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Package gammp (in gammp.i) -
Index of documented functions or symbols:
DOCUMENT 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))
DOCUMENT 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).
DOCUMENT 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).