double alnorm ( double x, bool upper );
void beta_noncentral_cdf_values ( int *n_data, double *a, double *b, 
  double *lambda, double *x, double *fx );
double betain ( double x, double p, double q, double beta, int *ifault );
double betanc ( double x, double a, double b, double lambda, int *ifault );
double gammad ( double x, double p, int *ifault );
double ncbeta ( double a, double b, double lambda, double x, double errmax, 
  int *ifault );
double r8_min ( double x, double y );