def posterior(x, n, p1, p2):
"""
Calculates the posterior probability that the probability of
developing severe side effects falls within a specific range
given the data
"""
if type(n) is not int or n < 1:
raise ValueError('n must be a positive integer')
if type(x) is not int or x < 0:
raise ValueError('x must be an integer that is ' +
'greater than or equal to 0')
if x > n:
raise ValueError('x cannot be greater than n')
if type(p1) is not float or p1 < 0 or p1 > 1:
raise ValueError('p1 must be a float in the range [0, 1]')
if type(p2) is not float or p2 < 0 or p2 > 1:
raise ValueError('p2 must be a float in the range [0, 1]')
if p2 <= p1:
raise ValueError('p2 must be greater than p1')
cdf_beta1 = beta.cdf(p1, x + 1, n - x + 1)
cdf_beta2 = beta.cdf(p2, x + 1, n - x + 1)
my_posterior = cdf_beta2 - cdf_beta1
return my_posterior
def warp_input(self, X, alpha=None, beta=None):
bounds = np.array(self.bounds)
if alpha is None:
alpha = self._alpha
if beta is None:
beta = self._beta
if X is None:
return None
X = np.array(X)
X_warped = np.empty((X).shape)
for n in range(self.ndim):
# a hack way to deal with the numpy shapes problem. This should be fixed
try:
X_warped[:, n:n +
1] = (X[:, n:n + 1] - bounds[n, 0]) / (bounds[n, 1] -
bounds[n, 0])
# use beta CDF warping
X_warped[:, n:n + 1] = beta_dist.cdf(X_warped[:, n:n + 1],
alpha[n], beta[n])
X_warped = (bounds[n, 1] - bounds[n, 0]) * X_warped + bounds[n,
0]
except:
X_warped = (X - bounds[n, 0]) / (bounds[n, 1] - bounds[n, 0])
# use beta CDF warping
X_warped[:] = beta_dist.cdf(X_warped[:], alpha[n], beta[n])
X_warped = (bounds[n, 1] - bounds[n, 0]) * X_warped + bounds[n,
0]
return X_warped
def create_gauss_scalingfactors(cdfs):
""" Create the scaling factor distributions needed to sample
uncertainty in the Gaussian non-CO2 radiative forcings"""
#Scale based on combined gaussian components
rf_2011_mid = np.array([1.82, 2.83, 0.35, 0.07, -0.15, 0.04, -0.9])
rf_2011_up = [2.18, 3.4, 0.559, 0.121, -0.047, 0.09, -0.1]
rf_2011_low = [1.46, 2.26, 0.141, 0.019, -0.253, 0.019, -1.9]
#Estimate sd using 5-95 intervals
erf_sigs = (np.array(rf_2011_up) - np.array(rf_2011_low)) / (2 * 1.654)
sig_wmghg = np.copy(erf_sigs[1])
#Find the non-CO2 GHG forcing uncertainty
sig_owmghg = np.sqrt(erf_sigs[1]**2 - erf_sigs[0]**2)
erf_sigs[1] = sig_owmghg
sig_tot = np.sqrt(np.sum(erf_sigs[1:-2]**2))
rf_2011_mid_a = np.copy(rf_2011_mid)
rf_2011_mid_a[1] = rf_2011_mid[1] - rf_2011_mid[0]
#Calculate the scaling factors
#Derive the scaling factors to span 5-95% AR5 guassian forcing uncertainty
#assuming +/- 20% uncertainty in WMGHG forcings
#Map the TCR cdf to the forcing scaling cdf using a beta function cdf
beta_cdf_sf = root(lambda var: 0.05 - beta.cdf(0.5 - 1.0 / 3.0, var, var),
x0=2.0).x[0]
cdfs_gauss = 1.0 - beta.cdf(cdfs, beta_cdf_sf, beta_cdf_sf)
sf_gauss = (np.sum(rf_2011_mid_a[1:-2]) +
np.sqrt(2.0) * erfinv(2 * cdfs_gauss - 1) * sig_tot) / np.sum(
rf_2011_mid_a[1:-2])
return sf_gauss
def Beta(length, popularity, be=10):
x = [i / length for i in range(length + 1)]
cdfs = [
beta.cdf(x[i + 1], popularity, be) - beta.cdf(x[i], popularity, be)
for i in range(length)
]
return cdfs
def Jeffrey(self, df, x, y, z):
#df is a dataframe object that contains columns x, y and z
#x aggregation variable (rating grade for PD test)
#y modelled variable
#z observed variable (expected to be binary)
#alpha = D + 1/2
#beta = Nc- D + 1/2
aggregation = df.groupby(x).agg({
x: 'count',
y: ['sum', 'count', 'mean'],
z: ['sum', 'count', 'mean']
})
aggregation['Observed'] = aggregation[(z, 'mean')]
aggregation['alpha'] = aggregation[(z, 'sum')] + 1 / 2
aggregation['beta'] = aggregation[(z,
'count')] - aggregation['alpha'] + 1
aggregation['H0'] = aggregation[(y, 'mean')]
aggregation['p_val'] = beta.cdf(aggregation['H0'],
aggregation['alpha'],
aggregation['beta'])
aggregation.loc['Portfolio'] = aggregation.sum()
aggregation['Observed'].loc['Portfolio'] = df.agg({z: 'mean'}).values
aggregation['alpha'].loc['Portfolio'] = df.agg({
z: 'sum'
}).values + 1 / 2
aggregation['beta'].loc['Portfolio'] = df.agg({
z: 'count'
}).values - aggregation['alpha'].loc['Portfolio'] + 1
aggregation['H0'].loc['Portfolio'] = df.agg({y: 'mean'}).values
aggregation['p_val'].loc['Portfolio'] = beta.cdf(
aggregation['H0'].loc['Portfolio'],
aggregation['alpha'].loc['Portfolio'],
aggregation['beta'].loc['Portfolio'])
return aggregation
def allocated_rollouts(self):
fraction_of_budget_used = (self.currently_used_budget +
1) / self.max_budget
yvals = beta.cdf([fraction_of_budget_used], self.alpha_param,
self.beta_param)
fractional_improvment_we_should_be_at = yvals[0]
# This is based on the total overall improvement how much effort should we have spent
number_of_rollouts_we_shouldve_used = fractional_improvment_we_should_be_at * self.max_rollout
if not self.waste_unused_rollouts:
# Subtracts the already spent rollouts from the rollouts we shouldve used
number_of_free_rollouts = number_of_rollouts_we_shouldve_used - self.currently_used_rollout
else:
#not wasting rollouts. Thus, number_of_free_rollouts = {cdf (budget+1) - cdf(budget)} * max_rollouts.
