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_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 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_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_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_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_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_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 __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)
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_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_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_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 __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 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 __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()