def test_Fit_Beta_2P():
dist = Beta_Distribution(alpha=5, beta=4)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Beta_2P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.alpha, 7.429048118107467, rtol=rtol, atol=atol)
assert_allclose(MLE.beta, 6.519338516778177, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 4.947836247236739, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 6.233418441403544, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -0.12097694714778129, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 63.64510718930826, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_alpha_beta,
9.993273704064205,
rtol=rtol,
atol=atol)
LS = Fit_Beta_2P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.alpha, 6.699688942917093, rtol=rtol, atol=atol)
assert_allclose(LS.beta, 5.9477941734033575, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 5.02116420233583, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 6.306746396502635, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -0.1576409246973265, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 63.661784208694066, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_alpha_beta, 8.194012965628652, rtol=rtol, atol=atol)
def test_Fit_Everything():
dist = Beta_Distribution(alpha=5, beta=4)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Everything(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False,show_histogram_plot=False,show_PP_plot=False,print_results=False)
assert_allclose(fit.best_distribution.alpha, 0.5796887217806559,rtol=rtol,atol=atol)
assert_allclose(fit.best_distribution.beta, 4.205258772699503,rtol=rtol,atol=atol)
assert_allclose(fit.Beta_2P_BIC, 30.739845510058352,rtol=rtol,atol=atol)
def test_Fit_Beta_2P():
dist = Beta_Distribution(alpha=5, beta=4)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Beta_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.alpha, 7.429034112498652,rtol=rtol,atol=atol)
assert_allclose(fit.beta, 6.519320902041194,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 4.947836247294108,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_alpha_beta, 9.9955246167663,rtol=0.0005,atol=0.005) # I don't know why travis-CI gives slightly different results for this one. Maybe it uses an older version of scipy
assert_allclose(fit.loglik, -0.1209769471764659,rtol=rtol,atol=atol)
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 __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
]:
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)) + ')'))
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)) +
')'))
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_Fit_Everything():
dist = Beta_Distribution(alpha=5, beta=4)
rawdata = dist.random_samples(200, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Everything(failures=data.failures, right_censored=data.right_censored, method='MLE', show_probability_plot=False, show_histogram_plot=False, show_PP_plot=False, show_best_distribution_probability_plot=False, print_results=False)
LS = Fit_Everything(failures=data.failures, right_censored=data.right_censored, method='LS', show_probability_plot=False, show_histogram_plot=False, show_PP_plot=False, show_best_distribution_probability_plot=False, print_results=False)
assert_allclose(MLE.best_distribution.alpha, 0.5796887225805948, rtol=rtol, atol=atol) # best fit here is a Beta distribution
assert_allclose(MLE.best_distribution.beta, 4.205258710807067, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_alpha, 0.5796887225805948, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_beta, 4.205258710807067, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_AICc, 22.509958498975394, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_BIC, 29.04567952648771, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_loglik, -9.224522396695818, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_2P_AD, 543.31193295208, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_alpha, 0.5796887225805948, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_beta, 4.205258710807067, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_AICc, 24.571493772983473, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_BIC, 34.343996893035744, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_loglik, -9.224522396695818, rtol=rtol, atol=atol)
assert_allclose(MLE.Weibull_3P_AD, 543.31193295208, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_alpha, 0.06343366643685251, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_beta, 8.730724670235508, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_AICc, 29.72088918292124, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_BIC, 36.25661021043356, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_loglik, -12.829987738668741, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_2P_AD, 543.5598195358288, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_alpha, 0.06343366643685251, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_beta, 8.730724670235508, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_AICc, 31.78242445692932, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_BIC, 41.55492757698159, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_loglik, -12.829987738668741, rtol=rtol, atol=atol)
assert_allclose(MLE.Gamma_3P_AD, 543.5598195358288, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_alpha, 0.5327695781726263, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_beta, 4.959959950671738, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_AICc, 26.2468431389576, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_BIC, 32.78256416646992, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_loglik, -11.092964716686922, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_2P_AD, 543.3968941075816, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_alpha, 0.5327695781726263, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_beta, 4.959959950671738, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_AICc, 28.30837841296568, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_BIC, 38.08088153301795, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_loglik, -11.092964716686922, rtol=rtol, atol=atol)
