def __update_params(_, self):
value1 = self.s0.val
value2 = self.s1.val
value3 = self.s2.val
if self.name == 'Weibull':
dist = Weibull_Distribution(alpha=value1, beta=value2, gamma=value3)
elif self.name == 'Loglogistic':
dist = Loglogistic_Distribution(alpha=value1, beta=value2, gamma=value3)
elif self.name == 'Gamma':
dist = Gamma_Distribution(alpha=value1, beta=value2, gamma=value3)
elif self.name == 'Loglogistic':
dist = Loglogistic_Distribution(alpha=value1, beta=value2, gamma=value3)
elif self.name == 'Lognormal':
dist = Lognormal_Distribution(mu=value1, sigma=value2, gamma=value3)
elif self.name == 'Beta':
dist = Beta_Distribution(alpha=value1, beta=value2)
elif self.name == 'Normal':
dist = Normal_Distribution(mu=value1, sigma=value2)
elif self.name == 'Exponential':
dist = Exponential_Distribution(Lambda=value1, gamma=value2)
else:
raise ValueError(str(self.name + ' is an unknown distribution name'))
plt.sca(self.ax_pdf)
plt.cla()
dist.PDF()
plt.title('PDF')
plt.xlabel('')
plt.ylabel('')
plt.sca(self.ax_cdf)
plt.cla()
dist.CDF()
plt.title('CDF')
plt.xlabel('')
plt.ylabel('')
plt.sca(self.ax_sf)
plt.cla()
dist.SF()
plt.title('SF')
plt.xlabel('')
plt.ylabel('')
plt.sca(self.ax_hf)
plt.cla()
dist.HF()
plt.title('HF')
plt.xlabel('')
plt.ylabel('')
plt.sca(self.ax_chf)
plt.cla()
dist.CHF()
plt.title('CHF')
plt.xlabel('')
plt.ylabel('')
plt.subplots_adjust(left=0.07, right=0.98, top=0.9, bottom=0.25, wspace=0.18, hspace=0.30)
plt.suptitle(dist.param_title_long, fontsize=15)
plt.draw()
def test_Fit_Loglogistic_2P():
dist = Loglogistic_Distribution(alpha=50, beta=8)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Loglogistic_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.alpha, 50.25178196536296,rtol=rtol,atol=atol)
assert_allclose(fit.beta, 7.869850445508078,rtol=rtol,atol=atol)
assert_allclose(fit.gamma, 0,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 941.946173470838,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_alpha_beta, 0.14731251998744946,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -468.9426298826271,rtol=rtol,atol=atol)
assert_allclose(fit.initial_guess[1], 7.304622930677989,rtol=rtol,atol=atol)
def test_Fit_Loglogistic_3P():
dist = Loglogistic_Distribution(alpha=50, beta=8, gamma=500)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Loglogistic_3P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.alpha, 64.54473158929677,rtol=rtol,atol=atol)
assert_allclose(fit.beta, 10.513230464353654,rtol=rtol,atol=atol)
assert_allclose(fit.gamma, 485.6731344659153,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 943.8101901715909,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_alpha_beta, 0.18812547180218483,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -468.84387059599953,rtol=rtol,atol=atol)
assert_allclose(fit.initial_guess[1], 4.981027237709373,rtol=rtol,atol=atol)
def test_Fit_Loglogistic_3P():
dist = Loglogistic_Distribution(alpha=50, beta=8, gamma=500)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Loglogistic_3P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.alpha, 62.33031514341089, rtol=rtol, atol=atol)
assert_allclose(MLE.beta, 10.105811228561391, rtol=rtol, atol=atol)
assert_allclose(MLE.gamma, 487.8907948039738, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 943.8128239547301, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 953.5853270747824, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -468.84518748756915, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 582.5424432519599, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_alpha_beta,
-0.18172584774539235,
rtol=rtol,
atol=atol)
LS = Fit_Loglogistic_3P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.alpha, 62.356306952705054, rtol=rtol, atol=atol)
assert_allclose(LS.beta, 10.033505691693987, rtol=rtol, atol=atol)
