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log_normal_truncated_ab.cpp
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# include <cmath>
# include <cstdlib>
# include <cstring>
# include <ctime>
# include <iomanip>
# include <iostream>
using namespace std;
# include "log_normal_truncated_ab.hpp"
//****************************************************************************80
double log_normal_cdf ( double x, double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_CDF evaluates the Log Normal CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 September 2004
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, the argument of the PDF.
// 0.0 < X.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Output, double LOG_NORMAL_CDF, the value of the CDF.
//
{
double cdf;
double logx;
if ( x <= 0.0 )
{
cdf = 0.0;
}
else
{
logx = log ( x );
cdf = normal_cdf ( logx, mu, sigma );
}
return cdf;
}
//****************************************************************************80
double log_normal_cdf_inv ( double cdf, double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_CDF_INV inverts the Log Normal CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 September 2004
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double CDF, the value of the CDF.
// 0.0 <= CDF <= 1.0.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double LOG_NORMAL_CDF_INV, the corresponding argument.
//
{
double logx;
double x;
if ( cdf < 0.0 || 1.0 < cdf )
{
cerr << "\n";
cerr << "LOG_NORMAL_CDF_INV - Fatal error!\n";
cerr << " CDF < 0 or 1 < CDF.\n";
exit ( 1 );
}
logx = normal_cdf_inv ( cdf, mu, sigma );
x = exp ( logx );
return x;
}
//****************************************************************************80
double log_normal_pdf ( double x, double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_PDF evaluates the Log Normal PDF.
//
// Discussion:
//
// PDF(A,B;X)
// = exp ( - 0.5 * ( ( log ( X ) - MU ) / SIGMA )^2 )
// / ( SIGMA * X * sqrt ( 2 * PI ) )
//
// The Log Normal PDF is also known as the Cobb-Douglas PDF,
// and as the Antilog_normal PDF.
//
// The Log Normal PDF describes a variable X whose logarithm
// is normally distributed.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 September 2004
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, the argument of the PDF.
// 0.0 < X
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Output, double LOG_NORMAL_PDF, the value of the PDF.
//
{
double pdf;
const double r8_pi = 3.14159265358979323;
double y;
if ( x <= 0.0 )
{
pdf = 0.0;
}
else
{
y = ( log ( x ) - mu ) / sigma;
pdf = exp ( - 0.5 * y * y ) / ( sigma * x * sqrt ( 2.0 * r8_pi ) );
}
return pdf;
}
//****************************************************************************80
double log_normal_truncated_ab_cdf ( double x, double mu, double sigma,
double a, double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_CDF evaluates the Log Normal truncated AB CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, the argument of the PDF.
// 0.0 < X.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Output, double LOG_NORMAL_TRUNCATED_AB_CDF, the value of the CDF.
//
{
double cdf;
bool check;
double lncdf_a;
double lncdf_b;
double lncdf_x;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_CDF - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
if ( x <= a )
{
cdf = 0.0;
}
else if ( b <= x )
{
cdf = 1.0;
}
else
{
lncdf_a = log_normal_cdf ( a, mu, sigma );
lncdf_b = log_normal_cdf ( b, mu, sigma );
lncdf_x = log_normal_cdf ( x, mu, sigma );
cdf = ( lncdf_x - lncdf_a ) / ( lncdf_b - lncdf_a );
}
return cdf;
}
//****************************************************************************80
double log_normal_truncated_ab_cdf_inv ( double cdf, double mu, double sigma,
double a, double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_CDF_INV inverts the Log Normal truncated AB CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double CDF, the value of the CDF.
// 0.0 <= CDF <= 1.0.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Input, double LOG_NORMAL_TRUNCATED_AB_CDF_INV, the corresponding argument.