assert_allclose(MLE.Loglogistic_3P_AD, 543.3968941075816, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_mu, -0.6258670209896524, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_sigma, 0.3859306240146529, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_AICc, 36.58934382876143, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_BIC, 43.125064856273745, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_loglik, -16.264215061588835, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_2P_AD, 543.7578077426027, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_mu, -0.6258670209896524, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_sigma, 0.3859306240146529, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_AICc, 38.65087910276951, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_BIC, 48.42338222282178, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_loglik, -16.264215061588835, rtol=rtol, atol=atol)
assert_allclose(MLE.Lognormal_3P_AD, 543.7578077426027, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_mu, 0.5313204293962966, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_sigma, 0.14842166096827056, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_AICc, 23.0363966340782, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_BIC, 29.572117661590518, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_loglik, -9.487741464247222, rtol=rtol, atol=atol)
assert_allclose(MLE.Normal_2P_AD, 543.3042437249142, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_mu, 0.5706624792367315, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_sigma, 0.10182903954122995, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_AICc, 26.09054970134011, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_BIC, 32.626270728852425, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_loglik, -11.014817997878176, rtol=rtol, atol=atol)
assert_allclose(MLE.Gumbel_2P_AD, 543.3089024789034, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_alpha, 5.586642953718748, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_beta, 4.950693419749502, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_AICc, 24.204124482547897, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_BIC, 30.739845510060213, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_loglik, -10.07160538848207, rtol=rtol, atol=atol)
assert_allclose(MLE.Beta_2P_AD, 543.3809275359781, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_lambda, 1.5845505775713558, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_gamma, 0.12428161981215716, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_AICc, 127.11230931613672, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_BIC, 133.64803034364903, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_loglik, -61.52569780527648, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_2P_AD, 548.8966650502098, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_lambda, 1.1776736956890317, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_AICc, 192.73284561137785, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_BIC, 196.01096095772388, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_loglik, -95.35632179558792, rtol=rtol, atol=atol)
assert_allclose(MLE.Exponential_1P_AD, 551.326873807673, rtol=rtol, atol=atol)
assert_allclose(LS.best_distribution.mu, 0.5350756091376212, rtol=rtol, atol=atol) # best fit here is a Normal distribution
assert_allclose(LS.best_distribution.sigma, 0.15352298167936318, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_alpha, 0.5948490848650297, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_beta, 3.850985192722524, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_AICc, 24.002343535956285, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_BIC, 30.538064563468602, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_loglik, -9.970714915186264, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_2P_AD, 543.3536598333712, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_alpha, 0.5796887225805948, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_beta, 4.205258710807067, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_AICc, 24.571493772983473, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_BIC, 34.343996893035744, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_loglik, -9.224522396695818, rtol=rtol, atol=atol)
assert_allclose(LS.Weibull_3P_AD, 543.31193295208, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_alpha, 0.047474493713487956, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_beta, 11.56120649983023, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_AICc, 34.77520772749797, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_BIC, 41.31092875501029, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_loglik, -15.357147010957107, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_2P_AD, 543.5555679280225, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_alpha, 0.06343366643685251, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_beta, 8.730724670235508, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_AICc, 31.78242445692932, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_BIC, 41.55492757698159, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_loglik, -12.829987738668741, rtol=rtol, atol=atol)
assert_allclose(LS.Gamma_3P_AD, 543.5598195358288, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_alpha, 0.5489258630949324, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_beta, 4.282869717868545, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_AICc, 29.55884374185365, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_BIC, 36.09456476936597, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_loglik, -12.748965018134946, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_2P_AD, 543.4725652046802, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_alpha, 0.5327695781726263, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_beta, 4.959959950671738, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_AICc, 28.30837841296568, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_BIC, 38.08088153301795, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_loglik, -11.092964716686922, rtol=rtol, atol=atol)
