# The Kuiper GOF:
# this is the most correcrt:
Vn, Vc, pVn, H0_K2, lev_K2 = DFST.Kuiper_GOF( cX_c )
print('Kuiper GOF =', Vn, pVn, H0_K2, lev_K2)
# The R2 coefficient:
fX_r2 = np.zeros(len(x1),)
for mu, kap, pii in zip(loc_mle, kap_mle, p_mle):
temp = stats.vonmises( kap, mu, scal_ )
fX_r2 += pii*temp.pdf( x1 )
dx = np.diff(x1)
cX_r2 = np.ones(len(x1),)
cX_r2[0:-1] = np.cumsum(fX_r2[0:-1]*dx)
R2 = DFST.myR2( cX_r2, cfX_obs )
print('R2 =', R2)
if R2 > 0.90:
H0_R2 = "Do not reject"
else:
H0_R2 = "Reject"
# Plot the Probability-Probability Plot:
DFST.PP_GOF( cX_r2, cfX_obs )
# ---------------------------------------------------------------------- #
#%% Collect all results into a Pandas dataFrame:
gof_list = ["Waston", "Kuiper", "R2"]
gof_stats = np.array([U2, Vn, R2])
gof_crVal = np.array([uc, Vc, 1.0])
gof_pvals = np.array([pu2, pVn, 1.0])
U2, Us, uc, pu2, pus = DFst.watson( cfX_tot, alphal=2 )
print('1st DFst.watson =',U2, Us, uc, pu2, pus)
Vn, pVn = DFst.Kuiper_GOF( cfX_tot )
print('1st Kuiper:', Vn, pVn)
# --------------------------------------------------------------- #
# get the CDF of the postulated distribution:
# using the bins from the histogram of the random sample:
# so the CDF is computed over equally-spaced points:
print('# ------- Case with bins from histogram (equally-spaced): -------- #')
cfX_temp1 = fX_i.cdf(bins)
# make the P-P plot:
DFst.PP_GOF( cfX_temp1[0:-1], cdfX_samp )
# compute the R2 coefficient:
R2 = DFst.myR2( cfX_temp1[0:-1], cdfX_samp )
print('R2 (cumsum-1):', R2)
# make the P-P plot:
DFst.PP_GOF( cfX_temp1[0:-1], EEE )
# compute the R2 coefficient:
R2 = DFst.myR2( cfX_temp1[0:-1], EEE )
print('R2 (cumsum-2):', R2)
# a. compute the K-S statistic
# we CAN because of the form of the statistic, being the difference of the
# model and the emprirical CDFs:
d00 = np.array([1.63, 1.36, 1.22])/np.sqrt(len(cdfX_samp))
Dm = abs(cfX_temp1[0:-1] - cdfX_samp)
D = max(Dm)
sqnD = np.sqrt(len(cdfX_samp))*D
pval = 1 - DFst.KS_CDF( sqnD )
dx = abs(x[0] - x[1])
fig, ax = plt.subplots(1, 1, figsize=(4, 3))
ax.set_title('CDF plot')
ax.plot(x, cfX_obs, 'b', lw=3, alpha=0.6, label='ECDF, ecdf()')
ax.plot(x,
np.cumsum(X_tot * dx),
'r--',
lw=2,
alpha=0.6,
label='CDF model')
#ax.plot(x, cXtot, 'g', lw=2, alpha=0.6, label='CDF fit +=')
ax.set_xlabel(r'$\theta$ (rads)', fontsize=12)
ax.set_ylabel('Cumulative distribution', fontsize=12)
ax.legend()
R2 = DFST.myR2(np.cumsum(X_tot * dx), cfX_obs)
print('R2:', R2)
DFST.PP_GOF(np.cumsum(X_tot * dx), cfX_obs)
# this returns wrong conclusion:
U2, Us, uc, pu2, pus = DFST.watson_GOF(np.cumsum(X_tot * dx), alphal=2)
print('1st DFst.watson =', U2, Us, uc, pu2, pus)
#%% ------------------------------------------------------------------- #
# based on populated points for every angle based on its intensity:
# CAUTION !!!
# THIS IS THE CORRECT APPROACH !!!
aa = np.sort(p_X)
fX_t = np.zeros(len(aa), )
cX_t = np.zeros(len(aa), )