# for a given cdf i.e. fixed alpha and beta
fractional_improvment_we_are_at = \
beta.cdf([(self.currently_used_budget) / self.max_budget], self.alpha_param, self.beta_param)[0]
number_of_rollouts_we_have_used = fractional_improvment_we_are_at * self.max_rollout
number_of_free_rollouts = number_of_rollouts_we_shouldve_used - number_of_rollouts_we_have_used
logging.getLogger(
self.logger_name).debug(f"Rollouts {number_of_free_rollouts}")
if number_of_free_rollouts < self.K + 2:
return self.K + 2
return int(number_of_free_rollouts)
def PyNy(y_hat, PD_LEN):
PD_y_hat = y_hat[:PD_LEN]
PD_y_hat_mean = Mean_1d(PD_y_hat)
PD_y_hat_var = Variance_1d(PD_y_hat, PD_y_hat_mean)
PD_a, PD_b = AandB(PD_y_hat_mean, PD_y_hat_var)
nonPD_y_hat = y_hat[PD_LEN:]
nonPD_y_hat_mean = Mean_1d(nonPD_y_hat)
nonPD_y_hat_var = Variance_1d(nonPD_y_hat, nonPD_y_hat_mean)
N_a, N_b = AandB(nonPD_y_hat_mean, nonPD_y_hat_var)
cdf_x = np.linspace(0, 1, 1001)
P_y = beta.cdf(cdf_x, PD_a, PD_b)
N_y = beta.cdf(cdf_x, N_a, N_b)
# plot 을 안쓰실때는 # 으로 막아두시길
for i in range(len(N_y)):
N_y[i] = 1 - N_y[i]
# 측정된 cdf 값을 그리는 plt
plt.plot(cdf_x, P_y, 'red')
#main emotion
plt.plot(cdf_x, N_y, 'blue')
#non_emotion
plt.ylim(0, 2)
plt.show()
# y_hat 값에 대한 histogram 을 그리는 plt
if PD_a > 0:
plt.hist([y_hat[:PD_LEN], y_hat[PD_LEN:]])
plt.show()
return P_y, N_y
def integrand(x):
pdf1 = beta.pdf(x,a1,b1)
pdf2 = beta.pdf(x,a2,b2)
cdf1 = beta.cdf(x,a1,b1)
cdf2 = beta.cdf(x,a2,b2)
rho = pdf1 * cdf2 + pdf2 * cdf1
return -rho * np.log(rho)
def f_dp(x, alpha_aa, alpha_c, a_aa0, b_aa0, a_c0, b_c0, a_aa1, b_aa1, a_c1,
b_c1):
f_c = (lambda x_c: alpha_c * beta.cdf(x_c, a_c1, b_c1, 0, 1) +
(1 - alpha_c) * beta.cdf(x_c, a_c0, b_c0, 0, 1))
inv_f_c = inversefunc(f_c, domain=[0, 1], open_domain=[False, False])
return float(
inv_f_c(alpha_aa * beta.cdf(x, a_aa1, b_aa1) +
(1 - alpha_aa) * beta.cdf(x, a_aa0, b_aa0)))
def diff_between(k1, n1, k2, n2, p=0.96, a=0.05, b=1, Nsamp=10000):
""" Bayesian maximum a posteriori estimate of the difference in prevalence
when the same test is applied to two groups
k1 : number of participants significant in group 1 out of
n1 : total number of participants in group 1
k2 : number of participants significant in group 2 out of
n2 : total number of participants in group 2
p : coverage for highest-posterior density interval (in [0 1])
a : alpha value of within-participant test (default=0.05)
b : sensitivity/beta of within-participant test (default=1)
Nsamp : number of samples from the posterior
Outputs:
map : maximum a posteriori estimate of the difference in prevalence:
gamma_1 - gamma_2
post_x : x-axis for kernel density fit of posterior distribution of the
above
post : posterior distribution from kernel density fit
hpdi : highest-posterior density interval with coverage p
probGT : estimated posterior probability that the prevalence is higher in group 1
logoddsGT : estimated log odds in favour of the hypothesis that the prevalence is higher in group 1
samples : posterior samples
"""
# gamma priors = Beta(r,s)
r1 = 1; s1 = 1
r2 = 1; s2 = 1
# Parameters for Beta posteriors
m11 = k1 + r1
m12 = n1 - k1 + s1
m21 = k2 + r2
m22 = n2 - k2 + s2
# Generate truncated beta samples
th1 = beta.ppf(np.random.uniform(beta.cdf(a,m11,m12),beta.cdf(b,m11,m12), Nsamp), m11, m12)
th2 = beta.ppf(np.random.uniform(beta.cdf(a,m21,m22),beta.cdf(b,m21,m22), Nsamp), m21, m22)
# vector of estimates of prevalence differences
samples = (th1 - th2) / (b-a)
# kernel density estimate of posterior
post_x = np.linspace(-1,1,200)
kde = sp.stats.gaussian_kde(samples)
post = kde(post_x)
map = post_x[np.argmax(post)]
# Estimate the posterior probability, and logodds, that the prevalence is higher for group 1.
# Laplace's rule of succession used to avoid estimates of 0 or 1
probGT = (np.sum(samples>0)+1)/(Nsamp+2)
logoddsGT = np.log(probGT / (1-probGT))
hpdi = _hpdi(samples, p)
res = {"map": map, "post_x": post_x, "post": post, "hpdi": hpdi, "probGT": probGT,
"logoddsGT": logoddsGT, "samples": samples}
return res
def _Cough_Chen(self):
"""
Distribution fitted from Chen.
:return:
"""
# Small droplets. < 10micron
nparticles_small = 230
k = 3.75
D_small = numpy.arange(0, 20, 0.1)
Fcdf_small = gamma.cdf(D_small, 3.75)
Dsmall_avg = (D_small[:-1] + D_small[1:]) / 2.
F_small = numpy.diff(Fcdf_small)
Volume_small = (4.0 / 3.0) * numpy.pi * (
Dsmall_avg * 1e-6)**3 * F_small * nparticles_small
vol_small_ml = (Volume_small.sum() * m**3).asUnit(ml)
# medium droplets 10micron < x < 225 micron
# upto 100 evaporates in air.
nparticles_medium = 210
params = dict(a=0.2, b=1, loc=53, scale=200)
D_medium = numpy.arange(10, 100, 1)
Fcdf_medium = beta.cdf(D_medium, **params)
Dmedium_avg = (D_medium[:-1] + D_medium[1:]) / 2.
F_medium = numpy.diff(Fcdf_medium)
Volume_small = (4.0 / 3.0) * numpy.pi * (
Dmedium_avg * 1e-6)**3 * F_medium * nparticles_medium
vol_medium_ml = (Volume_small.sum() * m**3).asUnit(ml)
evaporatingDropletsVolume = vol_small_ml + vol_medium_ml
##### == None evaporating
D_medium = numpy.arange(100, 225, 1)
Fcdf_medium = beta.cdf(D_medium, **params)
Dmedium_avg = (D_medium[:-1] + D_medium[1:]) / 2.