assert_allclose(LS.gamma, 487.9071761434245, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 943.8204940620113, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 953.5929971820636, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -468.84902254120976, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 582.5422083314535, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_alpha_beta,
-0.1864715435778476,
rtol=rtol,
atol=atol)
def test_Fit_Loglogistic_2P():
dist = Loglogistic_Distribution(alpha=50, beta=8)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Loglogistic_2P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.alpha, 50.25178370302894, rtol=rtol, atol=atol)
assert_allclose(MLE.beta, 7.869851191923439, rtol=rtol, atol=atol)
assert_allclose(MLE.gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 941.9461734708389, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 948.4818944983512, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -468.94262988262756, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 582.5464625675626, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_alpha_beta,
-0.14731273967044273,
rtol=rtol,
atol=atol)
LS = Fit_Loglogistic_2P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.alpha, 50.657493341191135, rtol=rtol, atol=atol)
assert_allclose(LS.beta, 7.389285094946194, rtol=rtol, atol=atol)
assert_allclose(LS.gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 942.5623765547977, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 949.09809758231, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -469.25073142460695, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 582.5637861880587, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_alpha_beta,
-0.1828511494829605,
rtol=rtol,
atol=atol)
def __update_distribution(name, self):
self.name = name
if self.name == 'Weibull':
dist = Weibull_Distribution(alpha=100, beta=2, gamma=0)
param_names = ['Alpha', 'Beta', 'Gamma']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0.1, valmax=500, valinit=dist.alpha)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.2, valmax=25, valinit=dist.beta)
try: # clear the slider axis if it exists
plt.sca(self.ax2)
plt.cla()
except ValueError: # if the slider axis does no exist (because it was destroyed by a 2P distribution) then recreate it
self.ax2 = plt.axes([0.1, 0.05, 0.8, 0.03], facecolor=self.background_color)
self.s2 = Slider(self.ax2, param_names[2], valmin=0, valmax=500, valinit=dist.gamma)
elif self.name == 'Gamma':
dist = Gamma_Distribution(alpha=100, beta=5, gamma=0)
param_names = ['Alpha', 'Beta', 'Gamma']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0.1, valmax=500, valinit=dist.alpha)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.2, valmax=25, valinit=dist.beta)
try: # clear the slider axis if it exists
plt.sca(self.ax2)
plt.cla()
except ValueError: # if the slider axis does no exist (because it was destroyed by a 2P distribution) then recreate it
self.ax2 = plt.axes([0.1, 0.05, 0.8, 0.03], facecolor=self.background_color)
self.s2 = Slider(self.ax2, param_names[2], valmin=0, valmax=500, valinit=dist.gamma)
elif self.name == 'Loglogistic':
dist = Loglogistic_Distribution(alpha=100, beta=8, gamma=0)
param_names = ['Alpha', 'Beta', 'Gamma']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0.1, valmax=500, valinit=dist.alpha)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.2, valmax=50, valinit=dist.beta)
try: # clear the slider axis if it exists
plt.sca(self.ax2)
plt.cla()
except ValueError: # if the slider axis does no exist (because it was destroyed by a 2P distribution) then recreate it
self.ax2 = plt.axes([0.1, 0.05, 0.8, 0.03], facecolor=self.background_color)
self.s2 = Slider(self.ax2, param_names[2], valmin=0, valmax=500, valinit=dist.gamma)
elif self.name == 'Lognormal':
dist = Lognormal_Distribution(mu=2.5, sigma=0.5, gamma=0)
