from scipy import stats
import rejectionSample
# Use rejection sampling to estimate the Nakagami distribution with nu = 1.0.
# Note that the distribution is only defined for x > 0. The reference
# distributin used is a gaussian centered about x = 1 with stdev = 1.
[samples, M, tAccept] = rejectionSample.rejectionSampler( \
'2 * 1**1 / gamma(1) * x**(2*1-1) * exp(-1.0*x**2)',\
'norm(1,1)', 5000, gzOnly=True )
from scipy import stats
import rejectionSample
# Calculate the samples according to the student t dist. with 2 deg. of
# freedom
[samples, M, tAccept] = rejectionSample.rejectionSampler( \
'(1/2.0)*exp(-abs(x))', 't(2)', 1000 )
# Use the ks test to test the samples for goodness of fit with the true
# laplacian distribution
(s, p) = stats.kstest(samples, 'laplace')
print '''The p-value from the k-s test of the rejection samples versus the
laplace distribution was: %s ''' %(p)
# Compare the acceptance rate to that of partb
[samples, M, cauchyAccept] = rejectionSample.rejectionSampler( \
'(1/2.0)*exp(-abs(x))', 'cauchy', 1000, verbose=False )
print '''The proportion accepted using the cauchy reference distribution: %s\nThe proportion accepted using the t(2) reference distribution: %s\n%s higher portion of samples were accepted from the t(2) reference ''' \
%(cauchyAccept, tAccept, abs(tAccept - cauchyAccept))
from scipy import stats
import rejectionSample
# Generate samples using the rejection scheme with the cauchy as a reference
[samples, M, proportion] = rejectionSample.rejectionSampler( \
'(1/2.0)*exp(-abs(x))', 'cauchy', 1000 )
# Perform the Kolmogorov-Smirinov test
(s, p) = stats.kstest(samples, 'laplace')
print '''The p-value from the k-s test of the rejection samples versus the
laplace distribution was: %s ''' %(p)