F_medium = numpy.diff(Fcdf_medium)
Volume_small = (4.0 / 3.0) * numpy.pi * (
Dmedium_avg * 1e-6)**3 * F_medium * nparticles_medium
vol_medium_ml = (Volume_small.sum() * m**3).asUnit(ml)
nparticles_large = 20
D_large = numpy.arange(225, 800, 1)
Fcdf_large = uniform.cdf(D_large, loc=225, scale=800 - 225)
Dlarge_avg = (D_large[:-1] + D_large[1:]) / 2.
F_large = numpy.diff(Fcdf_large)
Volume_small = (4.0 / 3.0) * numpy.pi * (
Dlarge_avg * 1e-6)**3 * F_large * nparticles_large
vol_large_ml = (Volume_small.sum() * m**3).asUnit(ml)
nonEvaporatingDropletsVolume = vol_large_ml + vol_medium_ml
return evaporatingDropletsVolume, nonEvaporatingDropletsVolume
def rhomax_integrand(x,a1,a2,b1,b2):
pdf1 = beta.pdf(x,a1,b1)
pdf2 = beta.pdf(x,a2,b2)
cdf1 = beta.cdf(x,a1,b1)
cdf2 = beta.cdf(x,a2,b2)
rho = pdf1 * cdf2 + pdf2 * cdf1
integrand = -rho * np.log( rho )
return integrand
def Rhomax(x, a1, a2, b1, b2):
# Takes numbers and returns a prob. number
pdf1 = beta.pdf(x, a1, b1)
pdf2 = beta.pdf(x, a2, b2)
cdf1 = beta.cdf(x, a1, b1)
cdf2 = beta.cdf(x, a2, b2)
rho = pdf1 * cdf2 + pdf2 * cdf1
return rho
def bibeta_roc(Y,p):
def logL(ab):
a0,b0,a1,b1 = ab
LL = beta.logpdf(p[Y==0],a0,b0).sum() + beta.logpdf(p[Y==1],a1,b1).sum()
return -LL
result = minimize(logL,[1,3,3,1],bounds=[(1e-7,None)]*4)
a0,b0,a1,b1 = result.x
threshold = np.linspace(0,1,1000)
fpr = 1-beta.cdf(threshold,a0,b0)
tpr = 1-beta.cdf(threshold,a1,b1)
return threshold,fpr,tpr
def demand_sampler(random_state, size):
demand = numpy.zeros([size, T, len(I) * len(J)])
for i_idx, i in enumerate(I):
for j_idx, j in enumerate(J):
gamma_k, gamma_theta, beta_a, beta_b = airFare.loc[i, j][:4]
G = random_state.gamma(gamma_k, gamma_theta,
size=size) * (1 - Rate[i])
for t in range(1, T):
B = (beta.cdf(1 - day[t] / day[0], beta_a, beta_b) -
beta.cdf(1 - day[t - 1] / day[0], beta_a, beta_b))
demand[:, t, 6 * i_idx + j_idx] = random_state.poisson(G * B)
return demand
def rhomax_integrand(x, a1, a2, b1, b2):
# Takes numbers and returns a prob. number
pdf1 = beta.pdf(x, a1, b1)
pdf2 = beta.pdf(x, a2, b2)
cdf1 = beta.cdf(x, a1, b1)
cdf2 = beta.cdf(x, a2, b2)
rho = pdf1 * cdf2 + pdf2 * cdf1
integrand = -rho * np.log(rho)
return integrand
def target_func_AnotB(z_AnotB):
if (z_AnotB < 0 or z_AnotB > 1 or (pA - z_AnotB * (1 - pB)) / pB < 0
or (pA - z_AnotB * (1 - pB)) / pB > 1):
return sys.float_info.max
cdf_AnotB = beta.cdf(z_AnotB, a2, b2)
#substitute z_AB
cdf_AB = beta.cdf((pA - z_AnotB * (1 - pB)) / pB, a1, b1)
if (cdf_AB == 0 or cdf_AnotB == 0):
return sys.float_info.max
return max(cdf_AnotB / cdf_AB, cdf_AB / cdf_AnotB)
def target_func_AB(z_AB):
if (z_AB < 0 or z_AB > 1 or (pA - z_AB * pB) / (1 - pB) < 0
or (pA - z_AB * pB) / (1 - pB) > 1):
return sys.float_info.max
cdf_AB = beta.cdf(z_AB, a1, b1)
#substitute z_AnotB
cdf_AnotB = beta.cdf((pA - z_AB * pB) / (1 - pB), a2, b2)
if (cdf_AB == 0 or cdf_AnotB == 0):
return sys.float_info.max
return max(cdf_AnotB / cdf_AB, cdf_AB / cdf_AnotB)
def eva_policy(theta_aa, theta_c, a_aa0, b_aa0, a_aa1, b_aa1, a_c0, b_c0, a_c1,
b_c1):
tpr = []
fpr = []
tpr.append(1 - beta.cdf(theta_aa, a_aa1, b_aa1))
tpr.append(1 - beta.cdf(theta_c, a_c1, b_c1))
fpr.append(1 - beta.cdf(theta_aa, a_aa0, b_aa0))
fpr.append(1 - beta.cdf(theta_c, a_c0, b_c0))
return tpr, fpr
def compute_covariance(self, x, y, diag=False): x, y = format_data(x), format_data(y) x, y = np.copy(x), np.copy(y) assert(x.shape[1] == self.N and y.shape[1] == self.N) for i in range(x.shape[1]): a, b = self.parameters[-2*self.N + 2*i].value, self.parameters[-2*self.N + 2*i + 1].value x[:,i] = beta.cdf(x[:,i], a, b) y[:,i] = beta.cdf(y[:,i], a, b) val = self.kernel.compute_covariance(x, y, diag=diag) return val
def hopkins(X: np.array, alpha=0.05):
'''
Hopkins is a metric of how uniformly distributed an array is.
