internal override double LogFSecond(double mu, SGNFnAParam A)
{
double z = mu / A.S;
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
return(A.N / A.S2 * (z * lphio.R[0] + lphio.R2[0] - 1));
}
internal static LPhiObject LPhi(double[] z)
{
//# z: can be scalar or vector
LPhiObject rep = new LPhiObject(z.Length);
/*
* lphi <- function(z)
* {
# z: can be scalar or vector
#
# log.phi <- dnorm(z, log=T) # log(phi(z))
# log.Phi <- pnorm(z, log.p=T) # log(Phi(z))
#
# r <- exp(log.phi-log.Phi) # phi(z)/Phi(z)
# r2 <- exp(2*(log.phi-log.Phi)) # phi^2(z) / Phi^2 (z)
#
# list(r=r, r2=r2) # r and r2 are of same length as z
# } # end of lphi
*/
double[] tmp = NormalDistribution.DNorm(z, give_log: true).Substract(NormalDistribution.PNorm(z, log_p: true));
rep.R = tmp.Exp(); // phi(z)/Phi(z)
rep.R2 = tmp.Multiply(2).Exp(); // phi^2(z) / Phi^2 (z)
return(rep);
}
internal override double LogFPrime(double mu, SGNFnAParam A)
{
double z = mu / A.S;
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
return(-A.N * (mu - A.MuMean) / A.S2 - A.N * lphio.R[0] / A.S);
}
internal override double LogFSecond(double s, SGNFnAParam A)
{
double z = A.Mu / s;
LPhiObject l = WebExpoFunctions3.LPhi(z);
return(A.N / Math.Pow(s, 2) - 6.0 * A.B / Math.Pow(s, 4) + A.N * z * ((Math.Pow(z, 2) - 2.0) * l.R[0] + z * l.R2[0]) / Math.Pow(s, 2));
}
internal override double LogFPrime(double s, SGNFnAParam A)
{
double z = A.Mu / s;
LPhiObject l = WebExpoFunctions3.LPhi(z);
return(-A.N / s + 2.0 * A.B / Math.Pow(s, 3) + A.N * z * l.R[0] / s);
}
internal override double LogFPrime(double v, SGNFnAParam A)
{
LPhiObject l = WebExpoFunctions3.LPhi(1 / v);
return
(-A.N / v
+ 2.0 * A.B / Math.Pow(v, 3)
+ A.N * l.R[0] / Math.Pow(v, 2));
}
internal override double LogFSecond(double s, SGNFnAParam A)
{
// log.f.prime <- function(s, A){z <- exp(s)/A$ksi; l <- lphi(z); -l$r*z + A$y*z/A$ksi - z^2 - (s-A$mu)/A$sigma2}
double[] z = new double[] { Math.Exp(s) / A.Ksi };
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
double r0 = lphio.R[0];
double z0 = z[0];
return(r0 * (Math.Pow(z0, 3) - z[0]) + Math.Pow(r0 * z0, 2) + (A.Y * Math.Exp(s) - 2.0 * Math.Exp(2 * s)) / A.Ksi2 - 1.0 / A.Sigma2);
}
internal override double LogFSecond(double v, SGNFnAParam A)
{
LPhiObject l = WebExpoFunctions3.LPhi(1 / v);
double v2 = Math.Pow(v, 2);
double v4 = Math.Pow(v2, 2);
return
(A.N / v2
- 6.0 * A.B / v4
+ A.N / v4 * (l.R[0] * (1 / v - 2.0 * v) + l.R2[0]));
}
internal override double LogFPrime(double s, SGNFnAParam A)
{
double z = A.Mu / s;
LPhiObject l = WebExpoFunctions3.LPhi(z);
return
(-(A.N + 1.0) / s
+ 2.0 * A.B / Math.Pow(s, 3)
- (Math.Log(s) - A.LM) / A.LS2 / s
+ A.N * z * l.R[0] / s);
}
internal override double LogFPrime(double s, SGNFnAParam A)
{
// log.f.prime <- function(s, A){z <- exp(s)/A$ksi; l <- lphi(z); -l$r*z + A$y*z/A$ksi - z^2 - (s-A$mu)/A$sigma2}
double z = Math.Exp(s) / A.Ksi;
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
return
(-lphio.R[0] * z
+ A.Y * z / A.Ksi
- Math.Pow(z, 2) - (s - A.Mu) / A.Sigma2);
}