def test_exponentiated_weibull_distribution_cdf():
"""
Tests the CDF of the exponentiated Weibull distribution.
"""
# Define dist with parameters from the distribution fitted to
# dataset A with the MLE in https://arxiv.org/pdf/1911.12835.pdf .
dist = ExponentiatedWeibullDistribution(alpha=0.0373,
beta=0.4743,
delta=46.6078)
# CDF(1) should be roughly 0.7, see Figure 12 in
# https://arxiv.org/pdf/1911.12835.pdf .
p = dist.cdf(1)
np.testing.assert_allclose(p, 0.7, atol=0.1)
# CDF(4) should be roughly 0.993, see Figure 12 in
# https://arxiv.org/pdf/1911.12835.pdf .
p = dist.cdf(4)
assert p > 0.99
assert p < 0.999
# CDF(negative value) should be 0
p = dist.cdf(-1)
assert p == 0
def test_ExponentiatedWeibull_pdf_cdf_icdf(exp_weibull_reference_data):
OMAE2020_param = {"alpha": 10.0, "beta": 2.42, "delta": 0.761}
x = np.linspace(2, 15, num=100)
p = np.linspace(0.01, 0.99, num=100)
my_expweibull = ExponentiatedWeibullDistribution(**OMAE2020_param)
my_pdf = my_expweibull.pdf(x)
my_cdf = my_expweibull.cdf(x)
my_icdf = my_expweibull.icdf(p)
ref_pdf = exp_weibull_reference_data["ref_pdf"]
ref_cdf = exp_weibull_reference_data["ref_cdf"]
ref_icdf = exp_weibull_reference_data["ref_icdf"]
np.testing.assert_allclose(my_pdf, ref_pdf)
np.testing.assert_allclose(my_cdf, ref_cdf)
np.testing.assert_allclose(my_icdf, ref_icdf)
def test_fitting_exponentiated_weibull():
"""
Tests estimating the parameters of the exponentiated Weibull distribution.
"""
dist = ExponentiatedWeibullDistribution()
# Draw 1000 samples from a Weibull distribution with shape=1.5 and scale=3,
# which represents significant wave height.
hs = sts.weibull_min.rvs(1.5, loc=0, scale=3, size=1000, random_state=42)
dist.fit(hs, method="wlsq", weights="quadratic")
# shape parameter/ beta should be about 1.5.
assert dist.parameters["beta"] > 1
assert dist.parameters["beta"] < 2
# scale parameter / alpha should be about 3.
assert dist.parameters["alpha"] > 2
assert dist.parameters["alpha"] < 4
# shape2 parameter / delta should be about 1.
assert dist.parameters["delta"] > 0.5
assert dist.parameters["delta"] < 2
dist = ExponentiatedWeibullDistribution(f_delta=1)
dist.fit(hs, method="wlsq", weights="quadratic")
# shape parameter/ beta should be about 1.5.
assert dist.parameters["beta"] > 1
assert dist.parameters["beta"] < 2
# scale parameter / alpha should be about 3.
assert dist.parameters["alpha"] > 2
assert dist.parameters["alpha"] < 4
# shape2 parameter / delta should be 1.
assert dist.parameters["delta"] == 1
# Check whether the fitted distribution has a working CDF and PDF.
assert dist.cdf(2) > 0
assert dist.pdf(2) > 0
def test_ExponentiatedWeibull_wlsq_fit(exp_weibull_reference_data_wlsq_fit):
x = np.linspace(2, 15, num=100)
p = np.linspace(0.01, 0.99, num=100)
true_alpha = 10
true_beta = 2.42
true_delta = 0.761
expweibull_samples = sts.exponweib.rvs(a=true_delta,
c=true_beta,
loc=0,
scale=true_alpha,
size=100,
random_state=42)
my_expweibull = ExponentiatedWeibullDistribution()
my_expweibull.fit(expweibull_samples, method="lsq", weights="quadratic")
my_pdf = my_expweibull.pdf(x)
my_cdf = my_expweibull.cdf(x)
my_icdf = my_expweibull.icdf(p)
my_alpha = my_expweibull.alpha
my_beta = my_expweibull.beta
my_delta = my_expweibull.delta
ref_pdf = exp_weibull_reference_data_wlsq_fit["ref_pdf"]
ref_cdf = exp_weibull_reference_data_wlsq_fit["ref_cdf"]
ref_icdf = exp_weibull_reference_data_wlsq_fit["ref_icdf"]
ref_alpha = exp_weibull_reference_data_wlsq_fit["ref_alpha"]
ref_beta = exp_weibull_reference_data_wlsq_fit["ref_beta"]
ref_delta = exp_weibull_reference_data_wlsq_fit["ref_delta"]
np.testing.assert_allclose(my_alpha, ref_alpha)
np.testing.assert_allclose(my_beta, ref_beta)
np.testing.assert_allclose(my_delta, ref_delta)
np.testing.assert_allclose(my_pdf, ref_pdf)
np.testing.assert_allclose(my_cdf, ref_cdf)
np.testing.assert_allclose(my_icdf, ref_icdf)
true_alpha = 10
true_beta = 2.42
true_delta = 0.761
expweibull_samples = sts.exponweib.rvs(
a=true_delta, c=true_beta, loc=0, scale=true_alpha, size=100, random_state=42
)
# %%
# my_expweibull = ExponentiatedWeibullDistribution(**OMAE2020_param)
my_expweibull = ExponentiatedWeibullDistribution()
my_expweibull.fit(expweibull_samples, method="lsq", weights="quadratic")
my_pdf = my_expweibull.pdf(x)
my_cdf = my_expweibull.cdf(x)
my_icdf = my_expweibull.icdf(p)
my_alpha = my_expweibull.alpha
my_beta = my_expweibull.beta
my_delta = my_expweibull.delta
# %%
import sys
sys.path.append("../viroconcom")
from viroconcom.distributions import ExponentiatedWeibullDistribution
# ref_expweibull = ExponentiatedWeibullDistribution(shape=OMAE2020_param["beta"],
# scale=OMAE2020_param["alpha"],
# shape2=OMAE2020_param["delta"])