def fit_and_plot_weibull(wind_speeds, x_plot, line_styling, line_label,
percentiles):
"""Fit Weibull distribution to histogram data and plot result. The used fitting method yielded better fits than
weibull_min.fit().
Args:
wind_speeds (list): Series of wind speeds.
x_plot (list): Wind speeds for which the Weibull fit is plotted.
format string (str): A format string for setting basic line properties.
line_label (str): Label name of line in legend.
percentiles (list): Heights above the ground at which the wind speeds are evaluated.
"""
# Perform curve fitting.
starting_point = curve_fit_starting_points.get(line_label, None)
# Actual histogram data is used to fit the Weibull distribution to.
hist, bin_edges = np.histogram(wind_speeds, 100, range=(0., 35.))
bin_width = bin_edges[1] - bin_edges[0]
bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2
def weibull_fit_fun(x, c, loc, scale):
y = weibull_min.pdf(x, c, loc, scale)
return y * len(wind_speeds) * bin_width
wb_fit, _ = curve_fit(weibull_fit_fun,
bin_centers,
hist,
p0=starting_point,
bounds=((-np.inf, 0, -np.inf), (np.inf, np.inf,
np.inf)))
# Plot fitted curve.
y_plot = weibull_min.pdf(x_plot, *wb_fit)
plt.plot(x_plot, y_plot, line_styling, label=line_label)
# Plot percentile markers.
x_percentile_markers = np.percentile(wind_speeds, percentiles)
y_percentile_markers = weibull_min.pdf(x_percentile_markers, *wb_fit)
for x_p, y_p, m, p in zip(x_percentile_markers, y_percentile_markers,
marker_cycle, percentiles):
plt.plot(x_p,
y_p,
m,
color=line_styling,
markersize=8,
markeredgewidth=2,
markerfacecolor='None')
return x_percentile_markers, wb_fit
def truncatedweibull_pdf(data, c, scale):
epsilon = 1e-200
term2 = (weibull_min.pdf(data, c, scale=scale, loc=0.0) /
(weibull_min.cdf(1.0, c, scale=scale, loc=0.0) -
weibull_min.cdf(0.0, c, scale=scale, loc=0.0))) * (data < 1.0)
return term2 + epsilon
def adjustar_Weibull(mid_pointa, histoa):
a_ajustar_wei = lambda x,c,l,s: weibull_min.pdf(x, c, l, s)
popt_wei, pcov = curve_fit(a_ajustar_wei, mid_pointa, histoa)
print(popt_wei, pcov)
ajustado_wey = a_ajustar_wei(mid_pointa, popt_wei[0], popt_wei[1], popt_wei[2])
savez('adjTemp.npz', parametros=popt_wei)
return(ajustado_wey)
def plot_weibull(sample,
c,
loc,
scale,
ks,
pVal,
p,
q,
figname="Lily_weibull_test.png"):
# compare the sample histogram and fitting result
fig, ax = plt.subplots(1, 1)
x = np.linspace(-1.01 * max(sample), -0.99 * min(sample), 100)
ax.plot(x,
weibull_min.pdf(x, c, loc, scale),
'r-',
label='fitted pdf ' + p + '-bnd')
ax.hist(-sample, normed=True, bins=20, histtype='stepfilled')
ax.legend(loc='best', frameon=False)
plt.xlabel('-Lips_' + q)
plt.ylabel('pdf')
plt.title(
'c = {:.2f}, loc = {:.2f}, scale = {:.2f}, ks = {:.2f}, pVal = {:.2f}'.
