
The distribution function of a random variable X distributed according to the Student's t distribution with 2 degrees of freedom is the continuous function, F(x) = P(X < x), given by F(x) = 
[ 1 + x / √(2 + x^{ 2}) ] / 2  for ∞ < x < ∞  

The corresponding probability density function, f(x) = dF(x)/dx, is f(x) =  [ 1 / ( n^{½} B(1/2,n/2) ) ] (1 + x² / n) ^{ (n+1) / 2} 


 double t2_Distribution( double x )
This function returns F(x) where F(x) is described above.
 double t2_Density( double x )
This function returns f(x) where f(x) is described above.
 void t2_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 this routine:
 The file, t2_distribution.c, contains the source code for the function t2_Distribution.
Dependencies: No external dependencies.
 The file, t2_density.c, contains the source code for the function t2_Density.
Dependencies: No external dependencies.
 The file, t2_dist_tables.c, contains the source code for the function t2_Distribution_Tables.
Dependencies: No external dependencies.
 The file, testt2dist.c, contains a test program of t2_Distribution( ) written in C. This test program requires the file t2_distribution.c.
 The file, T2DistributionTest.txt, contains the results of the test program testt2dist.c.
 The file, testt2dist.sh, contains the shell script used to compile, link, and execute the test program testt2dist.c.
 The file, testt2density.c, contains a test program of t2_Density( ) written in C. This test program requires the file t2_density.c.
 The file, T2DensityTest.txt, contains the results of the test program testt2density.c.
 The file, testt2density.sh, contains the shell script used to compile, link, and execute the test program testt2density.c.
 The file, testt2tables.c, contains a test program of t2_Distribution_Tables( ) written in C. This test program requires the files t2_distribution.c and t2_density.c listed above.
 The file, T2TablesTest.txt, contains the results of the test program testt2tables.c.
 The file, testt2tables.sh, contains the shell script used to compile, link, and execute the test program testt2tables.c.