- Close to 1 is evidence of substructure
- Close to .5 is normally distributed
- Close to 0 indicates regularity
Input:
X: An (n,) or (n,m) list or numpy array
Output:
H: float, Hopkin's Statistic
D: string, Decision on if we have regularity, no structure, or clusters
p: float, P-Value from the cdf of Beta(m,m) distribution
'''
X = np.array(X)
if len(X.shape) == 1:
X = X.reshape(-1,1)
d = X.shape[1]
n = len(X)
m = int(0.1 * n)
nbrs = NearestNeighbors(n_neighbors=1).fit(X)
rand_X = sample(range(0, n, 1), m)
ujd = []
wjd = []
for j in range(0, m):
# Get distance to a random point
random_uniform = np.random.uniform(np.min(X, axis=0), np.max(X, axis=0), d).reshape(1,-1)
u_dist, _ = nbrs.kneighbors(random_uniform, 2, return_distance=True)
ujd.append(u_dist[0][1]**d)
# Get distance to another sample
random_sample = X[rand_X[j]].reshape(1,-1)
w_dist, _ = nbrs.kneighbors(random_sample, 2, return_distance=True)
wjd.append(w_dist[0][1]**d)
denom = np.sum(ujd) + np.sum(wjd)
if denom == 0:
raise RuntimeWarning('The Hopkins denominator was 0, cannot proceed')
else:
H = np.sum(ujd) / denom
if H > 0.5:
p = 1 - beta.cdf(H, m, m)
if p < alpha:
D = 'There is evidence of clusters'
else:
D = 'There is no evidence of structure'
else:
p = beta.cdf(H, m, m)
if p < alpha:
D = 'There is evidence of regularity'
else:
D = 'There is no evidence of structure'
return H, D, p
def generate_conditional_ps(self):
# p(TiN|Somatic) and p(TiN|Germline)
n_af_w = np.zeros([self.number_of_sites, len(self.af)])
t_af_w = np.zeros([self.number_of_sites, len(self.af)])
t_het_direction = np.ones([self.number_of_sites, len(self.af)])
t_het_direction[:, 0:np.int(np.round(np.true_divide(len(self.af), 2))
)] = -1
for i, f in enumerate(self.af):
n_af_w[:,
i] = self.rv_normal_af.cdf(f) - self.rv_normal_af.cdf(f -
0.005)
t_af_w[:,
i] = self.rv_tumor_af.cdf(f) - self.rv_tumor_af.cdf(f -
0.005)
# ac given somatic
t_af = np.multiply(f, self.n_depth)
n_ac_given_tin = np.multiply(t_af[:, np.newaxis], self.CN_ratio)
# ac given heterozygous
f_t_af = 0.5 - np.abs((.5 - f))
psi_t_af = 0.5 - f_t_af
psi_t_af = np.multiply(psi_t_af, t_het_direction[:, i])
exp_f = 0.5 + np.multiply(psi_t_af[:, np.newaxis], self.CN_ratio)
n_het_ac_given_tin = np.multiply(exp_f, self.n_depth[:,
np.newaxis])
for TiN_idx, TiN in enumerate(self.TiN_range):
self.p_TiN_given_S[:, TiN_idx] += np.multiply(
beta.cdf(
self.normal_f[:] + .01, n_ac_given_tin[:, TiN_idx] + 1,
self.n_depth[:] - n_ac_given_tin[:, TiN_idx] + 1) -
beta.cdf(self.normal_f[:], n_ac_given_tin[:, TiN_idx] + 1,
self.n_depth[:] - n_ac_given_tin[:, TiN_idx] + 1),
t_af_w[:, i])
self.p_TiN_given_het[:, TiN_idx] += np.multiply(
beta.cdf(
self.normal_f[:] + .01,
n_het_ac_given_tin[:, TiN_idx] + 1,
self.n_depth[:] - n_het_ac_given_tin[:, TiN_idx] + 1) -
beta.cdf(
self.normal_f[:], n_het_ac_given_tin[:, TiN_idx] + 1,
self.n_depth[:] - n_het_ac_given_tin[:, TiN_idx] + 1),
t_af_w[:, i])
self.p_artifact = self.rv_tumor_af.cdf(self.normal_f +
.01) - self.rv_tumor_af.cdf(
self.normal_f)
self.p_TiN_given_G = np.multiply(1 - self.p_artifact[:, np.newaxis],
self.p_TiN_given_het) + np.multiply(
self.p_artifact[:, np.newaxis],
1 - self.p_TiN_given_het)
def calculate_aep_curve(elt, grid_size=2**14, max_loss_factor=5):
""" This function calculates the OEP of a given ELT
----------
elt : pandas dataframe containing PLT
grid_size: grid size used for ep calculations
max_loss_factor: factor used to extimate max loss
Returns
-------
EPCurve :
exceedance probability curve
"""
elt_lambda = ELT(elt).get_lambda()
max_loss = _max_loss(elt, max_loss_factor)
dx = max_loss / grid_size
xx = np.arange(1, grid_size + 1) * dx
severity_distribution, severity_density_function = calculate_severity_distribution(
elt, grid_size, max_loss_factor)
elt['dx'] = dx / elt['ExpValue']
elt['xx'] = ''
elt['FX'] = ''
elt['FX2'] = ''
fx2 = [0] * grid_size
for index, row in elt.iterrows():
row['xx'] = np.true_divide(xx, row['ExpValue'])
row['FX'] = beta.cdf(row['xx'], row['alpha'], row['beta'])
row['FX2'] = beta.cdf(row['xx'][0] - row['dx'] / 2, row['alpha'],
row['beta'])
cdf2 = beta.cdf(row['xx'][:-1] + row['dx'] / 2, row['alpha'],
row['beta'])
cdf1 = beta.cdf(row['xx'][:-1] - row['dx'] / 2, row['alpha'],
row['beta'])
row['FX2'] = np.insert(cdf2 - cdf1, 0, row['FX2'])
fx2 = fx2 + (row['Rate'] / elt_lambda) * row['FX2']
elt.at[index] = row
fx_hat = fft(fx2)
fs_hat = numpy.exp(-elt_lambda * (1 - fx_hat))
fs = numpy.real(ifft(fs_hat, norm="forward") / grid_size)
fs_cum = numpy.cumsum(fs)
severity_density_function['AEP'] = 1 - fs_cum
aep = severity_density_function.rename(columns={
'AEP': 'Probability',
'threshold': 'Loss'
})
return ep_curve.EPCurve(aep, ep_type=ep_curve.EPType.AEP)
def hpdi(p, k, n, a=0.05, b=1):
""" Bayesian highest posterior density interval of population prevalence gamma
under a uniform prior
p : HPDI to return (e.g. 0.95 for 95%)
k : number of participants significant out of
n : total number of participants
a : alpha value of within-participant test (default=0.05)
b : sensitivity/beta of within-participant test (default=1)
"""
b1 = k+r
b2 = n-k+s
# truncated beta pdf/cdf/icdf
tbpdf = lambda x: beta.pdf(x,b1,b2) / (beta.cdf(b,b1,b2)-beta.cdf(a,b1,b2))
tbcdf = lambda x: (beta.cdf(x,b1,b2)-beta.cdf(a,b1,b2)) / (beta.cdf(b,b1,b2)-beta.cdf(a,b1,b2))
tbicdf = lambda x: beta.ppf( (1-x)*beta.cdf(a,b1,b2) + x*beta.cdf(b,b1,b2),b1,b2 )
if k==a:
x = np.array([a, tbicdf(p)])
elif k==n:
x = np.array([tbicdf(1-p), b])
else:
f = lambda x: np.array([tbcdf(x[1])-tbcdf(x[0])-p, tbpdf(x[1])-tbpdf(x[0])]);
