def rchisq(n,df,ncp=0):
"""
Generates random variables from the chi-square distribution
"""
from scipy.stats import chi2,ncx2
if ncp==0:
result=chi2.rvs(size=n,df=df,loc=0,scale=1)
else:
result=ncx2.rvs(size=n,df=df,nc=ncp,loc=0,scale=1)
return result
def direct_simulation(k, lamda, theta, X_0, T, N):
dt = T / N
c = (2 * k) / ((1 - np.exp(-k * dt)) * theta**2)
df = 4 * k * lamda / theta**2
X_temp = X_0
X_sol = np.zeros(N + 1)
X_sol[0] = X_0
for j in range(1, N + 1):
nc = 2 * c * X_temp * np.exp(-k * dt)
Y = ncx2.rvs(df, nc, size=1)
X_temp = Y / (2 * c)
X_sol[j] = X_temp
return np.linspace(0, T, N + 1), X_sol
def draw_signalData(Nsamp=1, alpha=__alpha, beta=__beta, **kwargs):
"""
draw an SNR from the signal distribution
"""
return np.array([ncx2.rvs(__noise_df, nc) for nc in __draw_truncatedPareto(Nsamp, alpha=alpha, beta=beta)])
def Gen_var_t(delta, kappa, theta, xi, var_s):
return c(delta, kappa, xi) * ncx2.rvs(d(kappa, theta, xi),
lbd(delta, kappa, xi, var_s))
fig = plt.figure(1, dpi=150)
ax = fig.add_subplot(111)
ax.set_xlim((0, 42))
ax.set_title('Analysis of PE')
ax.set_xlabel('TS')
ax.set_ylabel('pdf, normalized')
# parameters of non central chi squared distribution
df, nc = 10.09, 2.51
# plot the pdf
x = np.linspace(0, 43, num=1000)
y = ncx2.pdf(x, df, nc)
ax.plot(x, y, label=f'pdf, $df={df}, nc={nc}$', color='black', linewidth=0.8)
# generate some random numbers, do some histogram things
random = ncx2.rvs(df, nc, size=1000)
n, bins, patches = ax.hist(random,
bins=nbins,
label='random numbers',
density=True,
color='grey')
cum_bins = bins.copy()
cum_bins[-1] = 50
# do fit from random numbers
# get x places:
dx = (bins[1] - bins[0]) / 2
x_r = np.linspace(bins[0] + dx / 2, bins[-1] - dx / 2, num=len(bins))
#ax.plot(bins+dx, np.zeros(bins.shape[0]), 'o')
def fit_func(x, df, nc):
# Display the probability density function (``pdf``): x = np.linspace(ncx2.ppf(0.01, df, nc), ncx2.ppf(0.99, df, nc), 100) ax.plot(x, ncx2.pdf(x, df, nc), 'r-', lw=5, alpha=0.6, label='ncx2 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 = ncx2(df, nc) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = ncx2.ppf([0.001, 0.5, 0.999], df, nc) np.allclose([0.001, 0.5, 0.999], ncx2.cdf(vals, df, nc)) # True # Generate random numbers: r = ncx2.rvs(df, nc, size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show()