format(c, loc, scale, ks, pVal))
plt.savefig(figname)
plt.close()
def fit_weibull(data, length=10):
trans_fun = lambda x: (x - 1) / 10 + 0.5
x = numpy.array(sorted(list(set([trans_fun(i) for i in numpy.arange(1, length + 1)]))))
confidence_vals = [[] for i in range(len(x))]
nums = numpy.array(data.groupby('user_id').apply(len).to_dict().values())
nums_groupped = defaultdict(list)
for num in nums:
nums_groupped[(num - 1) / 10].append(num)
nums_avg = {key: numpy.mean(values) / 10.0 for (key, values) in nums_groupped.iteritems()}
nums_trans = [nums_avg[(num - 1) / 10] for num in nums]
fit_values = weibull_min.fit(nums_trans, floc=0)
fit = weibull_min.pdf(x, *fit_values)
for i, f in enumerate(fit):
confidence_vals[i] = f
def _aggr(r):
return {
'value': r,
'confidence_interval_min': r,
'confidence_interval_max': r,
}
return {
'serie': map(_aggr, confidence_vals),
'params': list(fit_values),
}
def loglikelihood(I,a,b,T):
# calculates the inverse of the loglikelihood function for observing data I
# when the distribution is truncated at time T, given shape a and scale b
event1=I[:,0]; # first events
event2=I[:,1]; # second events
L = weibull_min.pdf(event2-event1,b,0,a)/weibull_min.cdf(T-event1,b,0,scale = a);
logL=(sum(np.log(L))**(-1)); # calculate inverse loglikelihood
return(logL);
def getWeibullPdf(dataset, nbins, bins):
c = 1.5
shape, loc, scale = weibull_min.fit(dataset, floc=0)
x = np.linspace(min(bins), max(bins), nbins)
print('WEI: shape=' + str(shape) + ', loc=' + str(loc) + ", scale=" +
str(scale))
pdf = weibull_min.pdf(x, shape, loc, scale)
return (x, pdf)
def truncatedweibull_pdf(data, prior, c, scale):
epsilon = 1e-200
term1 = prior * (data == 1.0)
term2 = (1 - prior) * (weibull_min.pdf(data, c, scale=scale, loc=0.0) /
(weibull_min.cdf(1.0, c, scale=scale, loc=0.0) -
weibull_min.cdf(0.0, c, scale=scale, loc=0.0))) * (
data < 1.0)
return term1 + term2 + epsilon
def fit_weibull(df_speed, x, weibull_params=None):
from scipy.stats import weibull_min
if not weibull_params:
k_shape, _, lamb_scale = weibull_params = weibull_min.fit(df_speed,
loc=0)
y_weibull = weibull_min.pdf(x, *weibull_params)
density_expected_weibull = weibull_min.cdf(
x[1:], *weibull_params) - weibull_min.cdf(x[:-1], *weibull_params)
y_cdf_weibull = 1 - exp(-(x / lamb_scale)**k_shape)
return weibull_params, y_weibull, density_expected_weibull, y_cdf_weibull
def interpret(parameters: np.ndarray, classes: np.ndarray, interval: float):
n_samples, n_components, n_classes = classes.shape
assert parameters.ndim == 3
assert parameters.shape == (n_samples, Weibull.N_PARAMETERS + 1, n_components)
shapes = np.expand_dims(relu(parameters[:, 0, :]), 2).repeat(n_classes, 2)
scales = np.expand_dims(relu(parameters[:, 1, :]), 2).repeat(n_classes, 2)
proportions = np.expand_dims(softmax(parameters[:, 2, :], axis=1), 1)
components = weibull_min.pdf(classes, shapes, scale=scales) * interval
m, v, s, k = weibull_min.stats(shapes[:, :, 0], scale=scales[:, :, 0], moments="mvsk")
return proportions, components, (m, np.sqrt(v), s, k)
def _update_canvas(self):
"""
Update the figure when the user changes an input value.
