def GetRandomDistribution(n):
# --- Definition of some standard given values -----------------------
AverageHousePrice = 228147 # [ £ ]
Gradient = 78147.0
Intercept = 150000
# --- Number holders -------------------------------------------------
x = np.linspace(moyal.ppf(0.01), moyal.ppf(0.99), 1000)
y = []
gen = []
# --- Calculating the distribution based on moyal curve --------------
for i in x:
y.append(moyal.pdf(i-2))
cdf = I.cumtrapz(y, dx = ((x[-1] - x[1])/len(x)), initial=0)
for i in range(n):
gen.append(np.interp(np.random.uniform(), cdf, x))
return gen
import numpy as np
from scipy.stats import moyal, crystalball
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# plot moyal pdf
loc, scale = 0, 0.625
x = np.linspace(moyal.ppf(0.01, loc, scale), moyal.ppf(0.99, loc, scale), 100)
ax.plot(x, moyal.pdf(x, loc, scale), 'r-', alpha=0.6, label='moyal pdf')
# plot crystal ball pdf
beta, m = 2, 3
x = np.linspace(crystalball.ppf(0.01, beta, m), crystalball.ppf(0.99, beta, m),
100)
ax.plot(x,
crystalball.pdf(x, beta, m),
'b-',
alpha=0.6,
label='crystalball pdf')
plt.legend()
plt.show()
def fitfunc(x, a, mu, sigma):
return a * moyal.pdf(x, mu, sigma)
) # / (%i MeV)"%(int(hEnergy[1][-1]-hEnergy[1][0])/len(hEnergy[0])))
ax2.set_xlabel("Total Energy Deposited in Hadronic Calorimeter [GeV]")
ax2.set_ylabel("Number of Events")
mu1, std1 = moyal.fit(100 - totalECAL[totalECAL < 1.1e5]) #this for electron
#mu1,std1=moyal.fit(totalECAL[totalECAL<1.1e5]) #this for proton and muon
mu2, std2 = moyal.fit(
totalHCAL[totalHCAL < 1.1e5]) #this for electron and muon
#mu2,std2=moyal.fit(100-totalHCAL[totalHCAL<1.1e5]) #this for proton
xVals1 = 100 - ((hECAL[1][1:] + hECAL[1][:-1]) / 2) #this for electron
#xVals1=((hECAL[1][1:]+hECAL[1][:-1])/2) #this for proton and muon
xVals2 = (hHCAL[1][1:] + hHCAL[1][:-1]) / 2 #this for electron and muon
#xVals2=100-(hHCAL[1][1:]+hHCAL[1][:-1])/2 #this for proton
normaliser1 = len(
totalECAL[totalECAL < 1.1e5]) * np.abs(hECAL[1][1] - hECAL[1][0])
fitVals1 = moyal.pdf(xVals1, mu1, std1) * normaliser1
normaliser2 = len(
totalHCAL[totalHCAL < 1.1e5]) * np.abs(hHCAL[1][1] - hHCAL[1][0])
fitVals2 = moyal.pdf(xVals2, mu2, std2) * normaliser2
#chiSqGauss=np.sum((h[0][boolChooseBins]-normaliser*norm.pdf(((h[1][boolChoose])[:-1]+(h[1][boolChoose])[1:])/2, mu, std))**2/(normaliser*norm.pdf(((h[1][boolChoose])[:-1]+(h[1][boolChoose])[1:])/2, mu, std))**2)/(len(boolChooseBins)-2)
chiSq1 = np.sum(((hECAL[0][hECAL[0] > 0] - fitVals1[hECAL[0] > 0]) /
np.sqrt(hECAL[0][hECAL[0] > 0]))**2) / (len(hECAL[0]) - 2)
chiSq2 = np.sum(((hHCAL[0][hHCAL[0] > 0] - fitVals2[hHCAL[0] > 0]) /
np.sqrt(hHCAL[0][hHCAL[0] > 0]))**2) / (len(hHCAL[0]) - 2)
ax1.plot(
np.linspace(hECAL[1][0], hECAL[1][-1], 1000),
normaliser1 *
moyal.pdf(100 - np.linspace(hECAL[1][0], hECAL[1][-1], 1000), mu1, std1),
plt.figure()
h = plt.hist(momentumValues,
bins="auto",
fill=False,
ec="b",
label="Entries: %i" % len(momentumValues))
momentumValues = np.array(momentumValues)
xmin, xmax = initMom - initMom / 100 * 35, initMom + initMom / 100 * 70
#mu,std=norm.fit(momentumValues[(momentumValues>xmin)&(momentumValues<xmax)])
mu, std = moyal.fit(momentumValues[(momentumValues > xmin)
& (momentumValues < xmax)])
xVals = np.linspace(xmin, xmax, 100)
# fitNumbers = norm.pdf(xVals, mu, std)
fitNumbers = moyal.pdf(xVals, mu, std)
boolChoose = (h[1] > xmin) & (h[1] < xmax
) #bool to choose bins within fitting area
boolChooseBins = (boolChoose[:-1].astype(int) +
boolChoose[1:].astype(int)) == 2
#boolChooseBins=[]
print(boolChooseBins)
normaliser = len(
momentumValues[(momentumValues > xmin)
& (momentumValues < xmax)]) * np.abs(h[1][1] - h[1][0])
#chiSqGauss=np.sum((h[0][boolChooseBins]-normaliser*norm.pdf(((h[1][boolChoose])[:-1]+(h[1][boolChoose])[1:])/2, mu, std))**2/(normaliser*norm.pdf(((h[1][boolChoose])[:-1]+(h[1][boolChoose])[1:])/2, mu, std))**2)/(len(boolChooseBins)-2)
chiSqGauss = np.sum(
(h[0][boolChooseBins] - normaliser * moyal.pdf(
((h[1][boolChoose])[:-1] + (h[1][boolChoose])[1:]) / 2, mu, std))**2 /
(normaliser * moyal.pdf(
from scipy.stats import moyal import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) # Calculate a few first moments: mean, var, skew, kurt = moyal.stats(moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(moyal.ppf(0.01), moyal.ppf(0.99), 100) ax.plot(x, moyal.pdf(x), 'r-', lw=5, alpha=0.6, label='moyal 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 = moyal() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = moyal.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], moyal.cdf(vals)) # True # Generate random numbers: r = moyal.rvs(size=1000)
import numpy as np
from scipy.stats import moyal, norm
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# plot moyal pdf
loc, scale = 0.004, 0.006
x = np.linspace(moyal.ppf(0.01, loc=loc, scale=scale),
moyal.ppf(0.99, loc=loc, scale=scale), 100)
ax.plot(x,
moyal.pdf(x, loc=loc, scale=scale),
'r',
alpha=0.6,
label='moyal pdf')
# plot moyal samples
s_moyal = moyal.rvs(loc, scale, size=1000)
ax.hist(s_moyal, 40, alpha=0.6, density=True, label='moyal histogram')
# plot normal pdf
mu, sigma = 0, 0.014 # mean and standard deviation
x = np.linspace(norm.ppf(0.01, loc=mu, scale=sigma),
norm.ppf(0.99, loc=mu, scale=sigma), 100)
ax.plot(x,
norm.pdf(x, loc=mu, scale=sigma),
'b',
alpha=0.6,
label='normal pdf')
# plot normal samples