x, info, ier, mesg = fsolve(f, np.array([tbicdf((1-p)/2), tbicdf((1+p)/2)]),full_output=True )
# limit to valid theta values
if (x[0]<a) or (x[1]<x[0]):
x = np.array([a, tbicdf(p)])
if x[1]>b:
x = np.array([tbicdf(1-p), b])
hpdi = (x-a)/(b-a)
return hpdi
def Beta_Entropy(w0, l0, w1, l1):
global MC_samples
seq.reset()
x = seq.get(MC_samples)
x = np.reshape(x, MC_samples)
pdf0 = beta.pdf(x, w0+1, l0+1)
pdf1 = beta.pdf(x, w1+1, l1+1)
cdf0 = beta.cdf(x, w0+1, l0+1)
cdf1 = beta.cdf(x, w1+1, l1+1)
rho = pdf0 * cdf1 + pdf1 * cdf0 + 1E-4
integral = np.mean( -rho * np.log( rho ) )
return integral
def func_2b():
sample_x = np.random.beta(8, 5, 1000)
sample_y = np.random.beta(4, 7, 1000)
observed_result = np.zeros((5, 5))
estimated_result = np.zeros((5, 5))
difference_result = np.zeros((5, 5))
estimated_x = [0] * 5
estimated_y = [0] * 5
chi_squared_result = 0
#take (sample_x[i],sample_y[i]) as a sample of (X,Y)
#print sample_x,"\n",sample_y
#divide the 2-way table into 5*5 areas
for i in range(0, 5): #row
for j in range(0, 5): #column
row_down = 0.2 * i
row_up = 0.2 * i + 0.2
column_down = 0.2 * j
column_up = 0.2 * j + 0.2
for sample_index in range(0, 1000):
if (int(sample_y[sample_index] >= row_down)
& int(sample_y[sample_index] < row_up)):
if (int(sample_x[sample_index] >= column_down)
& int(sample_x[sample_index] < column_up)):
observed_result[i][j] += 1
#calculation_result[i][j]/=1000
for i in range(0, 5):
estimated_x[i] = beta.cdf(0.2 * i + 0.2, 8, 5) - beta.cdf(
0.2 * i, 8, 5)
estimated_y[i] = beta.cdf(0.2 * i + 0.2, 4, 7) - beta.cdf(
0.2 * i, 4, 7)
for i in range(0, 5):
for j in range(0, 5):
estimated_result[i][j] = (estimated_y[i] * estimated_x[j] * 1000)
difference_result = estimated_result - observed_result
for i in range(0, 5):
for j in range(0, 5):
chi_squared_result += (difference_result[i][j]**2 /
estimated_result[i][j])
#print estimated_result
print "The observed result of RV X&Y is:\n", observed_result
#print difference_result
print "The Result of Chi-squared_test=\n", chi_squared_result
#Chi-squared distribution threshold can be acquired from charts, pick 95.0%
#the degree of freedom is 4*4=16, threshold=26.3
if chi_squared_result <= 26.3:
print "X & Y can be considered as independent"
else:
print "X & Y cannot be considered as independent"
def probf_baharev(df1, df2, noncen, fcrit):
x = 1 - special.btdtri(df1, df2, fcrit)
eps = 1.0e-7
itr_cnt = 0
f = None
while itr_cnt <= 10:
mu = noncen / 2.0
ql = poisson.ppf(eps, mu)
qu = poisson.ppf(1 - eps, mu)
k = qu
c = beta.cdf(x, df1 + k, df2)
d = x * (1.0 - x) / (df1 + k - 1.0) * beta.pdf(x, df1 + k - 1, df2, 0)
p = poisson.pmf(k, mu)
f = p * c
p = k / mu * p
k = qu - 1
while k >= ql:
c = c + d
d = (df1 + k) / (x * (df1 + k + df2 - 1)) * d
f = f + p * c
p = k / mu * p
k = k - 1
itr_cnt = itr_cnt + 1
if (itr_cnt == 11):
print("newton iteration failed")
return f
def checkBlockedUser(a, b, th=0.95):
# return beta.cdf(0.5, a, b) > th
s = beta.cdf(0.5, a, b)
blocked = False
if s > th:
blocked = True
return blocked
def t_inv_beta(p0):
""" A function to compute the inverse template for the beta family
Parameters
-----------------
p0: a numpy.ndarray of shape (B,m) ,
where m is the number of null hypotheses and B is typically the number
of permutations/bootstraps that contains the values on which to apply (column wise)
the inverse beta reference family
Returns
-----------------
a numpy.ndarray of shape ()
Examples
data = np.random.uniform(0,1,(10,10))
pr.t_inv_beta(data)
-----------------
"""
# Obtain the number of null hypotheses
m = p0.shape[1]
# Initialize the matrix of transformed p-values
transformed_pvalues = np.zeros(p0.shape)
# Transformed each column via the beta pdf
# (t_k^B)^{-1}(lambda) = F(lambda) where F (beta.pdf) is the cdf of the
# beta(k, m+1-k) distribution.
for k in np.arange(m):
transformed_pvalues[:, k] = beta.cdf(p0[:, k], k + 1, m + 1 - (k + 1))
return transformed_pvalues
def mid_p_interval(total, passed, conf=0.682689492137, is_upper=True):
alpha = 1. - conf
alpha_min = alpha / 2
vmin = alpha_min if is_upper else (1. - alpha_min)
tol = 1e-9 # tolerance
pmin = 0
pmax = 1
p = 0
# treat special case for 0<passed<1
# do a linear interpolation of the upper limit values
if passed > 0 and passed < 1:
p0 = mid_p_interval(total, 0.0, is_upper)
p1 = mid_p_interval(total, 1.0, is_upper)
p = (p1 - p0) * passed + p0
return p
while abs(pmax - pmin) > tol:
p = (pmin + pmax) / 2
# make it work for non integer using the binomial - beta relationship
v = 0.5 * beta.pdf(p, passed + 1., total - passed + 1) / (total + 1)
# compute the binomial cdf at passed -1
if passed >= 1:
v += 1 - beta.cdf(p, passed, total - passed + 1)
if v > vmin:
pmin = p
else:
pmax = p
return p
def _fap_cvm(freq, psd, psd_best_period):
"""
Computes false alarm probability for the cvm-distance-minimised beta distribution
"""
from scipy import optimize
from scipy.stats import beta
clip = 0.00001
temp = np.mean(psd) * (-np.mean(psd) + np.mean(psd) ** 2 + np.var(psd))
theta_1 = - temp / np.var(psd)
if theta_1 < 0:
theta_1 = clip
theta_2 = (theta_1 - theta_1 * np.mean(psd)) / np.mean(psd)
if theta_2 < 0:
theta_2 = clip
cvm_minimize = optimize.minimize(
_cvm,
[theta_1, theta_2],
args=(psd,),
bounds=((clip, None), (clip, None)),
)
fap = 1 - beta.cdf(psd_best_period, cvm_minimize.x[0], cvm_minimize.x[1]) ** len(freq)
return fap
def mapy2beta(self, y):
"""
mapping y to beta
parameters
----------
self: class object
hypothesis criteria
y: array_like
Input array
returns
-------
pair of beta CDF: Float
Returns a float.
