def HistogramPLOT_wbm(data, month, year): #Initiate Situation = [] mon = [ 'January', 'Febuary', 'March', 'April', 'May', 'June', 'July', 'August', 'September', 'October', 'November', 'December' ] data01 = data[['DateTime', 'WS95']].copy() data01.dropna(how='any', inplace=True) logicY = (data01["DateTime"].apply(lambda x: x.year) == (year)) data01 = data01[logicY].copy() fig = plt.figure(figsize=(20, 32), 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) if (np.sum(logic) != 0): ax.hist(ws, bins=30, density=True) hist, edge = np.histogram(np.array(ws), bins=1000, range=(0, 30), density=True) wbm = Fit_Weibull_Mixture(failures=failures, right_censored=censored, show_plot=False, print_results=False) 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, 0.18) ax.set_xlim(0, 30) ax.set_xticks([0, 5, 10, 15, 20, 25, 30]) ax.tick_params(axis="x", labelsize=30) ax.tick_params(axis="y", labelsize=26) ax.set_title('{}'.format(mon[i]), fontweight='bold', size=30) plt.tight_layout() plt.show()
def test_Fit_Weibull_Mixture(): group_1 = Weibull_Distribution(alpha=10, beta=3).random_samples(40, seed=2) group_2 = Weibull_Distribution(alpha=40, beta=4).random_samples(60, seed=2) raw_data = np.hstack([group_1, group_2]) data = make_right_censored_data(data=raw_data, threshold=40) fit = Fit_Weibull_Mixture(failures=data.failures, right_censored=data.right_censored, print_results=False, show_probability_plot=False) assert_allclose(fit.alpha_1, 8.711417800323375,rtol=rtol,atol=atol) assert_allclose(fit.alpha_2, 36.96927163816745, rtol=rtol, atol=atol) assert_allclose(fit.beta_1, 3.8780149153215278, rtol=rtol, atol=atol) assert_allclose(fit.beta_2, 4.901762153365169, rtol=rtol, atol=atol) assert_allclose(fit.AICc, 678.8135631521253, rtol=rtol, atol=atol) assert_allclose(fit.loglik, -334.08763263989243, rtol=rtol, atol=atol)
def test_Fit_Weibull_CR(): d1 = Weibull_Distribution(alpha=50, beta=2) d2 = Weibull_Distribution(alpha=40, beta=10) CR_model = Competing_Risks_Model(distributions=[d1, d2]) raw_data = CR_model.random_samples(100, seed=2) data = make_right_censored_data(data=raw_data, threshold=40) fit = Fit_Weibull_CR(failures=data.failures, right_censored=data.right_censored, print_results=False, show_probability_plot=False) assert_allclose(fit.alpha_1, 53.046588163359885,rtol=rtol,atol=atol) assert_allclose(fit.alpha_2, 38.029009901631845, rtol=rtol, atol=atol) assert_allclose(fit.beta_1, 1.9386519084349318, rtol=rtol, atol=atol) assert_allclose(fit.beta_2, 9.036248817085612, rtol=rtol, atol=atol) assert_allclose(fit.AICc, 665.5312987516257, rtol=rtol, atol=atol) assert_allclose(fit.loglik, -328.5551230600234, rtol=rtol, atol=atol)
def test_Fit_Weibull_CR(): d1 = Weibull_Distribution(alpha=50, beta=2) d2 = Weibull_Distribution(alpha=40, beta=10) CR_model = Competing_Risks_Model(distributions=[d1, d2]) raw_data = CR_model.random_samples(100, seed=2) data = make_right_censored_data(data=raw_data, threshold=40) MLE = Fit_Weibull_CR(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False) assert_allclose(MLE.alpha_1, 53.05674752263902, rtol=rtol, atol=atol) assert_allclose(MLE.beta_1, 1.9411091317375062, rtol=rtol, atol=atol) assert_allclose(MLE.alpha_2, 38.026383998212154, rtol=rtol, atol=atol) assert_allclose(MLE.beta_2, 9.033349805988692, rtol=rtol, atol=atol) assert_allclose(MLE.AICc, 665.5311523940719, rtol=rtol, atol=atol) assert_allclose(MLE.BIC, 675.5307805064454, rtol=rtol, atol=atol) assert_allclose(MLE.loglik, -328.5550498812465, rtol=rtol, atol=atol) assert_allclose(MLE.AD, 34.0918038201449, rtol=rtol, atol=atol)