:return:
"""
# Get the parameters from the form
loc = float(self.loc.text())
scale = float(self.scale.text())
shape_factor = float(self.shape_factor.text())
# Get the selected distribution from the form
distribution_type = self.distribution_type.currentText()
if distribution_type == 'Gaussian':
x = linspace(norm.ppf(0.001, loc, scale),
norm.ppf(0.999, loc, scale), 200)
y = norm.pdf(x, loc, scale)
elif distribution_type == 'Weibull':
x = linspace(weibull_min.ppf(0.001, shape_factor),
weibull_min.ppf(0.999, shape_factor), 200)
y = weibull_min.pdf(x, shape_factor, loc, scale)
elif distribution_type == 'Rayleigh':
x = linspace(rayleigh.ppf(0.001, loc, scale),
rayleigh.ppf(0.999, loc, scale), 200)
y = rayleigh.pdf(x, loc, scale)
elif distribution_type == 'Rice':
x = linspace(rice.ppf(0.001, shape_factor),
rice.ppf(0.999, shape_factor), 200)
y = rice.pdf(x, shape_factor, loc, scale)
elif distribution_type == 'Chi Squared':
x = linspace(chi2.ppf(0.001, shape_factor),
chi2.ppf(0.999, shape_factor), 200)
y = chi2.pdf(x, shape_factor, loc, scale)
# Clear the axes for the updated plot
self.axes1.clear()
# Display the results
self.axes1.plot(x, y, '')
# Set the plot title and labels
self.axes1.set_title('Probability Density Function', size=14)
self.axes1.set_xlabel('x', size=12)
self.axes1.set_ylabel('Probability p(x)', size=12)
# Set the tick label size
self.axes1.tick_params(labelsize=12)
# Turn on the grid
self.axes1.grid(linestyle=':', linewidth=0.5)
# Update the canvas
self.my_canvas.draw()
def fit_weibull_and_ecdf(df_speed, x=None):
from scipy.stats import weibull_min
max_speed = df_speed.max()
if x is None:
x = linspace(0, max_speed, 20)
# Fit Weibull
k_shape, _, lamb_scale = weibull_params = weibull_min.fit(df_speed, loc=0)
y_weibull = weibull_min.pdf(x, *weibull_params)
y_cdf_weibull = 1 - exp(-(x / lamb_scale) ** k_shape) # Weibull cdf
# Fit Ecdf
y_ecdf = sm.distributions.ECDF(df_speed)(x)
return x, y_weibull, y_cdf_weibull, weibull_params, y_ecdf
def moment_method( data ):
mean_ = mean( data )
var_ = var( data, ddof = 1 )
print '#### moment method ####'
print 'mean = ', mean_
print 'var = ', var_
params = fmin( moment_w, [2., 5.], args = ( mean_, var_ ) )
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
# plot the Weibull fit based on the moment method
e = linspace( 0., 0.3 * ( max( data ) - min( data ) ) + max( data ), 100 )
plt.plot( e, weibull_min.pdf( e, params[0], scale = params[1], loc = 0. ),
color = 'blue', linewidth = 2, label = 'moment method' )
def distrib(x, debut, largeur, hauteur, offset):
"""modèles de distribution (pour affichage de l'allure de la courbe [plot])"""
global ladistribution
if ladistribution == "alpha":
return alpha.pdf(x, 0.8, debut - largeur / 10,
largeur) * hauteur * largeur
elif ladistribution == "gauss":
return stat.norm.pdf(x, debut, largeur) * hauteur * largeur
elif ladistribution == "triangle":
return triang.pdf(x, 0, debut, largeur) * hauteur * largeur
elif ladistribution == "weibull":
return weibull_min.pdf(x, 1.1, debut + offset,
largeur) * hauteur * largeur
def maximum_likelihood( data ):
params = fmin( maxlike, [2., 5.], args = ( data ) )
moments = weibull_min( params[0], scale = params[1], loc = 0. ).stats( 'mv' )
print ' #### max likelihood #### '
print 'mean = ', moments[0]
print 'var = ', moments[1]
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
# plot the Weibull fit according to maximum likelihood
e = linspace( 0., 0.3 * ( max( data ) - min( data ) ) + max( data ), 100 )
