functions in gammp.i -

             betai(a, b, x)  
 
    return I_x(a,x) = int[0 to x]{ du * u^(a-1)*(1-u)^(b-1) } / beta(a,b)  
    the incomplete beta function  
    
    betai(a,b,x) = 1 - betai(b,a,1-x)  
    
    Note that Student's t-distribution is  
      A(t|nu) = 1 - betai(0.5*nu,0.5, nu/(nu+t^2))  
    The F-distribution is  
      Q(F|nu1,nu2) = betai(0.5*nu2,0.5*nu1, nu2/(nu2+F*nu1))  
    

             gammp(a, x)  
         or gammp(a, x, q, lg)  
 
    return P(a,x) = int[0 to x]{ du * u^(a-1)*exp(-u) } / gamma(a)  
    optionally return Q(a,x) = 1-P(a,x) and ln(gamma(a))  
    
    Note that erf(x)=gammp(0.5,x^2) and erfc(x)=gammq(0.5,x^2)  
    Also P(chi2|nu)=gammp(0.5*nu,0.5*chi2)  
     and Q(chi2|nu)=gammq(0.5*nu,0.5*chi2)  
    are the probabilities that an observed chi-square be less than  
    or greater than (P or Q) chi2 when there are nu degrees of freedom  
    (terms in the chi-square sum).  
    

             gammq(a, x)  
         or gammq(a, x, p, lg)  
 
    return Q(a,x) = 1 - int[0 to x]{ du * u^(a-1)*exp(-u) } / gamma(a)  
    optionally return P(a,x) = 1-Q(a,x) and ln(gamma(a))  
    
    Note that erf(x)=gammp(0.5,x^2) and erfc(x)=gammq(0.5,x^2)  
    Also P(chi2|nu)=gammp(0.5*nu,0.5*chi2)  
     and Q(chi2|nu)=gammq(0.5*nu,0.5*chi2)  
    are the probabilities that an observed chi-square be less than  
    or greater than (P or Q) chi2 when there are nu degrees of freedom  
    (terms in the chi-square sum).