def interpret(parameters: np.ndarray, classes: np.ndarray, interval: float):
n_samples, n_components, n_classes = classes.shape
assert parameters.ndim == 3
assert parameters.shape == (n_samples, SkewNormal.N_PARAMETERS + 1, n_components)
shapes = np.expand_dims(parameters[:, 0, :], 2).repeat(n_classes, 2)
locations = np.expand_dims(parameters[:, 1, :], 2).repeat(n_classes, 2)
scales = np.expand_dims(relu(parameters[:, 2, :]), 2).repeat(n_classes, 2)
proportions = np.expand_dims(softmax(parameters[:, 3, :], axis=1), 1)
components = skewnorm.pdf(classes, shapes, loc=locations, scale=scales) * interval
m, v, s, k = skewnorm.stats(shapes[:, :, 0], loc=locations[:, :, 0], scale=scales[:, :, 0], moments="mvsk")
return proportions, components, (m, np.sqrt(v), s, k)
def test_skewdist():
sd = SkewDist(num_interp=500)
a = random.choice([2., 3., 4.])
xs = skewnorm.rvs(a, size=1000)
for x in xs:
sd.update(value=x)
percentiles = [0.25, 0.5, 0.75]
skew_quantiles = [sd.inv_cdf(p) for p in percentiles]
actual_quantiles = [np.quantile(xs, q) for q in percentiles]
assert all(abs(z1 - z2) < 2.0 for z1, z2 in zip(skew_quantiles, actual_quantiles))
sd_stats = [sd.state.mean, sd.state.var(), sd.state.skewness(), sd.state.kurtosis()]
moment_comparison = list(zip(sd_stats, skewnorm.stats(a, moments='mvsk')))
pass
#The skewed normal distributions are fitted through Bayesian optimization using the scipy module
plt.figure(3)
plt.xlabel('distance bin')
plt.ylabel('sizes (m)')
n = 1
x = np.arange(0, 200,
0.1) #range needed to create probability distribution function
skewed_mean_distances = []
skewed_std_distances = []
skewed_variance_distances = []
skewed_kurtosis_distances = []
skewed_skew_distances = []
for bins in size_nest_distances:
if len(bins) > 10:
a, loc, scale = skewnorm.fit(bins) #I fit all distance bins
mean, var, skew, kurt = skewnorm.stats(a, loc, scale, moments='mvsk')
skewed_mean_distances.append(mean)
skewed_std_distances.append(skewnorm.std(
a, loc, scale)) #Calculate the std of all distributions
skewed_variance_distances.append(
var) #Calcualate variance if interesting
skewed_skew_distances.append(skew) #calculate skewness if interesting
skewed_kurtosis_distances.append(
kurt) #calculate kurtosis if interesting
pdf = skewnorm.pdf(x, a, loc,
scale) #create probability distribution function
#I now plot all of the fitted distributions with their respective histograms
plt.subplot(1, len(size_nest_distances), n)
plt.hist(bins, bins=50, normed=True)
plt.plot(x, pdf)
n += 1
from scipy.stats import skewnorm
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
a = 4
mean, var, skew, kurt = skewnorm.stats(a, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(skewnorm.ppf(0.01, a),
skewnorm.ppf(0.99, a), 100)
ax.plot(x, skewnorm.pdf(x, a),
'r-', lw=5, alpha=0.6, label='skewnorm pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = skewnorm(a)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = skewnorm.ppf([0.001, 0.5, 0.999], a)
np.allclose([0.001, 0.5, 0.999], skewnorm.cdf(vals, a))
# True
def get_moments(*args) -> dict:
assert len(args) == len(SkewNormalDistribution.get_parameter_names())
m, v, s, k = skewnorm.stats(*args, moments="mvsk")
std = np.sqrt(v)
moments = dict(mean=m, std=std, skewness=s, kurtosis=k)
return moments