def test_Fit_Normal_2P():
dist = Normal_Distribution(mu=50, sigma=8)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
MLE = Fit_Normal_2P(failures=data.failures,
right_censored=data.right_censored,
method='MLE',
show_probability_plot=False,
print_results=False)
assert_allclose(MLE.mu, 49.01641649924297, rtol=rtol, atol=atol)
assert_allclose(MLE.sigma, 6.653242350482225, rtol=rtol, atol=atol)
assert_allclose(MLE.AICc, 91.15205546551952, rtol=rtol, atol=atol)
assert_allclose(MLE.BIC, 92.43763765968633, rtol=rtol, atol=atol)
assert_allclose(MLE.loglik, -43.223086556289175, rtol=rtol, atol=atol)
assert_allclose(MLE.AD, 63.64069171746617, rtol=rtol, atol=atol)
assert_allclose(MLE.Cov_mu_sigma, 1.0395705891908218, rtol=rtol, atol=atol)
LS = Fit_Normal_2P(failures=data.failures,
right_censored=data.right_censored,
method='LS',
show_probability_plot=False,
print_results=False)
assert_allclose(LS.mu, 48.90984235374872, rtol=rtol, atol=atol)
assert_allclose(LS.sigma, 6.990098677785364, rtol=rtol, atol=atol)
assert_allclose(LS.AICc, 91.21601631804141, rtol=rtol, atol=atol)
assert_allclose(LS.BIC, 92.50159851220822, rtol=rtol, atol=atol)
assert_allclose(LS.loglik, -43.25506698255012, rtol=rtol, atol=atol)
assert_allclose(LS.AD, 63.657853523044515, rtol=rtol, atol=atol)
assert_allclose(LS.Cov_mu_sigma, 1.0973540350799618, rtol=rtol, atol=atol)
def test_stress_strength_normal():
stress = Normal_Distribution(mu=50, sigma=5)
strength = Normal_Distribution(mu=80, sigma=7)
result = stress_strength_normal(stress=stress,
strength=strength,
print_results=False,
show_plot=False)
assert_allclose(result, 0.00024384404803800858, rtol=rtol, atol=atol)
def test_Probability_of_failure_normdist():
stress = Normal_Distribution(mu=50, sigma=5)
strength = Normal_Distribution(mu=80, sigma=7)
result = Probability_of_failure_normdist(stress=stress,
strength=strength,
print_results=False,
show_distribution_plot=False)
assert_allclose(result, 0.00024384404803800858, rtol=rtol, atol=atol)
def test_Fit_Normal_2P():
dist = Normal_Distribution(mu=50,sigma=8)
rawdata = dist.random_samples(20, seed=5)
data = make_right_censored_data(data=rawdata, threshold=dist.mean)
fit = Fit_Normal_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False)
assert_allclose(fit.mu, 49.01641765388186,rtol=rtol,atol=atol)
assert_allclose(fit.sigma, 6.653242153943476,rtol=rtol,atol=atol)
assert_allclose(fit.AICc, 91.15205546551915,rtol=rtol,atol=atol)
assert_allclose(fit.Cov_mu_sigma, 1.0395713921235965,rtol=rtol,atol=atol)
assert_allclose(fit.loglik, -43.22308655628899,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_Mixture_Model():
distributions = [Weibull_Distribution(alpha=30, beta=2), Normal_Distribution(mu=35, sigma=5)]
dist = Mixture_Model(distributions=distributions, proportions=[0.6,0.4])
assert_allclose(dist.mean, 29.952084649328917, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 11.95293368817564, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 142.87262375392413, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, 0.015505959874527537, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 3.4018343377801674, rtol=rtol, atol=atol)
assert dist.name2 == 'Mixture using 2 distributions'
assert_allclose(dist.quantile(0.2), 19.085648329240094, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 24.540270766923847, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(20), 14.686456940211107, 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), [0.0016309, 0.00509925, 0.01423464, 0.01646686, 0.00134902, 0.00016862], rtol=rtol, atol=atol)
assert_allclose(dist.CDF(xvals=xvals, show_plot=False), [0.00099994, 0.00999996, 0.10000006, 0.90000056, 0.99000001, 0.999], rtol=rtol, atol=atol)
