def test_findTruncNormalRoots(self):
"""Tests whether our root finder for a truncated normal
works in the case of a standard normal truncated at 0"""
from numpy import sqrt
from math import pi
# These are the analytic values of mean and variance of a standard normal
# truncated on the left at 0.
truncMean = 2.0 / sqrt(2*pi)
truncVarnce = 1.0 - 4.0/(2.0*pi)
muInit = truncMean
sigmaInit = sqrt(truncVarnce)
minThreshRefl = 0
mu, sigma = findTruncNormalRoots(truncMean,truncVarnce,
muInit,sigmaInit,
minThreshRefl)
self.assertAlmostEqual(mu, 0, places=10)
self.assertAlmostEqual(sigma, 1, places=10)
plt.xlabel('Time [' + time_offset_radar_refl.units + ']')
plt.ylabel('Altitude [m]')
plt.figure()
radar_refl_nc.close()
# Compute mean and variance of truncated time series
truncMean = mean( reflCompressed )
truncVarnce = var( reflCompressed )
print "truncMean = %s" %truncMean
print "sqrt(truncVarnce) = %s" %sqrt(truncVarnce)
# Compute parameters of truncated normal distribution
muInit = 2*truncMean
sigmaInit = 2*sqrt(truncVarnce)
mu, sigma = findTruncNormalRoots(truncMean,truncVarnce,muInit,sigmaInit,minThreshRefl)
print "mu = %s" %mu
print "sigma = %s" %sigma
# Compute empirical distribution function of data
reflCompressedSorted = sort(reflCompressed)
reflEdf = (rankdata(reflCompressedSorted) - 1)/lenReflCompressed
normCdf = norm.cdf( reflCompressedSorted, loc=truncMean, scale=sqrt(truncVarnce) )
truncNormCdf = ( norm.cdf(reflCompressedSorted,mu,sigma) \
- norm.cdf((minRefl-mu)/sigma) ) \
/(1.0-norm.cdf((minRefl-mu)/sigma))
minRefl = amin(reflCompressedSorted)
expMuLogN = (truncMean-minRefl)/sqrt(1+truncVarnce/((truncMean-minRefl)**2))
sigma2LogN = log(1+truncVarnce/((truncMean-minRefl)**2))
lognormCdf = lognorm.cdf( reflCompressedSorted - minRefl, sqrt(sigma2LogN),
loc=0, scale=expMuLogN )