plt.plot( e, weibull_min.pdf( e, params[0], scale = params[1], loc = 0. ),
color = 'red', linewidth = 2, label = 'max likelihood' )
plt.xlabel( 'strain' )
plt.ylabel( 'PDF' )
def weibull_ll_loop(params, data):
loop_prob = params[0]
complete_prob = params[1]
ln_false = params[2]
ln_true = params[3]
false_pdf1 = np.zeros(data.shape)
false_pdf2 = np.zeros(data.shape)
true_pdf = np.zeros(data.shape)
if ~np.isnan(ln_false[0]):
false_pdf1 = loop_prob * complete_prob * (data == 1.0)
false_pdf2 = loop_prob * (1 - complete_prob) * weibull_min.pdf(
data, ln_false[0], ln_false[1],
ln_false[2]) * (data > 0.0) * (data < 1.0)
if ~np.isnan(ln_true[0]):
true_pdf = (1 - loop_prob) * weibull_min.pdf(
np.abs(data), ln_true[0], ln_true[1], ln_true[2]) * (data < 0.0)
pdf = false_pdf1 + false_pdf2 + true_pdf + 1e-200
ll = -np.sum(np.log(pdf))
return ll
def moment_method(self, plot = True):
mean_ = np.mean(self.data)
var_ = np.var(self.data, ddof = 1)
print '#### moment method ####'
print 'mean = ', mean_
print 'var = ', var_
params = fmin(self.moment_w, [10., np.mean(self.data)], args = (mean_, var_))
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
print 'scale sV0 = ', params[1] * (pi * 13.e-3**2 * self.length)**(1./params[0])
if plot == True:
# plot the Weibull fit based on the moment method
e = np.linspace(0., 0.3 * (np.max(self.data) - np.min(self.data)) + np.max(self.data), 100)
plt.plot(e, weibull_min.pdf(e, params[0], scale = params[1], loc = 0.),
color = 'blue', linewidth = 2, label = 'moment method')
return params[0], params[1]
def fit_weibull(df_speed, x, weibull_params=None, floc=True):
from scipy.stats import weibull_min
if not weibull_params:
if floc:
# sometimes need to set as loc=0
k_shape, _, lamb_scale = weibull_params = weibull_min.fit(df_speed,
floc=0)
else:
k_shape, _, lamb_scale = weibull_params = weibull_min.fit(df_speed)
else:
k_shape, _, lamb_scale = weibull_params
y_weibull = weibull_min.pdf(x, *weibull_params)
density_expected_weibull = weibull_min.cdf(
x[1:], *weibull_params) - weibull_min.cdf(x[:-1], *weibull_params)
y_cdf_weibull = weibull_min.cdf(x, *weibull_params)
return weibull_params, y_weibull, density_expected_weibull, y_cdf_weibull
def maximum_likelihood(self, plot = True):
data = self.data
params = fmin(self.maxlike, np.array([10., np.mean(data)]))
moments = weibull_min(params[0], scale = params[1], loc = 0.).stats('mv')
print ' #### max likelihood #### '
print 'mean = ', moments[0]
print 'var = ', moments[1]
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
#print 'scale sV0 = ', params[1] * (pi * 13.e-3**2 * self.length)**(1./params[0])
if plot == True:
# plot the Weibull fit according to maximum likelihood
e = np.linspace(0., 0.3 * (np.max(data) - np.min(data)) + np.max(data), 100)
plt.plot(e, weibull_min.pdf(e, params[0], scale = params[1], loc = 0.),
color = 'red', linewidth = 2, label = 'max likelihood')
plt.xlabel('strain')
plt.ylabel('PDF')
return params[0], params[1]
def fit_distribution(data, fit_type, x_min, x_max, n_points=1000):
# Initialization of the variables
param, x, cdf, pdf = [-1, -1, -1, -1]
if fit_type == 'exponweib':
x = np.linspace(x_min, x_max, n_points)
# Fit data to the theoretical distribution
param = exponweib.fit(data, 1, 1, scale=02, loc=0)
# param = exponweib.fit(data, fa=1, floc=0)
# param = exponweib.fit(data)
cdf = exponweib.cdf(x, param[0], param[1], param[2], param[3])
pdf = exponweib.pdf(x, param[0], param[1], param[2], param[3])
elif fit_type == 'lognorm':
x = np.linspace(x_min, x_max, n_points)