//
{
bool check;
double lncdf_a;
double lncdf_b;
double lncdf_x;
double x;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_CDF_INV - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
if ( cdf <= 0.0 )
{
x = a;
}
else if ( 1.0 <= cdf )
{
x = b;
}
else
{
lncdf_a = log_normal_cdf ( a, mu, sigma );
lncdf_b = log_normal_cdf ( b, mu, sigma );
lncdf_x = lncdf_a + cdf * ( lncdf_b - lncdf_a );
x = log_normal_cdf_inv ( lncdf_x, mu, sigma );
}
return x;
}
//****************************************************************************80
bool log_normal_truncated_ab_check ( double mu, double sigma, double a,
double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_CHECK checks the Log Normal truncated AB PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Output, bool LOG_NORMAL_TRUNCATED_AB_CHECK, is true if the parameters
// are legal.
//
{
bool check;
check = true;
if ( sigma <= 0.0 )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_CHECK - Fatal error!\n";
cerr << " SIGMA <= 0.\n";
check = false;
}
return check;
}
//****************************************************************************80
double log_normal_truncated_ab_mean ( double mu, double sigma, double a,
double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_MEAN: mean of the Log Normal truncated AB PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Output, double LOG_NORMAL_TRUNCATED_AB_MEAN, the mean of the PDF.
//
{
double a0;
double b0;
double c1;
double c2;
double c3;
double c4;
bool check;
double ln_mean;
double mean;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_MEAN - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
a0 = ( log ( a ) - mu ) / sigma;
b0 = ( log ( b ) - mu ) / sigma;
c1 = normal_01_cdf ( sigma - a0 );
c2 = normal_01_cdf ( sigma - b0 );
c3 = normal_01_cdf ( + a0 );
c4 = normal_01_cdf ( + b0 );
ln_mean = exp ( mu + 0.5 * sigma * sigma );
mean = ln_mean * ( c1 - c2 ) / ( c4 - c3 );
return mean;
}
//****************************************************************************80
double log_normal_truncated_ab_pdf ( double x, double mu, double sigma,
double a, double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_PDF evaluates the Log Normal truncated AB PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, the argument of the PDF.
// 0.0 < X
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Output, double LOG_NORMAL_TRUNCATED_AB_PDF, the value of the PDF.
//
{
bool check;
double lncdf_a;
double lncdf_b;
double lnpdf_x;
double pdf;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_PDF - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
if ( x <= a )
{
pdf = 0.0;
}
else if ( b <= x )
{
pdf = 0.0;
}
else
{
lncdf_a = log_normal_cdf ( a, mu, sigma );
lncdf_b = log_normal_cdf ( b, mu, sigma );
lnpdf_x = log_normal_pdf ( x, mu, sigma );
pdf = lnpdf_x / ( lncdf_b - lncdf_a );
}
return pdf;
}
//****************************************************************************80
double log_normal_truncated_ab_sample ( double mu, double sigma, double a,
double b, int &seed )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_SAMPLE samples the Log Normal truncated AB PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Input/output, int &SEED, a seed for the random number generator.
//
// Output, double LOG_NORMAL_TRUNCATED_AB_SAMPLE, a sample of the PDF.
//
{
double cdf;
bool check;
double lncdf_a;
double lncdf_b;
double x;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_SAMPLE - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
lncdf_a = log_normal_cdf ( a, mu, sigma );
lncdf_b = log_normal_cdf ( b, mu, sigma );
cdf = r8_uniform_ab ( lncdf_a, lncdf_b, seed );
x = log_normal_cdf_inv ( cdf, mu, sigma );
return x;
}
//****************************************************************************80
double log_normal_truncated_ab_variance ( double mu, double sigma, double a,
double b )
//****************************************************************************80
//
// Purpose:
//
// LOG_NORMAL_TRUNCATED_AB_VARIANCE: variance of Log Normal truncated AB PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 March 2016
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Input, double A, B, the lower and upper truncation limits.
// A < B.
//
// Output, double LOG_NORMAL_TRUNCATED_AB_VARIANCE, the variance of the PDF.
