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