assert_allclose(dist.SF(xvals=xvals, show_plot=False), [0.99900006, 0.99000004, 0.89999994, 0.09999944, 0.00999999, 0.001], rtol=rtol, atol=atol)
assert_allclose(dist.HF(xvals=xvals, show_plot=False), [0.00163253, 0.00515076, 0.01581627, 0.16466956, 0.13490177, 0.16861429], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [1.00043950e-03, 1.00502998e-02, 1.05360581e-01, 2.30259070e+00, 4.60517090e+00, 6.90775056e+00], rtol=rtol, atol=atol)
def test_Competing_Risks_Model():
distributions = [Weibull_Distribution(alpha=30, beta=2), Normal_Distribution(mu=35, sigma=5)]
dist = Competing_Risks_Model(distributions=distributions)
assert_allclose(dist.mean, 23.707625152181073, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 9.832880925543204, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 96.68554729591138, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, -0.20597940178753704, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 2.1824677678598667, rtol=rtol, atol=atol)
assert dist.name2 == 'Competing risks using 2 distributions'
assert_allclose(dist.quantile(0.2), 14.170859470541174, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 17.908811127053173, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(20), 9.862745898092886, 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), [0.00210671, 0.00661657, 0.01947571, 0.02655321, 0.00474024, 0.00062978], rtol=rtol, atol=atol)
assert_allclose(dist.CDF(xvals=xvals, show_plot=False), [0.0010001, 0.00999995, 0.09999943, 0.90000184, 0.99000021, 0.99900003], rtol=rtol, atol=atol)
assert_allclose(dist.SF(xvals=xvals, show_plot=False), [0.9989999, 0.99000005, 0.90000057, 0.09999816, 0.00999979, 0.00099997], rtol=rtol, atol=atol)
assert_allclose(dist.HF(xvals=xvals, show_plot=False), [0.00210882, 0.00668341, 0.02163966, 0.265537, 0.47403341, 0.62980068], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [1.00059934e-03, 1.00502826e-02, 1.05359884e-01, 2.30260350e+00, 4.60519097e+00, 6.90778668e+00], 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 test_Normal_Distribution():
dist = Normal_Distribution(mu=5, sigma=2)
assert dist.mean == 5
assert dist.standard_deviation == 2
assert dist.variance == 4
def test_Normal_Distribution():
dist = Normal_Distribution(mu=5, sigma=2)
assert_allclose(dist.mean, 5, rtol=rtol, atol=atol)
assert_allclose(dist.standard_deviation, 2, rtol=rtol, atol=atol)
assert_allclose(dist.variance, 4, rtol=rtol, atol=atol)
assert_allclose(dist.skewness, 0, rtol=rtol, atol=atol)
assert_allclose(dist.kurtosis, 3, rtol=rtol, atol=atol)
assert dist.param_title_long == 'Normal Distribution (μ=5,σ=2)'
assert_allclose(dist.quantile(0.2), 3.3167575328541714, rtol=rtol, atol=atol)
assert_allclose(dist.inverse_SF(q=0.7), 3.9511989745839187, rtol=rtol, atol=atol)
assert_allclose(dist.mean_residual_life(10), 0.6454895953278145, 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), [0.00876415024678427, 0.001683545038531998, 0.01332607110172904, 0.08774916596624342, 0.08774916596624342, 0.01332607110172904, 0.001683545038531998], rtol=rtol, atol=atol)
assert_allclose(dist.CDF(xvals=xvals, show_plot=False), [0.006209665325776132, 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), [0.9937903346742238, 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), [0.00881891274345837, 0.0016852302688007987, 0.013460677880534384, 0.09749907329582604, 0.8774916596624335, 1.332607110172904, 1.6835450385319983], rtol=rtol, atol=atol)
assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [0.006229025485860027, 0.0010005003335835344, 0.01005033585350145, 0.1053605156578264, 2.302585092994045, 4.605170185988091, 6.907755278982137], rtol=rtol, atol=atol)