def truncated_normal_ab_cdf_inv ( cdf, mu, sigma, a, b ):
#*****************************************************************************80
#
## TRUNCATED_NORMAL_AB_CDF_INV inverts the truncated Normal CDF.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, real CDF, the value of the CDF.
# 0.0 <= CDF <= 1.0.
#
# Input, real MU, SIGMA, the mean and standard deviation of the
# parent Normal distribution.
#
# Input, real A, B, the lower and upper truncation limits.
#
# Output, real X, the corresponding argument.
#
from normal_01_cdf import normal_01_cdf
from normal_01_cdf_inv import normal_01_cdf_inv
from sys import exit
if ( cdf < 0.0 or 1.0 < cdf ):
print ( '' )
print ( 'TRUNCATED_NORMAL_AB_CDF_INV - Fatal error!' )
print ( ' CDF < 0 or 1 < CDF.' )
exit ( 'TRUNCATED_NORMAL_AB_CDF_INV - Fatal error!' )
alpha = ( a - mu ) / sigma
beta = ( b - mu ) / sigma
alpha_cdf = normal_01_cdf ( alpha )
beta_cdf = normal_01_cdf ( beta )
xi_cdf = ( beta_cdf - alpha_cdf ) * cdf + alpha_cdf
xi = normal_01_cdf_inv ( xi_cdf )
x = mu + sigma * xi
return x
def truncated_normal_a_cdf_inv ( cdf, mu, sigma, a ):
#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_CDF_INV inverts the lower truncated Normal CDF.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, real CDF, the value of the CDF.
# 0.0 <= CDF <= 1.0.
#
# Input, real MU, SIGMA, the mean and standard deviation of the
# parent Normal distribution.
#
# Input, real A, the lower truncation limit.
#
# Output, real X, the corresponding argument.
#
from normal_01_cdf import normal_01_cdf
from normal_01_cdf_inv import normal_01_cdf_inv
from sys import exit
if ( cdf < 0.0 or 1.0 < cdf ):
print ''
print 'TRUNCATED_NORMAL_A_CDF_INV - Fatal error!'
print ' CDF < 0 or 1 < CDF.'
exit ( 'TRUNCATED_NORMAL_A_CDF_INV - Fatal error!' )
alpha = ( a - mu ) / sigma
alpha_cdf = normal_01_cdf ( alpha )
beta_cdf = 1.0
xi_cdf = ( beta_cdf - alpha_cdf ) * cdf + alpha_cdf
xi = normal_01_cdf_inv ( xi_cdf )
x = mu + sigma * xi
return x
def truncated_normal_ab_sample(mu, sigma, a, b, seed):
#*****************************************************************************80
#
## TRUNCATED_NORMAL_AB_SAMPLE samples the Truncated Normal distribution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 08 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, real MU, SIGMA, the mean and standard deviation of the
# parent Normal distribution.
#
# Input, real A, B, the lower and upper truncation limits.
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, real X, a sample of the PDF.
#
# Output, integer SEED, a seed for the random number generator.
#
from normal_01_cdf import normal_01_cdf
from normal_01_cdf_inv import normal_01_cdf_inv
from r8_uniform_01 import r8_uniform_01
alpha = (a - mu) / sigma
beta = (b - mu) / sigma
alpha_cdf = normal_01_cdf(alpha)
beta_cdf = normal_01_cdf(beta)
u, seed = r8_uniform_01(seed)
xi_cdf = alpha_cdf + u * (beta_cdf - alpha_cdf)
xi = normal_01_cdf_inv(xi_cdf)
x = mu + sigma * xi
return x, seed
def truncated_normal_ab_sample ( mu, sigma, a, b, seed ): #*****************************************************************************80 # ## TRUNCATED_NORMAL_AB_SAMPLE samples the Truncated Normal distribution. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 08 March 2015 # # Author: # # John Burkardt # # Parameters: # # Input, real MU, SIGMA, the mean and standard deviation of the # parent Normal distribution. # # Input, real A, B, the lower and upper truncation limits. # # Input, integer SEED, a seed for the random number generator. # # Output, real X, a sample of the PDF. # # Output, integer SEED, a seed for the random number generator. # from normal_01_cdf import normal_01_cdf from normal_01_cdf_inv import normal_01_cdf_inv from r8_uniform_01 import r8_uniform_01 alpha = ( a - mu ) / sigma beta = ( b - mu ) / sigma alpha_cdf = normal_01_cdf ( alpha ) beta_cdf = normal_01_cdf ( beta ) u, seed = r8_uniform_01 ( seed ) xi_cdf = alpha_cdf + u * ( beta_cdf - alpha_cdf ) xi = normal_01_cdf_inv ( xi_cdf ) x = mu + sigma * xi return x, seed
def normal_ms_cdf_inv(cdf, mu, sigma):
#*****************************************************************************80
#
## NORMAL_MS_CDF_INV inverts the CDF of the Normal MS distribution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, real CDF, the value of the CDF.
# 0.0 <= CDF <= 1.0.
#
# Input, real MU, SIGMA, the parameters of the PDF.
# 0.0 < SIGMA.
#
# Output, real VALUE, the corresponding argument.
#
from normal_01_cdf_inv import normal_01_cdf_inv
if (cdf < 0.0 or 1.0 < cdf):
print ''
print 'NORMAL_MS_CDF_INV - Fatal error!'
print ' CDF < 0 or 1 < CDF.'
error('NORMAL_MS_CDF_INV - Fatal error!')
y = normal_01_cdf_inv(cdf)
value = mu + sigma * y
return value
def normal_ms_cdf_inv ( cdf, mu, sigma ):
#*****************************************************************************80
#
## NORMAL_MS_CDF_INV inverts the CDF of the Normal MS distribution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 05 March 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, real CDF, the value of the CDF.
# 0.0 <= CDF <= 1.0.
#
# Input, real MU, SIGMA, the parameters of the PDF.
# 0.0 < SIGMA.
#
# Output, real VALUE, the corresponding argument.
#
from normal_01_cdf_inv import normal_01_cdf_inv
if ( cdf < 0.0 or 1.0 < cdf ):
print ''
print 'NORMAL_MS_CDF_INV - Fatal error!'
print ' CDF < 0 or 1 < CDF.'
error ( 'NORMAL_MS_CDF_INV - Fatal error!' )
y = normal_01_cdf_inv ( cdf )
value = mu + sigma * y
return value
