def test_Fit_Gamma_3P():
dist = Gamma_Distribution(alpha=50, beta=2, gamma=500)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Gamma_3P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.alpha, 161.86588917785375,rtol=rtol,atol=atol)
assert_allclose(fit.beta, 0.5429156736189351,rtol=rtol,atol=atol)
assert_allclose(fit.gamma, 515.4451173341464,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 150.01356065455715,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_alpha_beta, 11.303022319282686,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -71.25678032727858,rtol=rtol,atol=atol)
assert_allclose(fit.initial_guess[1], 0.5957708701483985,rtol=rtol,atol=atol)
def test_Fit_Gamma_2P():
dist = Gamma_Distribution(alpha=50, beta=2)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Gamma_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.alpha, 30.895318057143644,rtol=rtol,atol=atol)
assert_allclose(fit.beta, 2.5300452644724367,rtol=rtol,atol=atol)
assert_allclose(fit.gamma, 0,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 154.33194705093553,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_alpha_beta, 11.610666775358292,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -74.81303234899717,rtol=rtol,atol=atol)
assert_allclose(fit.initial_guess[1], 4.878548406768285,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 test_Fit_Gamma_3P():
dist = Gamma_Distribution(alpha=50, beta=2, gamma=500)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Gamma_3P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.alpha, 161.8637212853173, rtol=1e-6,
atol=1e-4) # needs bigger tolerance for Python 3.8 and 3.9
assert_allclose(MLE.beta, 0.5429184966902371, rtol=1e-6,
atol=1e-6) # needs bigger tolerance for Python 3.8 and 3.9
assert_allclose(MLE.gamma, 515.4451173341464, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 150.0135606540687, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 151.50075747473068, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -71.25678032703435, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 38.63647775048046, rtol=rtol, atol=atol)
assert_allclose(
MLE.Cov_alpha_beta, 11.302538880460721, rtol=1e-4,
atol=0.0002) # needs bigger tolerance for Python 3.8 and 3.9
LS = Fit_Gamma_3P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.alpha, 67.82751726558604, rtol=1e-6,
atol=1e-4) # needs bigger tolerance for Python 3.8 and 3.9
assert_allclose(LS.beta, 31.29226170989501, rtol=1e-6,
atol=1e-6) # needs bigger tolerance for Python 3.8 and 3.9
assert_allclose(LS.gamma, 505.13533298746347, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 2727.0287032370256, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 2728.5159000576878, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -1359.7643516185128, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 574.8571449781781, rtol=rtol, atol=atol)
assert_allclose(
LS.Cov_alpha_beta, 2.4557691690459174, rtol=1e-4,
atol=0.0002) # needs bigger tolerance for Python 3.8 and 3.9
def test_Fit_Gamma_2P():
dist = Gamma_Distribution(alpha=50, beta=2)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Gamma_2P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.alpha, 30.895317427895733, rtol=rtol, atol=atol)
assert_allclose(MLE.beta, 2.5300452519936405, rtol=rtol, atol=atol)
assert_allclose(MLE.gamma, 0, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 154.33194705093553, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 155.61752924510233, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -74.81303234899717, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 38.004356262808585, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_alpha_beta,
-11.610946543514364,
rtol=rtol,
atol=atol)
LS = Fit_Gamma_2P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.alpha, 25.803340662553182, rtol=rtol, atol=atol)
assert_allclose(LS.beta, 2.8344248030280284, rtol=rtol, atol=atol)
assert_allclose(LS.gamma, 0, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 154.55898223226797, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 155.84456442643477, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -74.92654993966339, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 38.01670664187149, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_alpha_beta,