param_names = ['Mu', 'Sigma', 'Gamma']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0, valmax=5, valinit=dist.mu)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.01, valmax=2, valinit=dist.sigma)
try: # clear the slider axis if it exists
plt.sca(self.ax2)
plt.cla()
except ValueError: # if the slider axis does no exist (because it was destroyed by a 2P distribution) then recreate it
self.ax2 = plt.axes([0.1, 0.05, 0.8, 0.03], facecolor=self.background_color)
self.s2 = Slider(self.ax2, param_names[2], valmin=0, valmax=500, valinit=dist.gamma)
elif self.name == 'Normal':
dist = Normal_Distribution(mu=0, sigma=10)
param_names = ['Mu', 'Sigma', '']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=-100, valmax=100, valinit=dist.mu)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.01, valmax=20, valinit=dist.sigma)
try: # clear the slider axis if it exists
self.ax2.remove() # this will destroy the axes
except KeyError:
pass
elif self.name == 'Exponential':
dist = Exponential_Distribution(Lambda=1, gamma=0)
param_names = ['Lambda', 'Gamma', '']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0.001, valmax=5, valinit=dist.Lambda)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0, valmax=500, valinit=dist.gamma)
try: # clear the slider axis if it exists
self.ax2.remove() # this will destroy the axes
except KeyError:
pass
elif self.name == 'Beta':
dist = Beta_Distribution(alpha=2, beta=2)
param_names = ['Alpha', 'Beta', '']
plt.sca(self.ax0)
plt.cla()
self.s0 = Slider(self.ax0, param_names[0], valmin=0.01, valmax=5, valinit=dist.alpha)
plt.sca(self.ax1)
plt.cla()
self.s1 = Slider(self.ax1, param_names[1], valmin=0.01, valmax=5, valinit=dist.beta)
try: # clear the slider axis if it exists
self.ax2.remove() # this will destroy the axes
except KeyError:
pass
else:
raise ValueError(str(self.name + ' is an unknown distribution name'))
plt.suptitle(dist.param_title_long, fontsize=15)
distribution_explorer.__update_params(None, self)
distribution_explorer.__interactive(self)
plt.draw()
def __init__(self,
distribution,
include_location_shifted=True,
show_plot=True,
print_results=True,
number_of_distributions_to_show=3):
# ensure the input is a distribution object
if type(distribution) not in [
Weibull_Distribution, Normal_Distribution,
Lognormal_Distribution, Exponential_Distribution,
Gamma_Distribution, Beta_Distribution, Loglogistic_Distribution
]:
raise ValueError(
'distribution must be a probability distribution object from the reliability.Distributions module. First define the distribution using Reliability.Distributions.___'
)
# sample the CDF from 0.001 to 0.999. These samples will be used to fit all other distributions.
RVS = distribution.quantile(
np.linspace(0.001, 0.999, 698)
) # 698 samples is the ideal number for the points to align. Evidenced using plot_points.
# filter out negative values
RVS_filtered = []
negative_values_error = False
for item in RVS:
if item > 0:
RVS_filtered.append(item)
else:
negative_values_error = True
if negative_values_error is True:
print(
'WARNING: The input distribution has non-negligible area for x<0. Samples from this region have been discarded to enable other distributions to be fitted.'
)
fitted_results = Fit_Everything(
failures=RVS_filtered,
print_results=False,
show_probability_plot=False,
show_histogram_plot=False,
show_PP_plot=False
) # fit all distributions to the filtered samples
ranked_distributions = list(fitted_results.results.index.values)
ranked_distributions.remove(
distribution.name2
) # removes the fitted version of the original distribution
ranked_distributions_objects = []
ranked_distributions_labels = []
sigfig = 2
for dist_name in ranked_distributions:
if dist_name == 'Weibull_2P':
ranked_distributions_objects.append(
Weibull_Distribution(alpha=fitted_results.Weibull_2P_alpha,
beta=fitted_results.Weibull_2P_beta))
ranked_distributions_labels.append(
str('Weibull_2P (α=' +
str(round(fitted_results.Weibull_2P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Weibull_2P_beta, sigfig)) +