# Fit data to the theoretical distribution
param = lognorm.fit(data, loc=0)
cdf = lognorm.cdf(x, param[0], param[1], param[2])
pdf = lognorm.pdf(x, param[0], param[1], param[2])
elif fit_type == 'norm':
x = np.linspace(x_min, x_max, n_points)
# Fit data to the theoretical distribution
param = norm.fit(data, loc=0)
cdf = norm.cdf(x, param[0], param[1])
pdf = norm.pdf(x, param[0], param[1])
elif fit_type == 'weibull_min':
x = np.linspace(x_min, x_max, n_points)
# Fit data to the theoretical distribution
param = weibull_min.fit(data, floc=0)
cdf = weibull_min.cdf(x, param[0], param[1], param[2])
pdf = weibull_min.pdf(x, param[0], param[1], param[2])
return param, x, cdf, pdf
def calculate_pdf(distribution, linspace):
if distribution[0] == 'EXP':
lambda_ = distribution[1]
scale_ = 1 / lambda_
return expon.pdf(linspace, scale=scale_)
if distribution[0] == 'WEIBULL':
scale = distribution[1]
shape = distribution[2]
return weibull_min.pdf(linspace, shape, loc=0, scale=scale)
if distribution[0] == 'NORMAL':
mu = distribution[1]
sigma = distribution[2]
return norm.pdf(linspace, loc=mu, scale=sigma)
if distribution[0] == 'LOGNORM':
mu = distribution[1]
sigma = distribution[2]
scale = math.exp(mu)
return lognorm.pdf(linspace, sigma, loc=0, scale=scale)
def distrib(t, x, debut, scale, var, offset):
"""
renvoie la distribution selectionnee avec les parametres specifies
t : type de distribution, 'a' pour alpha, 't' pour triangulaire, 'w' pour weibull
x : array des abscisses
debut : abscisse où debute la distribution
scale : parametre de largeur
var : parametre de hauteur
offset : permet de decaler legerement le debut de la distribution pour alpha et triangulaire. Pour Weibull ce parametre au parametre de forme
"""
if t == 'a':
return alpha.pdf(
x, 0.8, debut - scale / 10 + offset, scale /
1.7) * var * scale if scale and var > 0 else [0] * len(x)
elif t == 'w':
return weibull_min.pdf(x, offset, debut, scale) * var
elif t == 't':
return triang.pdf(x, 0.1, debut + offset, scale) * scale * var
def moment_method(self, plot=True):
mean_ = np.mean(self.data)
var_ = np.var(self.data, ddof=1)
print '#### moment method ####'
print 'mean = ', mean_
print 'var = ', var_
params = fmin(self.moment_w, [10., np.mean(self.data)],
args=(mean_, var_))
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
print 'scale sV0 = ', params[1] * (pi * 13.e-3**2 *
self.length)**(1. / params[0])
if plot == True:
# plot the Weibull fit based on the moment method
e = np.linspace(
0., 0.3 * (np.max(self.data) - np.min(self.data)) +
np.max(self.data), 100)
plt.plot(e,
weibull_min.pdf(e, params[0], scale=params[1], loc=0.),
color='blue',
linewidth=2,
label='moment method')
return params[0], params[1]
def maximum_likelihood(self, plot=True):
data = self.data
params = fmin(self.maxlike, np.array([10., np.mean(data)]))
moments = weibull_min(params[0], scale=params[1], loc=0.).stats('mv')
print ' #### max likelihood #### '
print 'mean = ', moments[0]
print 'var = ', moments[1]
print 'Weibull shape = ', params[0]
print 'Weibull scale = ', params[1]
#print 'scale sV0 = ', params[1] * (pi * 13.e-3**2 * self.length)**(1./params[0])
if plot == True:
# plot the Weibull fit according to maximum likelihood
e = np.linspace(0.,
0.3 * (np.max(data) - np.min(data)) + np.max(data),
100)
plt.plot(e,
weibull_min.pdf(e, params[0], scale=params[1], loc=0.),
color='red',
linewidth=2,
label='max likelihood')
plt.xlabel('strain')
plt.ylabel('PDF')
return params[0], params[1]
def compute_probability(self, proxel, timestamp):
#print('Computing for ' + str(self.state))
