arange(1, s.max() + 1) + >>> k = np.arange(1, s.max() + 1) - >>> plt.bar(x, count[1:], alpha=0.5, label='sample count') - >>> plt.plot(x, n*(x**-a)/zeta(a), 'k.-', alpha=0.5, + >>> 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) diff --git a/numpy/random/mtrand.pyx b/numpy/random/mtrand.pyx index fa7e95412..280b0faac 100644 --- a/numpy/random/mtrand.pyx +++ b/numpy/random/mtrand.pyx @@ -3609,7 +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. @@ -3642,9 +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 ``k`` >= 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 @@ -3674,10 +3675,10 @@ cdef class RandomState: `bincount` provides a fast histogram for small integers. >>> count = np.bincount(s) - >>> x = np.arange(1, s.max() + 1) + >>> k = np.arange(1, s.max() + 1) - >>> plt.bar(x, count[1:], alpha=0.5, label='sample count') - >>> plt.plot(x, n*(x**-a)/zeta(a), 'k.-', alpha=0.5, + >>> 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) |