//
{
double a0;
double b0;
double c1;
double c2;
double c3;
double c4;
bool check;
double ln_xsquared;
double lntab_xsquared;
double mean;
double variance;
check = log_normal_truncated_ab_check ( mu, sigma, a, b );
if ( ! check )
{
cerr << "\n";
cerr << "LOG_NORMAL_TRUNCATED_AB_VARIANCE - Fatal error!\n";
cerr << " Parameters are not legal.\n";
exit ( 1 );
}
mean = log_normal_truncated_ab_mean ( mu, sigma, a, b );
a0 = ( log ( a ) - mu ) / sigma;
b0 = ( log ( b ) - mu ) / sigma;
c1 = normal_01_cdf ( 2.0 * sigma - a0 );
c2 = normal_01_cdf ( 2.0 * sigma - b0 );
c3 = normal_01_cdf ( + a0 );
c4 = normal_01_cdf ( + b0 );
ln_xsquared = exp ( 2.0 * mu + 2.0 * sigma * sigma );
lntab_xsquared = ln_xsquared * ( c1 - c2 ) / ( c4 - c3 );
variance = lntab_xsquared - mean * mean;
return variance;
}
//****************************************************************************80
double normal_01_cdf ( double x )
//****************************************************************************80
//
// Purpose:
//
// NORMAL_01_CDF evaluates the Normal 01 CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 February 1999
//
// Author:
//
// John Burkardt
//
// Reference:
//
// A G Adams,
// Areas Under the Normal Curve,
// Algorithm 39,
// Computer j.,
// Volume 12, pages 197-198, 1969.
//
// Parameters:
//
// Input, double X, the argument of the CDF.
//
// Output, double CDF, the value of the CDF.
//
{
double a1 = 0.398942280444;
double a2 = 0.399903438504;
double a3 = 5.75885480458;
double a4 = 29.8213557808;
double a5 = 2.62433121679;
double a6 = 48.6959930692;
double a7 = 5.92885724438;
double b0 = 0.398942280385;
double b1 = 3.8052E-08;
double b2 = 1.00000615302;
double b3 = 3.98064794E-04;
double b4 = 1.98615381364;
double b5 = 0.151679116635;
double b6 = 5.29330324926;
double b7 = 4.8385912808;
double b8 = 15.1508972451;
double b9 = 0.742380924027;
double b10 = 30.789933034;
double b11 = 3.99019417011;
double cdf;
double q;
double y;
//
// |X| <= 1.28.
//
if ( fabs ( x ) <= 1.28 )
{
y = 0.5 * x * x;
q = 0.5 - fabs ( x ) * ( a1 - a2 * y / ( y + a3 - a4 / ( y + a5
+ a6 / ( y + a7 ) ) ) );
//
// 1.28 < |X| <= 12.7
//
}
else if ( fabs ( x ) <= 12.7 )
{
y = 0.5 * x * x;
q = exp ( - y ) * b0 / ( fabs ( x ) - b1
+ b2 / ( fabs ( x ) + b3
+ b4 / ( fabs ( x ) - b5
+ b6 / ( fabs ( x ) + b7
- b8 / ( fabs ( x ) + b9
+ b10 / ( fabs ( x ) + b11 ) ) ) ) ) );
//
// 12.7 < |X|
//
}
else
{
q = 0.0;
}
//
// Take account of negative X.
//
if ( x < 0.0 )
{
cdf = q;
}
else
{
cdf = 1.0 - q;
}
return cdf;
}
//****************************************************************************80
double normal_01_cdf_inv ( double p )
//****************************************************************************80
//
// Purpose:
//
// NORMAL_01_CDF_INV inverts the standard normal CDF.
//
// Discussion:
//
// The result is accurate to about 1 part in 10**16.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 December 2004
//
// Author:
//
// Original FORTRAN77 version by Michael Wichura.
// C++ version by John Burkardt.
//
// Reference:
//
// Michael Wichura,
// The Percentage Points of the Normal Distribution,
// Algorithm AS 241,
// Applied Statistics,
// Volume 37, Number 3, pages 477-484, 1988.
//
// Parameters:
//
// Input, double P, the value of the cumulative probability
// densitity function. 0 < P < 1. If P is outside this range, an
// "infinite" value is returned.
//
// Output, double NORMAL_01_CDF_INV, the normal deviate value
// with the property that the probability of a standard normal deviate being
// less than or equal to this value is P.