# We look at if the state is False, and then we use reliability since we want the transition from
# state True to state False.
if proxel.state is False:
distribution = self.reliability_distribution
else:
distribution = self.maintainability_distribution
#print('Before Probability: ' + str(self.probability))
if distribution[0] == 'EXP':
lambda_ = distribution[1]
scale_ = 1 / lambda_
proxel.probability *= (expon.pdf(timestamp, scale=scale_)/(1 - expon.cdf(timestamp, scale=scale_))) \
* self.delta_time
if distribution[0] == 'WEIBULL':
scale = distribution[1]
shape = distribution[2]
proxel.probability *= (
weibull_min.pdf(timestamp, shape, loc=0, scale=scale) /
(1 - weibull_min.cdf(timestamp, shape, loc=0, scale=scale))
) * self.delta_time
if distribution[0] == 'NORMAL':
mu = distribution[1]
sigma = distribution[2]
proxel.probability *= (
norm.pdf(timestamp, loc=mu, scale=sigma) /
(1 -
norm.cdf(timestamp, loc=mu, scale=sigma))) * self.delta_time
if distribution[0] == 'LOGNORM':
mu = distribution[1]
sigma = distribution[2]
scale = math.exp(mu)
proxel.probability *= (
lognorm.pdf(timestamp, sigma, loc=0, scale=scale) /
(1 - lognorm.cdf(timestamp, sigma, loc=0, scale=scale))
) * self.delta_time
def fit_weibull(series, c=0, floc=0, scale=1, title=""):
"""
Fits a Weibull distribution, initialized with
given parameters. Plots the fitted distribution
against the ground-truth data.
Params
------
series: Pandas series
Pandas series containing the ground-truth values
Returns
-------
params : dictionary
Contains the fitted parameters
"""
# Fit distribution
(c, loc, scale) = weibull_min.fit(series, c, floc=floc, scale=scale)
# Plot
ax = plt.figure(figsize=(12,6)).gca()
# the histogram of the data
# Set as many bins as days
bins = int(series.max() - series.min() + 1)
n, bins, patches = plt.hist(series, bins, facecolor='green', alpha=1, density=True)
# add a 'best fit' line
y = weibull_min.pdf(bins, c, floc, scale)
l = plt.plot(bins, y, 'r--', linewidth=2)
plt.xlabel("Días")
plt.title(title)
# Only integer days
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
# Store parameters
params = {"c":c, "scale":scale}
return params
def distrib(x, debut, scale, var):
"""modèle de distribution"""
#return alpha.pdf(x, 0.8, debut-scale/10, scale)#*var*scale
#return stat.norm.pdf(x,debut,scale)#*var*scale
#return alpha.pdf(x, 0.8, debut, scale)*scale*var
return weibull_min.pdf(x, 1.1, debut, scale) * scale * var
def maxlike(self, v):
data = self.data
shape, scale = v
r = np.sum(np.log(weibull_min.pdf(data, shape, scale=scale, loc=0.)))
return -r
from scipy.stats import weibull_min
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
c = 1.79
mean, var, skew, kurt = weibull_min.stats(c, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(weibull_min.ppf(0.01, c), weibull_min.ppf(0.99, c), 100)
ax.plot(x,
weibull_min.pdf(x, c),
'r-',
lw=5,
alpha=0.6,
label='weibull_min pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = weibull_min(c)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = weibull_min.ppf([0.001, 0.5, 0.999], c)
import numpy as np
from scipy.stats import weibull_min
import pandas as pd
dat = pd.read_csv('./amalia_directionally_averaged_speeds.txt', sep=r'\s+')
power = pd.read_csv('./power.csv')
ws, dirs = [], []
#speeds = [ 8., 9., 10., ]
#speeds = [3., 4., 5., 6., 7.]
speeds = [3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15.]