def test_similar_distributions(): dist = Weibull_Distribution(alpha=50, beta=3.3) results = similar_distributions(distribution=dist, include_location_shifted=True, show_plot=False, print_results=False) assert_allclose(results.results[0].alpha, 49.22635661916984, rtol=rtol, atol=atol) assert_allclose(results.results[0].beta, 3.2573154824967254, rtol=rtol, atol=atol) assert_allclose(results.results[0].gamma, 0.723515074225681, rtol=rtol, atol=atol) assert_allclose(results.results[1].mu, 44.84713832685586, rtol=rtol, atol=atol) assert_allclose(results.results[1].sigma, 14.922616880719513, rtol=rtol, atol=atol) assert_allclose(results.results[2].alpha, 5.760745623490939, rtol=rtol, atol=atol) assert_allclose(results.results[2].beta, 7.7849536438935685, rtol=rtol, atol=atol) assert_allclose(results.results[2].gamma, 0, rtol=rtol, atol=atol)
def test_crosshairs(): plt.ion( ) # this is the key to enabling plt.close() to take control of a plot that is being blocked by plt.show() inside the plot generating function. Weibull_Distribution(alpha=50, beta=2).CDF() crosshairs(xlabel='t', ylabel='F') plt.close() plt.ioff()
def test_Fit_Weibull_2P(): data = Weibull_Distribution(alpha=50, beta=2).random_samples(20, seed=5) fit = Fit_Weibull_2P(failures=data, show_probability_plot=False, print_results=False) assert fit.alpha == 47.507980313141516 assert fit.beta == 2.492960611854891 #need to add more tests.
def test_Probability_of_failure(): stress = Weibull_Distribution(alpha=40, beta=4) strength = Lognormal_Distribution(mu=1.8, sigma=0.25, gamma=50) result = Probability_of_failure(stress=stress, strength=strength, print_results=False, show_distribution_plot=False) assert_allclose(result, 0.02155359226336879, rtol=rtol, atol=atol)
def test_stress_strength(): stress = Weibull_Distribution(alpha=40, beta=4) strength = Lognormal_Distribution(mu=1.8, sigma=0.25, gamma=50) result = stress_strength(stress=stress, strength=strength, print_results=False, show_plot=False) assert_allclose(result, 0.021559141113795574, rtol=rtol, atol=atol)
def test_Fit_Weibull_Mixture(): d1 = Weibull_Distribution(alpha=10, beta=3) d2 = Weibull_Distribution(alpha=40, beta=4) dist = Mixture_Model(distributions=[d1, d2], proportions=[0.2, 0.8]) raw_data = dist.random_samples(100, seed=2) data = make_right_censored_data(data=raw_data, threshold=dist.mean) MLE = Fit_Weibull_Mixture(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False) assert_allclose(MLE.alpha_1, 11.06604639424718, rtol=rtol, atol=atol) assert_allclose(MLE.beta_1, 2.735078296796997, rtol=rtol, atol=atol) assert_allclose(MLE.alpha_2, 34.325433665495346, rtol=rtol, atol=atol) assert_allclose(MLE.beta_2, 7.60238532821206, rtol=rtol, atol=atol) assert_allclose(MLE.proportion_1, 0.23640116719132157, rtol=rtol, atol=atol) assert_allclose(MLE.proportion_2, 0.7635988328086785, rtol=rtol, atol=atol) assert_allclose(MLE.AICc, 