')'))
elif dist_name == 'Gamma_2P':
ranked_distributions_objects.append(
Gamma_Distribution(alpha=fitted_results.Gamma_2P_alpha,
beta=fitted_results.Gamma_2P_beta))
ranked_distributions_labels.append(
str('Gamma_2P (α=' +
str(round(fitted_results.Gamma_2P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Gamma_2P_beta, sigfig)) +
')'))
elif dist_name == 'Normal_2P':
ranked_distributions_objects.append(
Normal_Distribution(mu=fitted_results.Normal_2P_mu,
sigma=fitted_results.Normal_2P_sigma))
ranked_distributions_labels.append(
str('Normal_2P (μ=' +
str(round(fitted_results.Normal_2P_mu, sigfig)) +
',σ=' +
str(round(fitted_results.Normal_2P_sigma, sigfig)) +
')'))
elif dist_name == 'Lognormal_2P':
ranked_distributions_objects.append(
Lognormal_Distribution(
mu=fitted_results.Lognormal_2P_mu,
sigma=fitted_results.Lognormal_2P_sigma))
ranked_distributions_labels.append(
str('Lognormal_2P (μ=' +
str(round(fitted_results.Lognormal_2P_mu, sigfig)) +
',σ=' +
str(round(fitted_results.Lognormal_2P_sigma, sigfig)) +
')'))
elif dist_name == 'Exponential_1P':
ranked_distributions_objects.append(
Exponential_Distribution(
Lambda=fitted_results.Expon_1P_lambda))
ranked_distributions_labels.append(
str('Exponential_1P (lambda=' +
str(round(fitted_results.Expon_1P_lambda, sigfig)) +
')'))
elif dist_name == 'Beta_2P':
ranked_distributions_objects.append(
Beta_Distribution(alpha=fitted_results.Beta_2P_alpha,
beta=fitted_results.Beta_2P_beta))
ranked_distributions_labels.append(
str('Beta_2P (α=' +
str(round(fitted_results.Beta_2P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Beta_2P_beta, sigfig)) + ')'))
elif dist_name == 'Loglogistic_2P':
ranked_distributions_objects.append(
Loglogistic_Distribution(
alpha=fitted_results.Loglogistic_2P_alpha,
beta=fitted_results.Loglogistic_2P_beta))
ranked_distributions_labels.append(
str('Loglogistic_2P (α=' + str(
round(fitted_results.Loglogistic_2P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Loglogistic_2P_beta,
sigfig)) + ')'))
if include_location_shifted is True:
if dist_name == 'Weibull_3P':
ranked_distributions_objects.append(
Weibull_Distribution(
alpha=fitted_results.Weibull_3P_alpha,
beta=fitted_results.Weibull_3P_beta,
gamma=fitted_results.Weibull_3P_gamma))
ranked_distributions_labels.append(
str('Weibull_3P (α=' + str(
round(fitted_results.Weibull_3P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Weibull_3P_beta,
sigfig)) + ',γ=' +
str(round(fitted_results.Weibull_3P_gamma,
sigfig)) + ')'))
elif dist_name == 'Gamma_3P':
ranked_distributions_objects.append(
Gamma_Distribution(
alpha=fitted_results.Gamma_3P_alpha,
beta=fitted_results.Gamma_3P_beta,
gamma=fitted_results.Gamma_3P_gamma))
ranked_distributions_labels.append(
str('Gamma_3P (α=' +
str(round(fitted_results.Gamma_3P_alpha, sigfig)) +
',β=' +
str(round(fitted_results.Gamma_3P_beta, sigfig)) +
',γ=' +
str(round(fitted_results.Gamma_3P_gamma, sigfig)) +
')'))
elif dist_name == 'Lognormal_3P':
ranked_distributions_objects.append(
Lognormal_Distribution(
mu=fitted_results.Lognormal_3P_mu,
sigma=fitted_results.Lognormal_3P_sigma,
gamma=fitted_results.Lognormal_3P_gamma))
ranked_distributions_labels.append(
str('Lognormal_3P (μ=' + str(
round(fitted_results.Lognormal_3P_mu, sigfig)) +
',σ=' + str(
round(fitted_results.Lognormal_3P_sigma,
sigfig)) + ',γ=' +
str(
round(fitted_results.Lognormal_3P_gamma,
sigfig)) + ')'))
elif dist_name == 'Exponential_2P':
ranked_distributions_objects.append(
Exponential_Distribution(
Lambda=fitted_results.Expon_1P_lambda,
gamma=fitted_results.Expon_2P_gamma))
ranked_distributions_labels.append(
str('Exponential_1P (lambda=' + str(
round(fitted_results.Expon_1P_lambda, sigfig)) +
',γ=' +
str(round(fitted_results.Expon_2P_gamma, sigfig)) +
')'))
elif dist_name == 'Loglogistic_3P':
ranked_distributions_objects.append(
Loglogistic_Distribution(
alpha=fitted_results.Loglogistic_3P_alpha,
