def compute_LogLikelihood(data, fisk_params, ig_params, lognorm_params,
gamma_params):
n_fisk_params = 2
n_ig_params = 3
n_lognorm_params = 3
n_gamma_params = 3
trunc_data = data[data != 1.0]
prob = np.sum(data == 1.0) / float(data.shape[0])
ll_fisk_trunc = np.sum(-np.log(fisk.pdf(trunc_data, *fisk_params)))
bic = np.log(trunc_data.shape[0]) * n_fisk_params - 2 * ll_fisk_trunc
#ll_fisk_nontrunc = np.sum(-np.log(prob * np.ones()))
ll_ig_trunc = np.sum(-np.log(invgauss.pdf(trunc_data, *ig_params)))
#ll_ig_nontrunc = np.sum(np.log(prob))
ll_ln_trunc = np.sum(-np.log(lognorm.pdf(trunc_data, *lognorm_params)))
#ll_ln_nontrunc = np.sum(np.log(prob))
ll_gamma_trunc = np.sum(-np.log(gamma.pdf(trunc_data, *gamma_params)))
#ll_exp_trunc = np.sum(-np.log(expon.pdf(trunc_data, *exp_params)))
#ll_exp_nontrunc = np.sum(np.log(prob))
return ll_fisk_trunc, ll_ig_trunc, ll_ln_trunc, ll_gamma_trunc
def truncfiskprior_pdf(data, c, scale):
epsilon = 1e-200
term2 = (fisk.pdf(data, c, loc=0.0, scale=scale) /
(fisk.cdf(1.0, c, loc=0.0, scale=scale) -
fisk.cdf(0.0, c, loc=0.0, scale=scale))) * (data < 1.0)
return term2 + epsilon
def LogLogisticLikelihood(Samples):
p1 = [1, 1.5, 2, 3]
p2 = [15, 16, 17, 18, 19, 20, 21, 22]
p3 = [30, 40, 50, 60, 70, 80, 90.100]
maximumLikelihood = float('-inf')
#ax = plt.axes(projection='3d')
for a in p1:
# plt.title("Maximum Likelihood")
# plt.tight_layout()
for b in p2:
Likelihood = []
for c in p3:
Logistic = fisk.pdf(Samples, a, loc=b, scale=c)
likelihood = 0
for p in Logistic:
likelihood += np.log(p)
Likelihood.append(likelihood[0])
if (likelihood > maximumLikelihood):
RetA = a
RetB = b
RetC = c
maximumLikelihood = likelihood
#ax.plot3D(p3, p2, Likelihood,label='a='+str(a))
#plt.plot(p3,Likelihood,lw=3,alpha=2.5,label="b="+str(b))
#plt.legend()
return RetA, RetB, RetC
def fit_fisk(signal, tag):
mu, loc, std = fisk.fit(signal["mean"].values)
confidence_interval = fisk.interval(CONFIDENCE, mu, loc=loc, scale=std)
if PLOTTING:
# Plot the histogram.
plt.subplots()
plt.hist(signal["mean"].values,
bins=25,
density=True,
alpha=0.6,
color="g")
# Plot the PDF.
xmin, xmax = plt.xlim()
x = np.linspace(xmin, xmax, 100)
p = fisk.pdf(x, mu, loc, std)
plt.plot(x, p, "k", linewidth=1)
title = "Fit results fisk: a=%2f loc = %.2f, std = %.2f" % (mu, loc,
std)
plt.title(title)
plt.axvline(x=confidence_interval[0])
plt.axvline(x=confidence_interval[1])
# Plot the confidence interval
plt.savefig(f"analysis/images/{slugify(tag)}_fit_fisk_histogram.png",
format="png")
return {
"distribution": "fisk",
"params": [{
"a": mu,
"loc": loc,
"std": std
}],
"confidence": [confidence_interval],
}
def truncfiskprior_pdf(data, prior, c, scale):
epsilon = 1e-200
term1 = prior * (data == 1.0)
term2 = (1 - prior) * (fisk.pdf(data, c, loc=0.0, scale=scale) /
(fisk.cdf(1.0, c, loc=0.0, scale=scale) - fisk.cdf(
0.0, c, loc=0.0, scale=scale))) * (data < 1.0)
return term1 + term2 + epsilon
def compute_LogLikelihood_ExtData(data, fisk_params, ig_params):
prob = fisk_params[0]
fisk_params = fisk_params[1]
num_one = np.sum(data == 1.0)
trunc_data = data[data != 1.0]
fisk_trunc_ll = np.sum(-np.log(fisk.pdf(trunc_data, *fisk_params)))
fisk_nontrunc_ll = -np.log(prob) * num_one
fisk_ll = fisk_trunc_ll + fisk_nontrunc_ll
ig_trunc_ll = np.sum(-np.log(invgauss.pdf(trunc_data, *fisk_params)))
ig_nontrunc_ll = -np.log(prob) * num_one
ig_ll = ig_trunc_ll + ig_nontrunc_ll
return fisk_ll, ig_ll
from scipy.stats import fisk
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
c = 3.09
mean, var, skew, kurt = fisk.stats(c, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(fisk.ppf(0.01, c),
fisk.ppf(0.99, c), 100)
ax.plot(x, fisk.pdf(x, c),
'r-', lw=5, alpha=0.6, label='fisk 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 = fisk(c)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = fisk.ppf([0.001, 0.5, 0.999], c)
np.allclose([0.001, 0.5, 0.999], fisk.cdf(vals, c))
# True
# plt.xscale('log',base=2)
#a,b,c=LogLogisticLikelihood(Runtimes[22:])
#logistic=fisk.pdf(Runtimes[22:],a,loc=b,scale=c)
# fig=plt.figure()
# plt.plot(Runtimes[22:],logistic,lw=3,alpha=2.5)
# plt.xscale('log',base=2)
#initialize the distributions
# dist=[]
# for i in range(len(gauss1)):
# dist.append((logistic[i]+gauss1[i])/2)
# fig = plt.figure()
gauss1 = gauss(Runtimes[0:21], [1, 0.865, 0.02])
logistic = fisk.pdf(Runtimes[21:], 1, loc=7.4859, scale=0.8139)
plt.subplot(2, 1, 1)
plt.plot(Runtimes[0:21], gauss1, lw=3, alpha=2.5)
plt.xscale('log', base=2)
plt.subplot(2, 1, 2)
plt.plot(Runtimes[21:], logistic, lw=3, alpha=2.5)
plt.xscale('log', base=2)
plt.tight_layout()
plt.show()
#dist=np.concatenate((gaussian,logistic))
# plt.title("the two distributions")
# plt.xscale('log',base=2)
# plt.tight_layout()
# plt.plot(Runtimes,dist,lw=3,alpha=2.5)
