def test_Fit_Gumbel_2P():
dist = Gumbel_Distribution(mu=50, sigma=8)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Gumbel_2P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.mu, 47.97813932110471, rtol=rtol, atol=atol)
assert_allclose(MLE.sigma, 5.487155810067562, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 83.17550426530995, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 84.46108645947676, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -39.23481095618439, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 76.43706903015115, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_mu_sigma, 1.8549915988421086, rtol=rtol, atol=atol)
LS = Fit_Gumbel_2P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.mu, 46.43212585298994, rtol=rtol, atol=atol)
assert_allclose(LS.sigma, 4.827795060868229, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 83.88382894786476, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 85.16941114203156, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -39.58897329746179, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 76.44737853267988, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_mu_sigma, 0.32622575178078633, rtol=rtol, atol=atol)
def test_Fit_Gumbel_2P():
dist = Gumbel_Distribution(mu=50,sigma=8)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Gumbel_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.mu, 47.978167597211396,rtol=rtol,atol=atol)
assert_allclose(fit.sigma, 5.487173373377182,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 83.17550426511939,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_mu_sigma, 1.8550359215645946,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -39.234810956089106,rtol=rtol,atol=atol)
def test_Gumbel_Distribution():
dist = Gumbel_Distribution(mu=15, sigma=2)
assert_allclose(dist.mean, 13.845568670196934, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 2.565099660323728, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 6.579736267392906, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, -1.1395470994046486, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 5.4, rtol=rtol, atol=atol)
assert dist.param_title_long == 'Gumbel Distribution (μ=15,σ=2)'
assert_allclose(dist.quantile(0.2), 12.00012002648097, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 12.938139133682554, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(10), 4.349172610672009, rtol=rtol, atol=atol)
xvals = [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), [0.0004997499166249747, 0.0049749162474832164, 0.04741223204602183, 0.11512925464970217, 0.0230258509299404, 0.003453877639491069], rtol=rtol, atol=atol)
assert_allclose(dist.CDF(xvals=xvals, show_plot=False), [0.0009999999999999998, 0.010000000000000002, 0.09999999999999999, 0.9000000000000001, 0.99, 0.999], rtol=rtol, atol=atol)
assert_allclose(dist.SF(xvals=xvals, show_plot=False), [0.999, 0.99, 0.9, 0.09999999999999984, 0.009999999999999969, 0.0010000000000000002], rtol=rtol, atol=atol)
assert_allclose(dist.HF(xvals=xvals, show_plot=False), [0.0005002501667917664, 0.0050251679267507236, 0.05268025782891314, 1.1512925464970236, 2.3025850929940472, 3.4538776394910684], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [0.0010005003335835344, 0.01005033585350145, 0.10536051565782628, 2.3025850929940472, 4.6051701859880945, 6.907755278982137], 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 == 'Gumbel':
dist = Gumbel_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 __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 AttributeError: # 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 AttributeError: # 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 AttributeError: # 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 AttributeError: # 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 == 'Gumbel':
dist = Gumbel_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, Gumbel_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:
colorprint(
'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.',
text_color='red')
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.Exponential_1P_lambda))
ranked_distributions_labels.append(
str('Exponential_1P (lambda=' + str(
round(fitted_results.Exponential_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)) + ')'))
elif dist_name == 'Gumbel_2P':
ranked_distributions_objects.append(
Gumbel_Distribution(mu=fitted_results.Gumbel_2P_mu,
sigma=fitted_results.Gumbel_2P_sigma))
ranked_distributions_labels.append(
str('Gumbel_2P (μ=' +
str(round(fitted_results.Gumbel_2P_mu, sigfig)) +
',σ=' +
str(round(fitted_results.Gumbel_2P_sigma, sigfig)) +
')'))
if include_location_shifted is True:
if dist_name == 'Weibull_3P':
if fitted_results.Weibull_3P_gamma is not 0:
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':
if fitted_results.Gamma_3P_gamma is not 0:
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':
if fitted_results.Lognormal_3P_gamma is not 0:
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':
if fitted_results.Exponential_2P_gamma is not 0:
ranked_distributions_objects.append(
Exponential_Distribution(
Lambda=fitted_results.Exponential_1P_lambda,
gamma=fitted_results.Exponential_2P_gamma))
ranked_distributions_labels.append(
str('Exponential_1P (lambda=' + str(
round(fitted_results.Exponential_1P_lambda,
sigfig)) + ',γ=' +
str(
round(fitted_results.Exponential_2P_gamma,
sigfig)) + ')'))
elif dist_name == 'Loglogistic_3P':
if fitted_results.Loglogistic_3P_gamma is not 0:
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()