#speeds = [3.]
#speeds = [10., 11., 12., 13., 14., 15.]
ouu_exp, ouu_det, det_det, det_exp = [], [], [], []
base_exp, base_det = [], []
spees, dees, pees = [], [], []
for ii in range(dat.shape[0]):
theseprobs = weibull_min.pdf(speeds, 3, scale=dat.average_speed[ii])
theseprobs /= np.sum(theseprobs)
if np.isnan(theseprobs.max()): hey
for jj in range(len(speeds)):
ws.append(speeds[jj])
dirs.append(dat.direction[ii])
fact = theseprobs[jj] * dat.probability[ii]
subpow = power[power.ws == speeds[jj]]
print(speeds[jj], int(dat.direction[ii]), fact * subpow.base_exp_power.values[0], subpow.base_det_power.values[0])
subsubpow = subpow[subpow.dir == int(dat.direction[ii])]
ouu_exp.append(fact * subsubpow.ouu_exp_power.values[0])
det_exp.append(fact * subsubpow.det_exp_power.values[0])
det_det.append(fact * subsubpow.det_det_power.values[0])
ouu_det.append(fact * subsubpow.ouu_det_power.values[0])
base_exp.append(fact * subsubpow.base_exp_power.values[0])
base_det.append(fact * subsubpow.base_det_power.values[0])
def weibull_pdf_genuines(x, c, scale):
return weibull_min.pdf(np.abs(x), c, scale=scale)
def maxlike(self, v):
data = self.data
shape, scale = v
r = np.sum(np.log(weibull_min.pdf(data, shape, scale = scale, loc = 0.)))
return -r
# Parameter estimates for generic data
shape1, loc1, scale1 = lognorm.fit(data2, floc=0)
mu1 = np.log(scale1)
sigma1 = shape1
y1 = lognorm.pdf(data2, s=sigma1, scale=np.exp(mu1))
log_likelihood1 = np.sum(np.log(y1))
print("Lognorm loglikelihood = " + str(log_likelihood1))
aic1= -2 * log_likelihood1 + 2 * num_params
print("Lognorm AIC = " + str(aic1))
# https://stackoverflow.com/questions/33070724/determine-weibull-parameters-from-data
# Parameter estimates for generic data
shape2, loc2, scale2 = weibull_min.fit(data2, floc=0)
c = shape2
b = scale2
y2 = weibull_min.pdf(data2, c, scale=b)
log_likelihood2 = np.sum(np.log(y2))
print("Weibull loglikelihood = " + str(log_likelihood2))
aic2= -2 * log_likelihood2 + 2 * num_params
print("Weibull AIC = " + str(aic2))
# https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.invgauss.html
# the argument floc=0 to ensure that it does not treat the location as a free parameter
# Parameter estimates for generic data
shape3, loc3, scale3 = invgauss.fit(data2, floc=0)
mu3 = shape3
lambda3 = scale3
# fitting the data with the estimated parameters
y3 = invgauss.pdf(data2, mu3, scale=lambda3)
# calculate the log_likelihood
log_likelihood3 = np.sum(np.log(y3))
kvar = [0.5, 1.0, 1.5, 5.0, 15.0]
lvar = [1.0, 1.25, 1.5, 1.75, 2.0]
pvar = [0.0, 0.5, 1.0, 1.5]
cmap = plt.get_cmap('Set1')
outpdf = PdfPages('weibull_example_plots.pdf')
x = np.arange(0.0, 10.0, 0.01)
lbda = 1.0
for i in range(5):
k = kvar[i]
c = cmap(i)
w = wbl.pdf(x, k, scale=lbda)
plt.plot(x, w, color=c, label='lambda = {0:0.2}, k = {1:0.1f}'.format(lbda, k), linewidth=1)
plt.xlim(0.0, 3.5)
plt.ylim(0.0, 2.5)
plt.legend()
plt.suptitle('Weibull PDF (Fixed Scale = 1.0)')
outpdf.savefig()
plt.close()
k = 0.5
for i in range(5):
lbda = lvar[i]
c = cmap(i)
w = wbl.pdf(x, k, scale=lbda)
plt.plot(x, w, color=c, label='lambda = {0:0.3}, k = {1:0.1f}'.format(lbda, k), linewidth=1)
def weibull_pdf_impostors(x, c, scale):
return weibull_min.pdf(np.abs(x), c, scale=scale)
def pdf(self, x):
"""
@brief Return the value of a probability density function for x.