//
{
double a[8] = {
3.3871328727963666080, 1.3314166789178437745e+2,
1.9715909503065514427e+3, 1.3731693765509461125e+4,
4.5921953931549871457e+4, 6.7265770927008700853e+4,
3.3430575583588128105e+4, 2.5090809287301226727e+3 };
double b[8] = {
1.0, 4.2313330701600911252e+1,
6.8718700749205790830e+2, 5.3941960214247511077e+3,
2.1213794301586595867e+4, 3.9307895800092710610e+4,
2.8729085735721942674e+4, 5.2264952788528545610e+3 };
double c[8] = {
1.42343711074968357734, 4.63033784615654529590,
5.76949722146069140550, 3.64784832476320460504,
1.27045825245236838258, 2.41780725177450611770e-1,
2.27238449892691845833e-2, 7.74545014278341407640e-4 };
double const1 = 0.180625;
double const2 = 1.6;
double d[8] = {
1.0, 2.05319162663775882187,
1.67638483018380384940, 6.89767334985100004550e-1,
1.48103976427480074590e-1, 1.51986665636164571966e-2,
5.47593808499534494600e-4, 1.05075007164441684324e-9 };
double e[8] = {
6.65790464350110377720, 5.46378491116411436990,
1.78482653991729133580, 2.96560571828504891230e-1,
2.65321895265761230930e-2, 1.24266094738807843860e-3,
2.71155556874348757815e-5, 2.01033439929228813265e-7 };
double f[8] = {
1.0, 5.99832206555887937690e-1,
1.36929880922735805310e-1, 1.48753612908506148525e-2,
7.86869131145613259100e-4, 1.84631831751005468180e-5,
1.42151175831644588870e-7, 2.04426310338993978564e-15 };
double q;
double r;
const double r8_huge = 1.0E+30;
double split1 = 0.425;
double split2 = 5.0;
double value;
if ( p <= 0.0 )
{
value = - r8_huge;
return value;
}
if ( 1.0 <= p )
{
value = r8_huge;
return value;
}
q = p - 0.5;
if ( fabs ( q ) <= split1 )
{
r = const1 - q * q;
value = q * r8poly_value_horner ( 7, a, r ) / r8poly_value_horner ( 7, b, r );
}
else
{
if ( q < 0.0 )
{
r = p;
}
else
{
r = 1.0 - p;
}
if ( r <= 0.0 )
{
value = r8_huge;
}
else
{
r = sqrt ( - log ( r ) );
if ( r <= split2 )
{
r = r - const2;
value = r8poly_value_horner ( 7, c, r ) / r8poly_value_horner ( 7, d, r );
}
else
{
r = r - split2;
value = r8poly_value_horner ( 7, e, r ) / r8poly_value_horner ( 7, f, r );
}
}
if ( q < 0.0 )
{
value = - value;
}
}
return value;
}
//****************************************************************************80
double normal_cdf ( double x, double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// NORMAL_CDF evaluates the Normal CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 September 2004
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, the argument of the CDF.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Output, double CDF, the value of the CDF.
//
{
double cdf;
double y;
y = ( x - mu ) / sigma;
cdf = normal_01_cdf ( y );
return cdf;
}
//****************************************************************************80
double normal_cdf_inv ( double cdf, double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// NORMAL_CDF_INV inverts the Normal CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 September 2004
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Algorithm AS 111,
// Applied Statistics,
// Volume 26, pages 118-121, 1977.
//
// Parameters:
//
// Input, double CDF, the value of the CDF.
// 0.0 <= CDF <= 1.0.
//
// Input, double MU, SIGMA, the parameters of the PDF.
// 0.0 < SIGMA.
//
// Output, double NORMAL_CDF_INV, the corresponding argument.
//
{
double x;
double x2;
if ( cdf < 0.0 || 1.0 < cdf )
{
cerr << "\n";
cerr << "NORMAL_CDF_INV - Fatal error!\n";
cerr << " CDF < 0 or 1 < CDF.\n";
exit ( 1 );
}
x2 = normal_01_cdf_inv ( cdf );
x = mu + sigma * x2;
return x;
}
//****************************************************************************80
bool normal_check ( double mu, double sigma )
//****************************************************************************80
//
// Purpose:
//
// NORMAL_CHECK checks the parameters of the Normal PDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//