def zipf_cdf(k, s, N):
"""
Gives the value of the Zipf cumulative distribution function
for the given k (k can be a whole, in [1, 2, ..., N])
and the specified parameters of the Zipf distribution-
s >= 0, N in [1, 2, ...]
"""
A = functions.generalized_harmonic_number_function(k, s)
B = functions.generalized_harmonic_number_function(N, s)
return A/B
def zipf_pmf(k, s, N):
"""
Gives the value of the Zipf probability mass function
for the given k (k can be a whole, in [1, 2, ..., N])
and the specified parameters of the Zipf distribution-
s >= 0, N in [1, 2, ...]
"""
A = 1/math.pow(k, s)
B = functions.generalized_harmonic_number_function(N, s)
return A/B
def __init__(self, s, N):
"""
Sets the parameters for the Zipf distribution.
s must be > 0.
"""
if s < 0:
raise IncorrectDistributionInicializationError()
self.s = s
self.N = N
A = functions.generalized_harmonic_number_function(N, s-1)
B = functions.generalized_harmonic_number_function(N, s)
self.mean = A/B
# http://mathworld.wolfram.com/ZipfDistribution.html
# http://mathworld.wolfram.com/RiemannZetaFunction.html
# - bad integral
# self.variance = "Implement me!"
self.mode = 1
