def moment(self, n, mu, sigma):
r"""
n-th (non central) moment of the Normal distribution
.. math::
E = ... complicated.
Parameters
----------
n : integer or numpy array of integers
The ordinal of the moment to calculate
mu : numpy array or scalar
The location parameter for the Normal distribution
sigma : numpy array or scalar
The scale parameter for the Normal distribution
Returns
-------
moment : scalar or numpy array
The moment(s) of the Normal distribution
Examples
--------
>>> from surpyval import Normal
>>> Normal.moment(2, 3, 4)
25.0
"""
return scipy_norm.moment(n, mu, sigma)
def generate_moments(self, max_moment):
'''
Calculate & store moments to retrieve more efficiently later
'''
self._moments = np.zeros((max_moment, 1))
#Rely on scipy.stats to return non-central moment
for i in range(max_moment):
self._moments[i] = scipynormal.moment(i+1, self._mean, self._std)
def norm_distribution(*args):
try:
a, b = float(args[0]), float(args[1])
except (ValueError, TypeError):
return {'is_valid': False}
if not b > 0:
return {'is_valid': False}
t = Symbol('t')
mean, var, mean2 = a, b, norm.moment(2, loc=a, scale=sqrt(b))
cf = exp(I * a * t - b * t**2 / 2)
d_cf = diff(cf, t)
dd_cf = diff(d_cf, t)
return {
'a': a,
'b': b,
'mean': mean,
'mean2': mean2,
'var': var,
'g': latex(nsimplify(cf, tolerance=0.1)),
'g1': latex(nsimplify(d_cf, tolerance=0.1)),
'g2': latex(nsimplify(dd_cf, tolerance=0.1)),
'type': type,
'is_valid': True,
}
def compute_moment(self, order):
if order not in self._moment_values.keys():
self._moment_values[order] = norm.moment(order,
loc=self._mean,
scale=self._variance**0.5)
return self._moment_values[order]
dir(rv)
dist_continu = [d for d in dir(stats) if isinstance(getattr(stats, d), stats.rv_continuous)]
dist_discrete = [d for d in dir(stats) if isinstance(getattr(stats, d), stats.rv_discrete)]
n = np.empty(1000)
for i in range(1000):
n[i] = norm.rvs()
plt.hist(n, bins = 50, density = 1)
plt.hist(norm.pdf(n), bins = 50, density = 1)
plt.hist(norm.cdf(n), bins = 50, density = 1)
plt.hist(norm.moment(n.any()), bins = 50, density = 1)
norm.mean()
norm.var()
norm.ppf(0.5) # median of 0-1 normal distribution
norm.rvs(size = 3)
norm.rvs(size = 3, random_state = 1234)
norm.rvs(3) # the first arguement is the loc (mean, in case of normal distrubution) parameter, not size
# Shifting and scaling
x = norm.rvs(size = 5, loc = 3, scale = 4)
norm.stats(x)
norm.stats(loc = 3, scale = 4, moments = "mv")