
The distribution function of a random variable X distributed according to the Gaussian distribution is a continuous function, F(x) = P(X < x), given by F(x) = 
[ 1 / √(2π) ] ∫_{∞}^{x} e^{ ½ t²} dt  for ∞ < x < ∞ 


The corresponding probability density function, f(x) = dF(x)/dx, is f(x) =  [ 1 / √(2π) ] e^{ ½ x²}  for ∞ < x < ∞ 


 double Gaussian_Distribution( double x )
This function returns F(x) where F(x) is described above.
 double Gaussian_Density( double x )
This function returns f(x) where f(x) is described above.
 void Gaussian_Distribution_Tables( double start, double delta, int nsteps, double *density, double* distribution_function )
This function returns f(x) where f(x) is described above in the array density, i.e. density[i] = f(x_{i}) where x_{i} = start + i delta, i = 0,...,nsteps and returns F(x) where F(x) is described above in the array distribution_function, i.e. distribution_function[i] = F(x_{i}) where x_{i} = start + i delta, i = 0,...,nsteps. Note that density must be declared double density[N] where N ≥ nsteps + 1 in the calling routine and similarly the distribution_function must be declared double distribution_function[N] where N ≥ nsteps + 1 in the calling routine.
C source code is available for these routines:
 The file, gaussian_distribution.c, contains the source code for the function Gaussian_Distribution().
Dependencies: No external dependencies.
 The file, gaussian_density.c contains the source code for the function Gaussian_Density().
Dependencies: No external dependencies.
 The file, gaussian_dist_tables.c contains the source code for the function Gaussian_Distribution_Tables().
Dependencies: In addition to the the file gaussian_dist_tables.c, the function Gaussian_Distribution_Tables() requires the following files:
 The file gaussian_distribution.c.
 The file gaussian_density.c.
 The file, testgaussdist.c, contains a test program of Gaussian_Distribution( ) written in C. This test program requires the file gaussian_distribution.c listed above.
 The file, GaussianDistributionTest.txt, contains the results of the test program testgaussdist.c.
 The file, testgaussdist.sh, contains the shell script used to compile, link, and execute the test program testgaussdist.c.
 The file, testgaussdensity.c, contains a test program of Gaussian_Density( ) written in C. This test program requires the file gaussian_density.c listed above.
 The file, GaussianDensityTest.txt, contains the results of the test program testgaussdensity.c.
 The file, testgaussdensity.sh, contains the shell script used to compile, link, and execute the test program testgaussdensity.c.
 The file, testgausstables.c, contains a test program of Gaussian_Distribution_Tables( ) written in C. This test program requires the files gaussian_distribution.c and gaussian_density.c listed above.
 The file, GaussianTablesTest.txt, contains the results of the test program testgausstables.c.
 The file, testgausstables.sh, contains the shell script used to compile, link, and execute the test program testgausstables.c.