471.97390405380236, rtol=rtol, atol=atol) assert_allclose(MLE.BIC, 484.3614571114024, rtol=rtol, atol=atol) assert_allclose(MLE.loglik, -230.66780309073096, rtol=rtol, atol=atol) assert_allclose(MLE.AD, 320.1963544647712, 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_histogram(): plt.ion() dist = Weibull_Distribution(alpha=30, beta=4) samples = dist.random_samples(500, seed=2) plt.subplot(121) histogram(samples, white_above=dist.mean) plt.subplot(122) histogram(samples, white_above=dist.mean, cumulative=True) plt.show() plt.close() plt.ioff()
def __init__(self): # initialise the 5 plots plt.figure('Distribution Explorer', figsize=(12, 7)) self.name = 'Weibull' # starting value dist = Weibull_Distribution(alpha=100, beta=2, gamma=0) plt.suptitle(dist.param_title_long, fontsize=15) self.ax_pdf = plt.subplot(231) dist.PDF() plt.title('PDF') plt.xlabel('') plt.ylabel('') self.ax_cdf = plt.subplot(232) dist.CDF() plt.title('CDF') plt.xlabel('') plt.ylabel('') self.ax_sf = plt.subplot(233) dist.SF() plt.title('SF') plt.xlabel('') plt.ylabel('') self.ax_hf = plt.subplot(234) dist.HF() plt.title('HF') plt.xlabel('') plt.ylabel('') self.ax_chf = plt.subplot(235) 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) # initialise the sliders x0 = 0.1 width = 0.8 height = 0.03 self.active_color = 'steelblue' self.background_color = 'whitesmoke' self.ax0 = plt.axes([x0, 0.15, width, height], facecolor=self.background_color) self.ax1 = plt.axes([x0, 0.1, width, height], facecolor=self.background_color) self.ax2 = plt.axes([x0, 0.05, width, height], facecolor=self.background_color) self.s0 = Slider(self.ax0, 'Alpha', valmin=0.1, valmax=500, valinit=dist.alpha, facecolor=self.active_color) self.s1 = Slider(self.ax1, 'Beta', valmin=0.2, valmax=25, valinit=dist.beta, facecolor=self.active_color) self.s2 = Slider(self.ax2, 'Gamma', valmin=0, valmax=500, valinit=dist.gamma, facecolor=self.active_color) plt.subplots_adjust(left=0.07, right=0.98, top=0.9, bottom=0.25, wspace=0.18, hspace=0.30) # initialise the radio button radio_ax = plt.axes([0.708, 0.25, 0.27, 0.28], facecolor=self.background_color) radio_ax.set_title('Distribution') self.radio = RadioButtons(radio_ax, ('Weibull', 'Gamma', 'Normal', 'Lognormal', 'Beta', 'Exponential', 'Loglogistic'), active=0, activecolor=self.active_color) # begin the interactive section distribution_explorer.__interactive(self, initial_run=True)
def test_Fit_Weibull_3P(): dist = Weibull_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_Weibull_3P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False) assert_allclose(fit.alpha, 41.38429989624438,rtol=rtol,atol=atol) assert_allclose(fit.beta, 0.6941872050001636,rtol=rtol,atol=atol) assert_allclose(fit.gamma, 514.5074549826453,rtol=rtol,atol=atol) assert_allclose(fit.AICc, 114.68964821342475,rtol=rtol,atol=atol) assert_allclose(fit.Cov_alpha_beta, 1.3076497743444904,rtol=rtol,atol=atol) assert_allclose(fit.loglik, -53.59482410671237,rtol=rtol,atol=atol) assert_allclose(fit.initial_guess[1], 1.2001459605994476,rtol=rtol,atol=atol)