-5.761109354575602,
rtol=rtol,
atol=atol)
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 __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 HistogramPLOT_all(data, month, year):
#Initiate
Situation = []
mon = [
'January', 'Febuary', 'March', 'April', 'May', 'June', 'July',
'August', 'September', 'October', 'November', 'December'
]
#Get just Full day data
logicF = (data["isFULL"].apply(lambda x: x) == (1))
data01 = data[logicF].copy()
data01.fillna(method='ffill', inplace=True)
logicY = (data01["DateTime"].apply(lambda x: x.year) == (year))
data01 = data01[logicY].copy()
fig = plt.figure(figsize=(24, 18), dpi=80, facecolor='w', edgecolor='r')
#Plotting 12 graph
xvals = np.linspace(0, 30, 1000)
for i in range(month):
ax = plt.subplot2grid((4, 3), (int(np.floor(i / 3)), int(i % 3)))
logic = (data01["DateTime"].apply(lambda x: x.month)) == (i + 1)
ws = data01['WS95'][logic]
ws = ws + 0.0001
failures = []
censored = []
threshold = 30
for item in ws:
if item > threshold:
censored.append(threshold)
else:
failures.append(item)
xvals = np.linspace(0, 30, 1000)
print(ws.shape)
if (np.sum(logic) != 0):
ax.hist(ws, bins=30, normed=True)
hist, edge = np.histogram(np.array(ws),
bins=1000,
range=(0, 30),
normed=True)
wb2 = Fit_Weibull_2P(failures=failures,
show_probability_plot=False,
print_results=False)
wb3 = Fit_Weibull_3P(failures=failures,
show_probability_plot=False,
print_results=False)
gm2 = Fit_Gamma_2P(failures=failures,
show_probability_plot=False,
print_results=False)
gm3 = Fit_Gamma_3P(failures=failures,
show_probability_plot=False,
print_results=False)
ln2 = Fit_Lognormal_2P(failures=failures,
show_probability_plot=False,
print_results=False)
wbm = Fit_Weibull_Mixture(failures=failures,
right_censored=censored,
show_plot=False,
print_results=False)
wb2_pdf = Weibull_Distribution(alpha=wb2.alpha, beta=wb2.beta).PDF(
xvals=xvals, show_plot=True, label='Weibull_2P')
wb3_pdf = Weibull_Distribution(alpha=wb3.alpha,
beta=wb3.beta,
gamma=wb3.gamma).PDF(
xvals=xvals,
show_plot=True,
label='Weibull_3P')
gm2_pdf = Gamma_Distribution(alpha=gm2.alpha,
beta=gm2.beta).PDF(xvals=xvals,
show_plot=True,
label='Gamma_2P')
gm3_pdf = Gamma_Distribution(alpha=gm3.alpha,
beta=gm3.beta,
gamma=gm3.gamma).PDF(xvals=xvals,
show_plot=True,
label='Gamma_3P')
ln2_pdf = Lognormal_Distribution(mu=ln2.mu, sigma=ln2.sigma).PDF(
xvals=xvals, show_plot=True, label='Lognormal_2P')
part1_pdf = Weibull_Distribution(alpha=wbm.alpha_1,
beta=wbm.beta_1).PDF(
xvals=xvals, show_plot=False)
part2_pdf = Weibull_Distribution(alpha=wbm.alpha_2,
beta=wbm.beta_2).PDF(
xvals=xvals, show_plot=False)
Mixture_PDF = part1_pdf * wbm.proportion_1 + part2_pdf * wbm.proportion_2
ax.plot(xvals, Mixture_PDF, label='Weibull_Mixture')
ax.legend()
ax.set_ylim(0, 0.16)
ax.set_xlim(0, 30)
ax.set_xticks([0, 5, 10, 15, 20, 25, 30])
ax.tick_params(axis="x", labelsize=20)
ax.tick_params(axis="y", labelsize=20)
ax.set_title('{}'.format(mon[i]), fontweight='bold', size=20)
plt.tight_layout()
plt.show()
def test_Gamma_Distribution():
dist = Gamma_Distribution(alpha=5, beta=2, gamma=10)
assert_allclose(dist.mean, 20, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 7.0710678118654755, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 50, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, 1.414213562373095, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 6, rtol=rtol, atol=atol)
assert dist.param_title_long == 'Gamma Distribution (α=5,β=2,γ=10)'
assert_allclose(dist.quantile(0.2), 14.121941545164923, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 15.486746053517457, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(20), 6.666666666666647, 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, 0.008677353779839614, 0.02560943552734864, 0.06249207734544239, 0.015909786387521992, 0.001738163417685293, 0.00018045617911753266], 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, 0.008686039819659272, 0.025868116694291555, 0.06943564149493599, 0.15909786387522004, 0.17381634176852898, 0.18045617911753245], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [-0.0, 0.0010005003335835344, 0.01005033585350145, 0.10536051565782628, 2.3025850929940463, 4.605170185988089, 6.907755278982136], rtol=rtol, atol=atol)