def testprobabilitieslogit(self):
prob = zeros((4,3))
obs_utility = self.data.calculate_equation(self.coefficients[0])
[shape_param] = [1,]*genlogistic.numargs
prob[:,0] = genlogistic.cdf(self.thresholds[0] - obs_utility, shape_param)
prob[:,1] = (genlogistic.cdf(self.thresholds[1] - obs_utility, shape_param) -
genlogistic.cdf(self.thresholds[0] - obs_utility, shape_param))
prob[:,2] = 1 - genlogistic.cdf(self.thresholds[1] -
obs_utility, shape_param)
prob_model = self.model.calc_probabilities(self.data)
prob_diff = all(prob == prob_model)
self.assertEqual(True, prob_diff)
def testprobabilitieslogit(self):
prob = zeros((4, 3))
obs_utility = self.data.calculate_equation(self.coefficients[0])
[shape_param] = [1, ] * genlogistic.numargs
prob[:, 0] = genlogistic.cdf(
self.thresholds[0] - obs_utility, shape_param)
prob[:, 1] = (genlogistic.cdf(self.thresholds[1] - obs_utility, shape_param) -
genlogistic.cdf(self.thresholds[0] - obs_utility, shape_param))
prob[:, 2] = 1 - genlogistic.cdf(self.thresholds[1] -
obs_utility, shape_param)
prob_model = self.model.calc_probabilities(self.data)
prob_diff = all(prob == prob_model)
self.assertEqual(True, prob_diff)
def calc_probabilities(self, data):
"""
The method returns the selection probability associated with the
the different choices.
Inputs:
data - DataArray object
"""
[shape_param] = [1,]*genlogistic.numargs
observed_utility = self.calc_observed_utilities(data)
num_choices = self.specification.number_choices
probabilities = zeros((data.rows, num_choices))
lower_bin = 0
for i in range(num_choices-1):
value = self.thresholds[i] - observed_utility
if self.distribution == 'logit':
upper_bin = genlogistic.cdf(value, shape_param)
else:
upper_bin = norm.cdf(value)
probabilities[:,i] = upper_bin - lower_bin
lower_bin = upper_bin
probabilities[:,i+1] = 1 - upper_bin
return probabilities
def calc_probabilities(self, data):
"""
The method returns the selection probability associated with the
the different choices.
Inputs:
data - DataArray object
"""
[shape_param] = [
1,
] * genlogistic.numargs
observed_utility = self.calc_observed_utilities(data)
num_choices = self.specification.number_choices
probabilities = zeros((data.rows, num_choices))
lower_bin = 0
for i in range(num_choices - 1):
value = self.thresholds[i] - observed_utility
if self.distribution == 'logit':
upper_bin = genlogistic.cdf(value, shape_param)
else:
upper_bin = norm.cdf(value)
probabilities[:, i] = upper_bin - lower_bin
lower_bin = upper_bin
probabilities[:, i + 1] = 1 - upper_bin
return probabilities
def transform_length(self, length):
p_l = 0.3
scale_l = genlogistic.ppf(0.99, p_l) - genlogistic.ppf(0.01, p_l)
loc_l = genlogistic.ppf(0.01, p_l)
length_score = 1 - genlogistic.cdf(
(1 - length / 15) * scale_l, p_l, -loc_l)
return length_score
def calc_probabilities(self, data):
"""
The method returns the selection probability associated with the
the different choices.
Inputs:
data - DataArray object
"""
[shape_param] = [1, ] * genlogistic.numargs
observed_utility = self.calc_observed_utilities(data)
num_choices = self.specification.number_choices
probabilities = df(columns=self.choices, index=data.index)
lower_bin = 0
for i in range(num_choices - 1):
value = self.thresholds[i] - observed_utility
if self.distribution == 'logit':
upper_bin = genlogistic.cdf(value, shape_param)
else:
upper_bin = norm.cdf(value)
choice = self.choices[i]
probabilities.loc[:, choice] = upper_bin - lower_bin
lower_bin = upper_bin
choice = self.choices[i+1] #Last ordered choice
probabilities.loc[:, choice] = 1 - upper_bin
return probabilities
def logistic(x, mu, sig, amp, skew):
from scipy.stats import genlogistic
return amp * genlogistic.cdf(x, skew, mu, sig)
def transform_coverage(coverage):
p_c = 0.3
scale_c = genlogistic.ppf(0.99,p_c)-genlogistic.ppf(0.01,p_c)
loc_c = genlogistic.ppf(0.01,p_c)
coverage_score = genlogistic.cdf(coverage*scale_c,p_c,-loc_c)
return coverage_score
genlogistic.pdf(x, c),
'r-',
lw=5,
alpha=0.6,
label='genlogistic 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 = genlogistic(c)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = genlogistic.ppf([0.001, 0.5, 0.999], c)
np.allclose([0.001, 0.5, 0.999], genlogistic.cdf(vals, c))
# True
# Generate random numbers:
r = genlogistic.rvs(c, size=1000)
# And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
if (j % 200 == 0): print(j*100.0/points,"% done")
generate_series(N, r1, r10, alpha, beta, delta, gamma)
q1r10[j] = np.quantile(r10, 0.01)
#remember sample
samples.append(q1r10)
#Fit the sample to generalized logistic distribution,
#with shape parameter lamb, as well as location and shape parameters
[lamb, loc, sc] = genlogistic.fit(q1r10)
#compute the location of the mode: maximum of probability density function
glmax = loc + sc * np.log(lamb)
print("Gen.logistic fit parameters:", lamb, loc, sc, " with max=",glmax)
#Calculate chi-square test statistic:
k = 33 #number of bins in histogram
#use numpy histogram for the expected value
observed, hist_binedges = np.histogram(q1r10, bins=k)
#use the cumulative density function (c.d.f.)
#of the distribution for the expected value
cdf = genlogistic.cdf(hist_binedges, lamb, loc, sc)
expected = len(q1r10) * np.diff(cdf)
#use scipy.stats chisquare function, where
#ddof is the adjustment to the k-1 degrees of freedom,
#which is the number of distribution parameters
chisq, pval = st.chisquare(observed, expected, ddof=3)
print("Chi-square = ", chisq)
#remember fit results
fitresult.append([[lamb, loc, sc], glmax, chisq])