assert_allclose(LS.Loglogistic_3P_AD, 543.3968941075816, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_mu, -0.5829545855241497, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_sigma, 0.42938026719038264, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_AICc, 39.2494098877054, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_BIC, 45.785130915217714, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_loglik, -17.59424809106082, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_2P_AD, 543.6895545238489, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_mu, -0.6258670209896524, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_sigma, 0.3859306240146529, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_AICc, 38.65087910276951, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_BIC, 48.42338222282178, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_loglik, -16.264215061588835, rtol=rtol, atol=atol)
assert_allclose(LS.Lognormal_3P_AD, 543.7578077426027, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_mu, 0.5350756091376212, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_sigma, 0.15352298167936318, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_AICc, 23.270071653194492, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_BIC, 29.80579268070681, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_loglik, -9.604578973805367, rtol=rtol, atol=atol)
assert_allclose(LS.Normal_2P_AD, 543.3018089629097, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_mu, 0.5575543755580943, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_sigma, 0.09267958281580514, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_AICc, 28.66352107358925, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_BIC, 35.19924210110157, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_loglik, -12.301303684002747, rtol=rtol, atol=atol)
assert_allclose(LS.Gumbel_2P_AD, 543.3456378838292, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_alpha, 6.54242621734743, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_beta, 5.795236872686599, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_AICc, 25.745158997195162, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_BIC, 32.28088002470748, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_loglik, -10.842122645805702, rtol=rtol, atol=atol)
assert_allclose(LS.Beta_2P_AD, 543.3718252593867, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_lambda, 1.1858797968873822, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_gamma, 0.12338161981215715, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_AICc, 136.25275877909922, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_BIC, 142.78847980661155, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_loglik, -66.09592253675774, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_2P_AD, 546.5849877012892, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_lambda, 1.0678223705385204, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_AICc, 193.7910857336068, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_BIC, 197.06920107995282, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_loglik, -95.88544185670239, rtol=rtol, atol=atol)
assert_allclose(LS.Exponential_1P_AD, 549.85986679373, 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=None,
include_location_shifted=True,
show_plot=True,
print_results=True,
monte_carlo_trials=1000,
number_of_distributions_to_show=3):
if type(distribution) not in [
Weibull_Distribution, Normal_Distribution,
Lognormal_Distribution, Exponential_Distribution,
Gamma_Distribution, Beta_Distribution
]:
raise ValueError(
'distribution must be a probability distribution object from the reliability.Distributions module. First define the distribution using Reliability.Distributions.___'
)
if monte_carlo_trials < 100:
print(
'WARNING: Using less than 100 monte carlo trials will lead to extremely inaccurate results. The number of monte carlo trials has been changed to 100 to ensure accuracy.'
)
monte_carlo_trials = 100
elif monte_carlo_trials >= 100 and monte_carlo_trials < 1000:
print(
'WARNING: Using less than 1000 monte carlo trials will lead to inaccurate results.'
)
if monte_carlo_trials > 10000:
print(
'The recommended number of monte carlo trials is 1000. Using over 10000 may take a long time to calculate.'
)
RVS = distribution.random_samples(
number_of_samples=monte_carlo_trials
) # draw random samples from the original distribution
# 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. Monte carlo 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)) + ')'))
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)) +
')'))
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='Input distribution', 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='Input distribution', 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_Beta_Distribution():
dist = Beta_Distribution(alpha=5, beta=2)
assert_allclose(dist.mean, 0.7142857142857143, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 0.15971914124998499, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 0.025510204081632654, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, -0.5962847939999439, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 2.88, rtol=rtol, atol=atol)
assert dist.param_title_long == 'Beta Distribution (α=5,β=2)'
assert_allclose(dist.quantile(0.2), 0.577552475153728, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 0.6396423096199797, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(0.5), 0.2518796992481146, rtol=rtol, atol=atol)
xvals = [0, 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, 0.026583776746547504, 0.15884542294682907, 0.8802849346924463, 1.883276908534153, 0.7203329063913153, 0.23958712288762668], 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, 0.026610387133681187, 0.16044992216851423, 0.9780943718804959, 18.832769085341553, 72.03329063913147, 239.58712288762646], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [-0.0, 0.0010005003335835344, 0.01005033585350145, 0.10536051565782628, 2.3025850929940472, 4.605170185988091, 6.907755278982136], rtol=rtol, atol=atol)