def test_Fit_Weibull_2P(): dist = Weibull_Distribution(alpha=50, beta=2) rawdata = dist.random_samples(20, seed=5) data = make_right_censored_data(data=rawdata, threshold=dist.mean) fit = Fit_Weibull_2P(failures=data.failures, right_censored=data.right_censored, show_probability_plot=False, print_results=False) assert_allclose(fit.alpha, 45.099010886086354,rtol=rtol,atol=atol) assert_allclose(fit.beta, 2.7827531773597975,rtol=rtol,atol=atol) assert_allclose(fit.gamma, 0,rtol=rtol,atol=atol) assert_allclose(fit.AICc, 115.66971887883678,rtol=rtol,atol=atol) assert_allclose(fit.Cov_alpha_beta, 0.9178064889295382,rtol=rtol,atol=atol) assert_allclose(fit.loglik, -55.4819182629478,rtol=rtol,atol=atol) assert_allclose(fit.initial_guess[1], 2.96571536864614,rtol=rtol,atol=atol)
def test_Weibull_Distribution(): dist = Weibull_Distribution(alpha=5, beta=2, gamma=10) assert_allclose(dist.mean, 14.4311346272637895, rtol=rtol, atol=atol) assert_allclose(dist.standard_deviation, 2.316256875880522, rtol=rtol, atol=atol) assert_allclose(dist.variance, 5.365045915063796, rtol=rtol, atol=atol) assert_allclose(dist.skewness, 0.6311106578189344, rtol=rtol, atol=atol) assert_allclose(dist.kurtosis, 3.2450893006876456, rtol=rtol, atol=atol) assert dist.param_title_long == 'Weibull Distribution (α=5,β=2,γ=10)' assert_allclose(dist.quantile(0.2), 12.361903635387193, rtol=rtol, atol=atol) assert_allclose(dist.inverse_SF(q=0.7), 12.9861134604144417, rtol=rtol, atol=atol) assert_allclose(dist.mean_residual_life(20), 1.1316926249544481, 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, 0.012639622357755485, 0.03969953988653618, 0.11685342455082046, 0.06069708517540586, 0.008583864105157392, 0.0010513043539513882], 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, 0.012652274632387873, 0.04010054533993554, 0.12983713838980052, 0.6069708517540585, 0.8583864105157389, 1.0513043539513862], rtol=rtol, atol=atol) assert_allclose(dist.CHF(xvals=xvals, show_plot=False), [0.0, 0.0010005003335835354, 0.010050335853501409, 0.10536051565782631, 2.3025850929940455, 4.605170185988091, 6.907755278982135], 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 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_Fit_Weibull_3P(): dist = Weibull_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_Weibull_3P(failures=data.failures, right_censored=data.right_censored, method='MLE', show_probability_plot=False, print_results=False) assert_allclose(MLE.alpha, 33.012333115455654, rtol=rtol, atol=atol) assert_allclose(MLE.beta, 1.3273429690012193, rtol=rtol, atol=atol) assert_allclose(MLE.gamma, 513.7219668227023, rtol=rtol, atol=atol) assert_allclose(MLE.AICc, 116.53275812088592, rtol=rtol, atol=atol) assert_allclose(MLE.BIC, 118.0199549415479, rtol=rtol, atol=atol) assert_allclose(MLE.loglik, -54.51637906044296, rtol=rtol, atol=atol) assert_allclose(MLE.AD, 55.6067996515715, rtol=rtol, atol=atol) assert_allclose(MLE.Cov_alpha_beta, -0.7687692976797089, rtol=rtol, atol=atol) LS = Fit_Weibull_3P(failures=data.failures, right_censored=data.right_censored, method='LS', show_probability_plot=False, print_results=False) assert_allclose(LS.alpha, 32.639290779819824, rtol=rtol, atol=atol) assert_allclose(LS.beta, 1.2701961119432184, rtol=rtol, atol=atol) assert_allclose(LS.gamma, 514.5065549826453, rtol=rtol, atol=atol) assert_allclose(LS.AICc, 119.47369772704523, rtol=rtol, atol=atol) assert_allclose(LS.BIC, 120.96089454770721, rtol=rtol, atol=atol) assert_allclose(LS.loglik, -55.98684886352262, rtol=rtol, atol=atol) assert_allclose(LS.AD, 55.70853682331155, rtol=rtol, atol=atol) assert_allclose(LS.Cov_alpha_beta, -0.8435523816679948, rtol=rtol, atol=atol)