beta=fitted_results.Loglogistic_3P_beta,
gamma=fitted_results.Loglogistic_3P_gamma))
ranked_distributions_labels.append(
str('Loglogistic_3P (α=' + str(
round(fitted_results.Loglogistic_3P_alpha,
sigfig)) + ',β=' + str(
round(fitted_results.Loglogistic_3P_beta,
sigfig)) + ',γ=' +
str(
round(fitted_results.Loglogistic_3P_gamma,
sigfig)) + ')'))
number_of_distributions_fitted = len(ranked_distributions_objects)
self.results = ranked_distributions_objects
self.most_similar_distribution = ranked_distributions_objects[0]
if print_results is True:
print('The input distribution was:')
print(distribution.param_title_long)
if number_of_distributions_fitted < number_of_distributions_to_show:
number_of_distributions_to_show = number_of_distributions_fitted
print('\nThe top', number_of_distributions_to_show,
'most similar distributions are:')
counter = 0
while counter < number_of_distributions_to_show and counter < number_of_distributions_fitted:
dist = ranked_distributions_objects[counter]
print(dist.param_title_long)
counter += 1
if show_plot is True:
plt.figure(figsize=(14, 6))
plt.suptitle(
str('Plot of similar distributions to ' +
distribution.param_title_long))
counter = 0
xlower = distribution.quantile(0.001)
xupper = distribution.quantile(0.999)
x_delta = xupper - xlower
plt.subplot(121)
distribution.PDF(label=str('Input distribution [' +
distribution.name2 + ']'),
linestyle='--')
while counter < number_of_distributions_to_show and counter < number_of_distributions_fitted:
ranked_distributions_objects[counter].PDF(
label=ranked_distributions_labels[counter])
counter += 1
plt.xlim([xlower - x_delta * 0.1, xupper + x_delta * 0.1])
plt.legend()
plt.title('PDF')
counter = 0
plt.subplot(122)
distribution.CDF(label=str('Input distribution [' +
distribution.name2 + ']'),
linestyle='--')
while counter < number_of_distributions_to_show and counter < number_of_distributions_fitted:
ranked_distributions_objects[counter].CDF(
label=ranked_distributions_labels[counter])
counter += 1
plt.xlim([xlower - x_delta * 0.1, xupper + x_delta * 0.1])
plt.legend()
plt.title('CDF')
plt.subplots_adjust(left=0.08, right=0.95)
plt.show()
def test_Loglogistic_Distribution():
dist = Loglogistic_Distribution(alpha=50, beta=8, gamma=10)
assert_allclose(dist.mean, 61.308607648851535, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 12.009521950735257, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 144.228617485192, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, 1.2246481827926854, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 8.342064360132765, rtol=rtol, atol=atol)
assert dist.param_title_long == 'Loglogistic Distribution (α=50,β=8,γ=10)'
assert_allclose(dist.quantile(0.2), 52.044820762685724, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 54.975179587474166, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(20), 41.308716243335226, rtol=rtol, atol=atol)
xvals = [dist.gamma - 1, dist.quantile(0.001), dist.quantile(0.01), dist.quantile(0.1), dist.quantile(0.9), dist.quantile(0.99), dist.quantile(0.999)]
assert_allclose(dist.PDF(xvals=xvals, show_plot=False), [0.0, 0.0003789929723245846, 0.0028132580909498313, 0.01895146578651591, 0.010941633873382936, 0.0008918684027148376, 6.741239934687115e-05], rtol=rtol, atol=atol)
assert_allclose(dist.CDF(xvals=xvals, show_plot=False), [0.0, 0.001, 0.01, 0.1, 0.9, 0.99, 0.999], rtol=rtol, atol=atol)
assert_allclose(dist.SF(xvals=xvals, show_plot=False), [1.0, 0.999, 0.99, 0.9, 0.1, 0.01, 0.001], rtol=rtol, atol=atol)
assert_allclose(dist.HF(xvals=xvals, show_plot=False), [0.0, 0.00037975209676602, 0.002870378625599256, 0.02339687134137767, 1.0941633873382928, 8.918684027148261, 67.412399346859], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [0.0, 0.001000500333583622, 0.010050335853501506, 0.10536051565782635, 2.302585092994045, 4.605170185988085, 6.907755278982047], rtol=rtol, atol=atol)