"""
a = beta.cdf(y, self._betaA, self._betaB)
i = 0
if y < self._ymin:
return 0
elif y > self._ymax:
return 1
else:
for i, z in enumerate(self._Y):
if y < z:
i = self._Y.index(z)
break
return a
def pInitial(self):
"""
Returns a distribution over initial states (z)
The distribution is discretized into the number of bins specified by self.bins
"""
cdf = Beta.cdf(self.quantiles,self.i[0],self.i[1])
return np.diff(cdf)
def plot_beta(a, b, fill = False):
betap = partial(beta.pdf, a, b)
xs = np.linspace(0,1, num = 150)
#y = list(map(betap, x))
y = [beta.pdf(x, a, b) for x in xs]
fills = [ x <= 0.5 for x in xs]
#sio = cStringIO.StringIO()
sio = io.BytesIO()
#sio = io.StringIO()
fig = plt.figure()
ax1 = fig.add_subplot(111)
#ax1.set_ylim(bottom=0)
#ax1.set_ylim(bottom
if fill: ax1.fill_between(xs ,y,0,where=fills , color='0.8')
ax1.plot(xs, y)
fig.savefig(sio, format='png')
enc = base64.b64encode(sio.getvalue())
plt.close("all")
#hex = enc.strip()
hex = enc.decode('utf-8')
#hex = sio.getvalue().encode("base64").strip()
prob = beta.cdf(0.5, a, b)
return hex, prob
def getbcdf_pval_swc(self, swc):
"""
get p-value of beta CDF with candidated sigma weight
parameters
----------
returns
-------
pval:
d:
Y:
ba:
bb:
bcdf: beta.cdf
"""
Y = [self.kernelizeisw(x, swc) for x in self._data]
Y.sort()
Y = featureScaling(Y)
y_m = np.mean(Y)
y_v = np.var(Y, ddof = 1)
if math.isnan(y_v) or y_v == 0:
return 0
ba = y_m ** 2 * ((1 - y_m) / y_v - 1 / y_m)
bb = ba * (1 - y_m) / y_m
bcdf = beta.cdf(Y, ba, bb)
# Y = featureScaling(Y)
d, pval = scistats.kstest(Y, lambda cdf: bcdf)
params = p3c(pval, d, Y, [x for x in swc], ba, bb, 0, bcdf)
return params
def g(x): prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) prob_diff=beta.pdf(x,alpha_param,beta_param)-beta.pdf(xx,alpha_param,beta_param) #print ' x=%f, prob_xx=%f, xx=%f, prob_diff=%f'%(x,prob_xx,xx,prob_diff) return(prob_diff)
def wat(x, s_n, ar): f = 1 for i in xrange(len(ar)): if i is s_n: f = f*beta.pdf(x, ar[i][0] + 1, ar[i][1] - ar[i][0] + 1) #f(Sa|Dt) #Dt is information available before reward else: f = f*beta.cdf(x, ar[i][0] + 1, ar[i][1] - ar[i][0] + 1) #F(S < Sa|Dt) #D is information available before reward return f
def pTransition(self,z,x):
"""
Returns a distribution over transitions to z given the current state (z) and observation (x)
The distribution is discretized into the number of bins specified by self.bins
"""
alpha = self.w[0]*z + sum([x[i]*w for i, w in enumerate(self.w[1:])])
cdf = Beta.cdf(self.quantiles, alpha[0], alpha[1])
return np.diff(cdf)
def kstest(self, x):
s = Sample(x).set(self.centroid['mean'], self.centroid['std'])
fss = featurescaling(s, x_min=self._stats_['min'], x_max=self._stats_['max'])
p = scibeta.cdf(fss, self.alpha, self.beta)
if Sample.x == Sample.m or Sample.x == Sample.c:
p = 1. - p
return 0 if math.isnan(p) else p
def betadist(betaparams,B,pcF):
#defining beta distribution parameters
a=float(betaparams['a'].value)
b=float(betaparams['b'].value)
loc=float(betaparams['loc'].value)
scale=float(betaparams['scale'].value)
#creating fitted data
model_pcF=beta.cdf(B,a,b,loc=loc,scale=scale)
#returning residual
return (model_pcF-pcF)
def _fap_pre(time, freq, psd_best_period):
"""
Computes false alarm probability for the pre-defined beta distribution
"""
from scipy.stats import beta
a = (3 - 1) / 2
b = (len(time) - 3) / 2
fap = 1 - beta.cdf(psd_best_period, a, b) ** len(freq)
return fap
def beta_rain(a,b,Pt,P):
try:
a>0
b>0
P['c_rain']=beta.cdf(np.linspace(0,1,len(P)),a,b)*Pt
P['i_rain']=P['c_rain'].diff(periods=1)
P.fillna(value=0,inplace=True)
return P
except:
print "parameter error/s"
def credible_interval(c, n, CI=0.95, alpha=1, beta=1):
lower_tail = (1.0 - CI) / 2.0
upper_tail = 1.0 - lower_tail
x = np.linspace(0, 1, 1000)
a = c + alpha
b = n - c + beta
mean = a / (a + b)
cdf = beta_distribution.cdf(x, a, b)
lower_bound = x[cdf > lower_tail][0]
upper_bound = x[cdf < upper_tail][-1]
return mean, lower_bound, upper_bound
def beta_slope_profile(numprofiles, max_a, min_a, max_b, min_b, elev,base):
#generating random parameters for beta distribution
a_list=np.random.rand(numprofiles)*(max_a-min_a)+min_a
b_list=np.random.rand(numprofiles)*(max_b-min_b)+min_b
b_list=a_list/b_list
x=np.linspace(0,base,numpts)
y_list=[]
for j in range(len(a_list)):
#3. Generating topo profiles
y=beta.cdf(x,a_list[j],b_list[j],loc=0,scale=base)
y_list.append(y[::-1])
return x,y_list
def __check__(self):
self.all_distances = [d / max(self.all_distances) for d in self.all_distances]
mean = numpy.mean(self.all_distances)
var = numpy.var(self.all_distances, ddof=1)
ii = len(self.all_distances)
while var >= (mean * (1 - mean)):
ii -= 1
mean = numpy.mean(self.all_distances[:ii])
var = numpy.var(self.all_distances[:ii], ddof=1)
alpha1 = mean * (mean * (1 - mean) / var - 1)
beta1 = alpha1 * (1 - mean) / mean
for d in sorted(self.all_distances):
print d, beta.cdf(d, alpha1, beta1)
def betadist_leastsquare_fitting(B,pcF,ai,bi,loc,scale):
#defining power law variables
betaparams = Parameters()
betaparams.add('a', value=ai, vary=True, min=0.001, max=None)
betaparams.add('b', value=bi, vary=True, min=0.001, max=None)
betaparams.add('loc', value=loc, vary=True, min=0, max=loc)
betaparams.add('scale', value=scale, vary=True, min=scale, max=90)
#minimizing residuals
result = minimize(betadist, betaparams, args=(B,pcF))
Bfit = np.linspace(betaparams['loc'].value,betaparams['scale']+betaparams['loc'].value,90*10+1)
pcFfit=beta.cdf(Bfit,
betaparams['a'].value,
betaparams['b'].value,
loc=betaparams['loc'].value,
scale=betaparams['scale'].value)
return Bfit,pcFfit, np.sqrt(np.mean((result.residual)**2)),betaparams['a'].value,betaparams['b'].value,betaparams['loc'].value,betaparams['scale'].value
def getProb(post): m = post.shape[0] prob = np.zeros((m, 1)) for i in xrange(m): b1, b2, b3 = post[i][:] #p = dblquad(integrand, 0.0, 0.5, lambda p2 : p2, lambda p2 : 1-p2, args=(b1, b2, b3))[0] p = 1-beta.cdf(0.5, b1, b2) #print(p) ''' if b3 == 0: p *= gamma(b1+b2)/(gamma(b1)*gamma(b2)) else: p *= gamma(b1+b2+b3)/(gamma(b1)*gamma(b2)*gamma(b3)) p /= 5000000 ''' prob[i] = p return prob
def _cvm(param, data):
"""
Cramer-von-Mises distance for beta distribution
"""
from scipy.stats import beta
a, b = param
ordered_data = np.sort(data, axis=None)
sumbeta = 0
for n in range(len(data)):
cdf = beta.cdf(ordered_data[n], a, b)
sumbeta += (cdf - (n - 0.5) / len(data)) ** 2.0
cvm_dist = (1. / len(data)) * sumbeta + 1. / (12 * (len(data) ** 2.))