def test_Fit_Weibull_2P(): dist = Weibull_Distribution(alpha=50, beta=2) rawdata = dist.random_samples(20, seed=5) data = make_right_censored_data(data=rawdata, threshold=dist.mean) MLE = Fit_Weibull_2P(failures=data.failures, right_censored=data.right_censored, method='MLE', show_probability_plot=False, print_results=False) assert_allclose(MLE.alpha, 45.099010886086354, rtol=rtol, atol=atol) assert_allclose(MLE.beta, 2.7827531773597984, rtol=rtol, atol=atol) assert_allclose(MLE.gamma, 0, rtol=rtol, atol=atol) assert_allclose(MLE.AICc, 115.66971887883678, rtol=rtol, atol=atol) assert_allclose(MLE.BIC, 116.95530107300358, rtol=rtol, atol=atol) assert_allclose(MLE.loglik, -55.4819182629478, rtol=rtol, atol=atol) assert_allclose(MLE.AD, 55.60004028891652, rtol=rtol, atol=atol) assert_allclose(MLE.Cov_alpha_beta, -0.9178064889295378, rtol=rtol, atol=atol) LS = Fit_Weibull_2P(failures=data.failures, right_censored=data.right_censored, method='LS', show_probability_plot=False, print_results=False) assert_allclose(LS.alpha, 42.91333312142757, rtol=rtol, atol=atol) assert_allclose(LS.beta, 2.9657153686461033, rtol=rtol, atol=atol) assert_allclose(LS.gamma, 0, rtol=rtol, atol=atol) assert_allclose(LS.AICc, 115.93668384456019, rtol=rtol, atol=atol) assert_allclose(LS.BIC, 117.222266038727, rtol=rtol, atol=atol) assert_allclose(LS.loglik, -55.61540074580951, rtol=rtol, atol=atol) assert_allclose(LS.AD, 55.62807482958476, rtol=rtol, atol=atol) assert_allclose(LS.Cov_alpha_beta, -0.1119680481788733, rtol=rtol, atol=atol)
def test_similar_distributions(): # ignores the runtime warning from scipy when the nelder-mean or powell optimizers are used and jac is not required warnings.filterwarnings(action="ignore", category=RuntimeWarning) dist = Weibull_Distribution(alpha=50, beta=3.3) results = similar_distributions(distribution=dist, include_location_shifted=True, show_plot=False, print_results=False) assert_allclose(results.results[0].alpha, 49.22622520639563, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[0].beta, 3.2573074120881964, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[0].gamma, 0.7236421159037678, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[1].mu, 44.847138326837566, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[1].sigma, 14.922616862230697, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[2].alpha, 5.760746660148767, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[2].beta, 7.784952297226461, rtol=rtol_big, atol=atol_big) assert_allclose(results.results[2].gamma, 0, rtol=rtol_big, atol=atol_big)
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_Weibull_Distribution(): dist = Weibull_Distribution(alpha=5, beta=2) assert dist.mean == 4.4311346272637895 assert dist.standard_deviation == 2.316256875880522 assert dist.variance == 5.365045915063796