"""
return weibull_min.pdf(x, self.shape, loc=self.loc, scale=self.scale)
def maxlike( v, *args ):
data = args
shape, scale = v
r = sum( log( weibull_min.pdf( data, shape, scale = scale, loc = 0. ) ) )
return - r
def X(self, x):
return weibull_min.pdf(x, self.X_shape, scale=self.X_scale, loc=self.X_loc)
def plot_weibull(name,
metric,
distribution,
times,
theoretical_distribution=None):
scale = distribution[1]
shape = distribution[2]
theoretical_scale = None
theoretical_shape = None
# Checks whether there is a theoretical distribution to compare it to
if theoretical_distribution is not None:
theoretical_scale = theoretical_distribution[1]
theoretical_shape = theoretical_distribution[2]
fig, subplots = setup_fig_subplots(metric)
fig.suptitle(name)
linspace = np.linspace(weibull_min.ppf(0.001, shape, loc=0, scale=scale),
weibull_min.ppf(0.999, shape, loc=0, scale=scale),
1000)
# First plot PDF
if theoretical_distribution is not None:
subplots[0].plot(linspace,
weibull_min.pdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6,
label='Reconstructed')
subplots[0].plot(linspace,
weibull_min.pdf(linspace,
theoretical_shape,
loc=0,
scale=theoretical_scale),
'b-',
lw=1,
alpha=0.6,
label='Theoretical')
subplots[0].legend()
else:
subplots[0].plot(linspace,
weibull_min.pdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6)
if times != EMPTY_LIST:
if metric == 'Reliability':
subplots[0].hist(times,
bins=20,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='Time to failures')
if metric == 'Maintainability':
subplots[0].hist(times,
bins=20,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='Time to repairs')
subplots[0].legend()
subplots[0].set_title('Weibull PDF')
# Second plot CDF and/or Maintainability
if theoretical_distribution is not None:
subplots[1].plot(linspace,
weibull_min.cdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6,
label='Reconstructed')
subplots[1].plot(linspace,
weibull_min.cdf(linspace,
theoretical_shape,
loc=0,
scale=theoretical_scale),
'b-',
lw=1,
alpha=0.6,
label='Theoretical')
subplots[1].legend()
else:
subplots[1].plot(linspace,
weibull_min.cdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6)
if metric == 'Reliability':
subplots[1].set_title('Weibull CDF')
if metric == 'Maintainability':
subplots[1].set_title('Weibull CDF (Maintainability)')
# Third plot Reliability
if metric == 'Reliability':
if theoretical_distribution is not None:
subplots[2].plot(
linspace,
1 - weibull_min.cdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6,
label='Reconstructed')
subplots[2].plot(linspace,
1 - weibull_min.cdf(linspace,
theoretical_shape,
loc=0,
scale=theoretical_scale),
'b-',
lw=1,
alpha=0.6,
label='Theoretical')
subplots[2].legend()
else:
subplots[2].plot(
linspace,
1 - weibull_min.cdf(linspace, shape, loc=0, scale=scale),
'r-',
lw=1,
alpha=0.6)
subplots[2].set_title(metric)
#plt.show()
plt.show(block=False)