mask = np.isfinite(cvm_dist)
cvm = cvm_dist[mask]
return cvm
def _fap_nll(time, freq, psd, psd_best_period):
"""
Computes false alarm probability for the negative logarithmic likelihood-minimised beta distribution
"""
from scipy import optimize
from scipy.stats import beta
a = (3 - 1) / 2
b = (len(time) - 3) / 2
clip = 0.00001
nll_minimize = optimize.minimize(
_nll,
[a, b],
args=(psd,),
bounds=((clip, None), (clip, None)),
)
fap = 1 - beta.cdf(psd_best_period, nll_minimize.x[0], nll_minimize.x[1]) ** len(freq)
return fap
def __check__(self):
"""
purely for debugging and dev - trying to understand the distribution of points in a cluster
:return:
"""
self.all_distances = [d/max(self.all_distances) for d in self.all_distances]
mean=numpy.mean(self.all_distances)
var=numpy.var(self.all_distances,ddof=1)
ii = len(self.all_distances)
while var >= (mean*(1-mean)):
ii -= 1
mean=numpy.mean(self.all_distances[:ii])
var=numpy.var(self.all_distances[:ii],ddof=1)
alpha1=mean*(mean*(1-mean)/var-1)
beta1=alpha1*(1-mean)/mean
for d in sorted(self.all_distances):
print d,beta.cdf(d,alpha1,beta1)
def inverse_beta_ml_band(z,i,N): alpha_param=i+1 beta_param=N-i+1 small=.5 if i<small: x=0 xx=beta.ppf(z,alpha_param,beta_param) elif i>N-small: x=beta.ppf(1.0-z,alpha_param,beta_param) xx=1 if np.isnan(x): print "NaN failure in beta edge case" IPython.embed() else: x_min=0 x_max=beta.ppf(1.0-z,alpha_param,beta_param) def g(x): prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) prob_diff=beta.pdf(x,alpha_param,beta_param)-beta.pdf(xx,alpha_param,beta_param) #print ' x=%f, prob_xx=%f, xx=%f, prob_diff=%f'%(x,prob_xx,xx,prob_diff) return(prob_diff) try: #print '*** (x_min,x_max)=%f,%f'%(x_min,x_max) x=brentq(g,x_min,x_max) #print ' (x)=%f\n'%(x) except: print "Failure at 'brentq'." IPython.embed() prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) larger_x=np.max((x,xx)) smaller_x=np.min((x,xx)) return((smaller_x,larger_x))
def guess_beta(num_weights,results,CI=.9,alpha=.3,color='green'): num_coins=fc.total_num_coins(results) x=np.linspace(0,1,num_weights) y=np.zeros(num_weights) lower=np.zeros(num_weights) upper=np.zeros(num_weights) for i,xx in enumerate(x): for num_flips in results: for heads in results[num_flips]: #print 'num_flips=%d,heads=%d'%(num_flips,heads) sum_weight=float(results[num_flips][heads])/float(num_coins) y[i]+=sum_weight * beta.cdf(xx,heads+1,num_flips-heads+1) if y[-1]>1.0: #print 'y[-1] = %f ! Fixing...'%(y[-1]) y/=y[-1] for i,xx in enumerate(x): (lower[i],upper[i])=nest.inverse_beta_ml_band(CI,y[i]*float(num_coins),num_coins) plt.plot(x,y,color=color,label='Estimate with %.1f%% credible interval'%(100.0*CI)) ax=plt.gca() ax.fill_between(x,lower,upper,alpha=alpha,color=color)
from scipy.stats import beta print(beta.cdf(2,3,4))
def gridSetting(data,options,Seed):
# Initialisierung
d = np.size(options['borders'],0)
X1D = []
'''Equal steps in cumulative distribution'''
if options['gridSetType'] == 'cumDist':
Like1D = np.zeros([options['GridSetEval'], 1])
for idx in range(d):
if options['borders'][idx, 0] < options['borders'][idx,1]:
X1D.append(np.zeros([1, options['stepN'][idx]]))
local_N_eval = options['GridSetEval']
while any(np.diff(X1D[idx]) == 0):
Xtest1D = np.linspace(options['borders'][idx,0], options['borders'][idx,1], local_N_eval)
alpha = Seed[0]
beta = Seed[1]
l = Seed[2]
gamma = Seed[3]
varscale = Seed[4]
if idx == 1:
alpha = Xtest1D
elif idx == 2:
beta = Xtest1D
elif idx == 3:
l = Xtest1D
elif idx == 4:
gamma = Xtest1D
elif idx == 5:
varscale = Xtest1D
Like1D = likelihood(data, options, [alpha, beta, l, gamma, varscale])
Like1D = Like1D + np.mean(Like1D)*options['UniformWeight']
Like1D = np.cumsum(Like1D)
Like1D = Like1D/max(Like1D)
wanted = np.linspace(0,1,options['stepN'][idx])
for igrid in range(options['stepN'][idx]):
X1D[idx].append(copy.deepcopy(Xtest1D[Like1D >= wanted, 0, 'first'])) #TODO check
local_N_eval = 10*local_N_eval
else:
X1D.append(copy.deepcopy(options['borders'][idx,0]))
''' equal steps in cumulative second derivative'''
elif (options['gridSetType'] in ['2', '2ndDerivative']):
Like1D = np.zeros([options['GridSetEval'], 1])
for idx in range(d):
if options['borders'][idx,0] < options['borders'][idx,1]:
X1D.append(np.zeros([1,options['stepN'][idx]]))
local_N_eval = options['GridSetEval']
while any(np.diff(X1D[idx] == 0)):
Xtest1D = np.linspace(options['borders'][idx,0], options['borders'][idx,1], local_N_eval)
alpha = Seed[0]
beta = Seed[1]
l = Seed[2]
gamma = Seed[3]
varscale = Seed[4]
if idx == 1:
alpha = Xtest1D
