"""
import copy
import math
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats
import statspy as sp
import statspy.interval
X = sp.RV("norm(x|mux=20,sigmax=5)")
x = X(size=100)
print 'True values: mu = 20, sigma = 5'
pdf_fit = sp.PF("pdf_fit=norm(x|mu=1,sigma=1)")
mu = sp.get_obj('mu')
sigma = sp.get_obj('sigma')
# First compute 95% CL bounds
mu.value = x.mean() - x.std()
sigma.value = x.std() * 0.5
mu.unc = 0
sigma.unc = 0
params, corr, quantile = statspy.interval.pllr(pdf_fit, x, cl=0.95)
bounds_95cl = []
for par in params:
bounds_95cl.append([par.value + par.neg_unc, par.value + par.pos_unc])
# Second compute 1-sigma positive/negative uncertainties (68.27% CL)
mu.value = x.mean() - x.std()
sigma.value = x.std() * 0.5
"""
import copy
import math
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats
import statspy as sp
import statspy.interval
X = sp.RV("norm(x|mux=20,sigmax=5)")
x = X(size=100)
print 'True values: mu = 20, sigma = 5'
pdf_fit = sp.PF("pdf_fit=norm(x|mu=1,sigma=1)")
mu = sp.get_obj('mu')
sigma = sp.get_obj('sigma')
# First compute 95% CL bounds
mu.value = x.mean() - x.std()
sigma.value = x.std() * 0.5
mu.unc = 0
sigma.unc = 0
params, corr, quantile = statspy.interval.pllr(pdf_fit, x, cl=0.95)
bounds_95cl = []
for par in params:
bounds_95cl.append([par.value + par.neg_unc, par.value + par.pos_unc])
# Second compute 1-sigma positive/negative uncertainties (68.27% CL)
mu.value = x.mean() - x.std()
sigma.value = x.std() * 0.5
handles, labels = ax_mul.get_legend_handles_labels()
ax_mul.legend(handles[::-1], labels[::-1])
# Division
X4 = sp.RV("norm(x4;mux4=1.,sigmax4=0.05)")
Y4 = sp.RV("norm(y4;muy4=1.,sigmay4=0.05)")
Z4 = X4 / Y4
ax_div = fig.add_subplot(324)
mean_Z4 = Z4.pf.mean()
rms_Z4 = Z4.pf.std()
z4 = np.linspace(mean_Z4 - 5 * rms_Z4, mean_Z4 + 5 * rms_Z4, 200)
ax_div.plot(z4, X4.pf(z4), label='X')
ax_div.plot(z4, Y4.pf(z4), label='Y')
ax_div.plot(z4, Z4.pf(z4), label='X/Y')
handles, labels = ax_div.get_legend_handles_labels()
ax_div.legend(handles[::-1], labels[::-1])
# Rescaling
mux = sp.get_obj('mux')
sigmax = sp.get_obj('sigmax')
Z5 = (X - mux) / sigmax
ax_res = fig.add_subplot(325)
z5 = np.linspace(mux.value - 7 * sigmax.value, mux.value + 3 * sigmax.value, 200)
ax_res.plot(z5, X.pf(z5), label='X')
ax_res.plot(z5, Z5.pf(z5), label='(X-$\mu$)/$\sigma$')
handles, labels = ax_res.get_legend_handles_labels()
ax_res.legend(handles[::-1], labels[::-1])
plt.show()
fig.savefig('rv_operations.png', dpi=fig.dpi)
nobs = scipy.stats.poisson.rvs(nexp, size=1)[0]
data = pdf_true.rvs(size=nobs)
fig = plt.figure()
fig.patch.set_color('w')
ax = fig.add_subplot(111)
# Build histogram of the data
ydata, bins, patches = ax.hist(data, 30, range=[50, 200], log=True,
facecolor='green', alpha=0.75, label='Data')
xdata = 0.5*(bins[1:]+bins[:-1]) # Bin centers
dx = bins[1:] - bins[:-1] # Bin widths
# Define the background and signal PFs
pdf_fit_bkg = sp.PF("pdf_fit_bkg=expon(x;offset=50,lambda=10)")
sp.get_obj("lambda").label = "\\lambda"
offset = sp.get_obj('offset')
offset.const = True # Fix parameter value
#pdf_fit_bkg.norm.value = nobs
#sidebands = np.logical_or((xdata < 100), (xdata > 150))
#pdf_fit_bkg.leastsq_fit(xdata, ydata, dx=dx, cond=sidebands)
pdf_fit_sig = sp.PF("pdf_fit_sig=norm(x;mu=120,sigma=20)")
sp.get_obj("mu").label = "\\mu"
sp.get_obj("sigma").label = "\\sigma"
pdf_fit = pdf_fit_bkg + pdf_fit_sig
pdf_fit.name = 'pdf_fit'
pdf_fit.norm.const = False # Fit total rate to data
pdf_fit.norm.label = 'Norm'
pdf_fit.norm.value = nobs
pdf_fit_sig.norm.label = 'frac(sig)'
# Least square fit to the data (whole data range)