double alngam ( double xvalue, int *ifault );
double alnorm ( double x, bool upper );
double betain ( double x, double p, double q, double beta, int *ifault );
double r8_abs ( double x );
void student_noncentral_cdf_values ( int *n_data, int *df, double *lambda, 
  double *x, double *fx );
void timestamp ( void );
double tnc ( double t, double df, double delta, int *ifault );