double alnorm ( double x, bool upper );
void chi_square_cdf_values ( int *n_data, int *a, double *x, double *fx );
double gammad ( double x, double p, int *ifault );
double ppchi2 ( double p, double v, double g, int *ifault );
double ppnd ( double p, int *ifault );
double r8_min ( double x, double y );