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 generate_data(output_dir, CPU_factor, GPU_factor, MEM_factor): ''' #generated wit mixture weibull in R alpha_mem = 1208 beta_mem = 0.871 alpha_gpu = 59666 beta_gpu = 0.934 alpha_cpu = 289484 beta_cpu = 2.778 ''' ##alpha and beta of real data #''' alpha_mem = 295647 beta_mem = 0.918 alpha_gpu = 44721 beta_gpu = 0.551 alpha_cpu = 1595690 beta_cpu = 0.758 #''' #################################################################### #extract real mtbf data x_cpu = [] x_gpu = [] x_mem = [] file_name = "../Data/Titan_Data/GPU_mtbf_epoch1.txt" with open(file_name) as log: for line in log: x_gpu.append(int(line)) file_name = "../Data/Titan_Data/CPU_mtbf_epoch1.txt" with open(file_name) as log: for line in log: x_cpu.append(int(line)) file_name = "../Data/Titan_Data/MEM_mtbf_epoch1.txt" with open(file_name) as log: for line in log: x_mem.append(int(line)) n_samples_gpu = int(int(len(x_gpu)) * float(GPU_factor)) n_samples_cpu = int(int(len(x_cpu)) * float(CPU_factor)) n_samples_mem = int(int(len(x_mem)) * float(MEM_factor)) gpu = Weibull_Distribution(alpha=alpha_gpu,beta=beta_gpu).random_samples(n_samples_gpu) cpu = Weibull_Distribution(alpha=alpha_cpu,beta=beta_cpu).random_samples(n_samples_cpu) mem = Weibull_Distribution(alpha=alpha_mem,beta=beta_mem).random_samples(n_samples_mem) shape, loc, scale = ss.weibull_min.fit(gpu, floc=0) mean_gpu, var = weibull_min.stats(shape,loc,scale, moments='mv') print("gpu total failures = "+ str(n_samples_gpu)) print("gpu shape = " + str(shape)) print("gpu scale = " + str(scale)) print("gpu Mean: "+str(mean_gpu)) print("-----------------") shape, loc, scale = ss.weibull_min.fit(cpu, floc=0) mean_cpu, var = weibull_min.stats(shape,loc,scale, moments='mv') print("cpu total failures = "+ str(n_samples_cpu)) print("cpu shape = " + str(shape)) print("cpu scale = " + str(scale)) print("cpu Mean: "+str(mean_cpu)) print("-----------------") shape, loc, scale = ss.weibull_min.fit(mem, floc=0) mean_mem, var = weibull_min.stats(shape,loc,scale, moments='mv') print("mem total failures = "+ str(n_samples_mem)) print("mem shape = " + str(shape)) print("mem scale = " + str(scale)) print("mem Mean: "+str(mean_mem)) #new proportions t = 0 t = n_samples_mem+n_samples_cpu+n_samples_gpu proportion_cpu = n_samples_cpu / t proportion_gpu = n_samples_gpu / t proportion_mem = n_samples_mem / t mixture_mean = mean_gpu * proportion_gpu + mean_mem * proportion_mem + mean_cpu * proportion_cpu print("-----------------") print("Total failures = "+ str(n_samples_mem+n_samples_cpu+n_samples_gpu)) print("mixture mean without mixture= " + str(mixture_mean/60/60)) print("-----------------") xvals = np.linspace(0,50,t) wei_cpu = Weibull_Distribution(alpha=alpha_cpu,beta=beta_cpu).CDF(xvals=xvals,show_plot=False) wei_gpu = Weibull_Distribution(alpha=alpha_gpu,beta=beta_gpu).CDF(xvals=xvals,show_plot=False) wei_mem = Weibull_Distribution(alpha=alpha_mem,beta=beta_mem).CDF(xvals=xvals,show_plot=False) Mixture_CDF = wei_gpu * proportion_gpu + wei_cpu * proportion_cpu + wei_mem * proportion_mem shape, loc, scale = ss.weibull_min.fit(Mixture_CDF, floc=0) meanw, var = weibull_min.stats(shape,loc,scale, moments='mv') print("Mix Mean: "+str(meanw/60/60)) #save all data (cpu + gpu + mem) all_data = np.hstack([gpu,cpu,mem]) file = open(output_dir + "TOTAL_mtbf_epoch1_exascale.txt", 'w+') for i in all_data: if int(i) != 0: file.write(str(int(i))+"\n") file.close() sys.exit()