elif idx == 2:
beta = Xtest1D
elif idx == 3:
l = Xtest1D
elif idx == 4:
gamma = Xtest1D
elif idx == 5:
varscale = Xtest1D
# calc likelihood on the line
Like1D = likelihood(data, options, [alpha, beta, l, gamma, varscale])
Like1D = np.abs(np.convolve(np.squeeze(Like1D), np.array([1,-2,1]), mode='same'))
Like1D = Like1D + np.mean(Like1D)*options['UniformWeight']
Like1D = np.cumsum(Like1D)
Like1D = Like1D/max(Like1D)
wanted = np.linspace(0,1,options['stepN'][idx])
for igrid in range(options['stepN'][idx]):
X1D[idx].append(copy.deepcopy(Xtest1D[Like1D >= wanted, 0, 'first'])) #ToDo
local_N_eval = 10*local_N_eval
if local_N_eval > 10**7:
X1D[idx] = np.unique(np.array(X1D)) # TODO check
break
else:
X1D.append(options['borders'][idx,0])
''' different choices for the varscale '''
''' We use STD now directly as parametrisation'''
elif options['gridSetType'] in ['priorlike', 'STD', 'exp', '4power']:
for i in range(4):
if options['borders'](i,0) < options['borders'](i,1):
X1D.append(np.linspace(options['borders'][i,0], options['borders'][i,1], options['stepN'][i]))
else:
X1D.append(copy.deepcopy(options['borders'][id,0]))
if options['gridSetType'] == 'priorlike':
maximum = b.cdf(options['borders'][4,1],1,options['betaPrior'])
minimum = b.cdf(options['borders'][4,0],1,options['betaPrior'])
X1D.append(b.ppf(np.linspace(minimum, maximum, options['stepN'][4]), 1, options['betaPrior']))
elif options['gridSetType'] == 'STD':
maximum = np.sqrt(options['borders'][4,1])
minimum = np.sqrt(options['borders'][4,0])
X1D.append((np.linspace(minimum, maximum, options['stepN'][4]))**2)
elif options['gridSetType'] == 'exp':
p = np.linspace(1,1,options['stepN'][4])
X1D.append(np.log(p)/np.log(.1)*(options['borders'][4,1] - options['borders'][4,0]) + options['borders'][4,0])
elif options['gridSetType'] == '4power':
maximum = np.sqrt(options['borders'][4,1])
minimum = np.sqrt(options['borders'][4,0])
X1D.append((np.linspace(minimum, maximum, options['stepN'][4]))**4)
return X1D
(0.5, 0.5),
(1, 1),
(4, 3),
(2, 5),
(6, 6)
]
for p in params:
y = beta.pdf(x, p[0], p[1])
plt.plot(x, y, label="$\\alpha=%s$, $\\beta=%s$" % p)
plt.xlabel("$\\theta$, Fairness")
plt.ylabel("PDF")
plt.legend(title="Parameters")
plt.show()
for p in params:
y = beta.cdf(x, p[0], p[1])
plt.plot(x, y, label="$\\alpha=%s$, $\\beta=%s$" % p)
plt.xlabel("$\\theta$, Fairness")
plt.ylabel("CDF")
plt.legend(title="Parameters")
plt.show()
for p in params:
y = beta.ppf(x, p[0], p[1])
plt.plot(x, y, label="$\\alpha=%s$, $\\beta=%s$" % p)
plt.xlabel("$\\theta$, Fairness")
plt.ylabel("PPF")
plt.legend(title="Parameters")
plt.show()
def betascores(r):
x = np.asarray(r, np.float)
n = x.size
x.sort()
p = beta.cdf(x=x, a=np.arange(1, n + 1), b=np.arange(n, 0, -1))
return p
def betacdf(j,alpha_a,beta_a,skala):
return beta.cdf(j,alpha_a,beta_a,loc=0, scale=skala)
print name,len(times[name])
print correct,incorrect
print np.mean(correct_times),np.mean(incorrect_times)
#print sum([1 for c in correct_times if c >= min(incorrect_times)])/float(len(correct_times))
#print
max_time = max(max(correct_times),max(incorrect_times))
min_time = min(min(correct_times),min(incorrect_times))
data = correct_times
data = [(t-min_time)/float(max_time-min_time) for t in data]
#print data
a,b,lower,scale = beta.fit(data)
#print a,b,lower,scale
#print
#print beta.cdf(0.8,a,b)
#----------------Fit using moments----------------
mean=np.mean(data)
var=np.var(data,ddof=1)
alpha1=mean**2*(1-mean)/var-mean
beta1=alpha1*(1-mean)/mean
print beta.cdf((incorrect_times[-1]-min_time)/(max_time-min_time),alpha1,beta1)
print
#break
#print correct_times
#print incorrect_times
#print times.keys()
#print user_collection.find_one({"name":"kellinora"})
def betacdf(j,alpha_a,beta_a,skala):
return beta.cdf(j,alpha_a,beta_a,loc=0, scale=skala)
def betapdf(j,alpha_a,beta_a,skala):
return beta.pdf(j,alpha_a,beta_a,loc=0, scale=skala)
while j < akhir:
#simulasi dalam detik
#utk tiap video:
if j >= multiple_of[0]*7200:
TASKS = [ (betacdf,(j, catalog[k]['alpha'],catalog[k]['beta'],skala) for k in range(numbervideo)]+[ (betapdf,(j, catalog[k]['alpha'],catalog[k]['beta'],skala) for k in range(numbervideo)]
for k in range(numbervideo):
alpha_a=catalog[k]['alpha']
beta_a=catalog[k]['beta']
#hitung pdf dan cdf
cdf_a = beta.cdf(j,alpha_a,beta_a,loc=0,scale=skala)
pdf_a = beta.pdf(j,alpha_a,beta_a,loc=0,scale=skala)
catalog[k]['cdf'][j]=cdf_a
catalog[k]['pdf'][j]=pdf_a
multiple_of.pop(0)
print j
j+=1
with open('catalog.pickle', 'wb') as handle:
pickle.dump(catalog, handle)
handle.close()
