Hi all;
I recently have been used 'maxLik' function for maximizing G2StNV178 function
with gradient function gradlik; for receiving this goal, I write the following
program; but I have been seen an error in calling gradient function;
The maxLik function can't enter gradlik function (definition of gradient
function); I guess my mistake is in line ******** ,that the vector  âhâ is
defined.
Â
I need your advices for resolve the error;
Sincerely yours
A. Kheradmandi
##########data vector
x=c(0,0,14,7,0,22,2,18,10,29,
16,11,59,6,33,5,1,0,28,17,
28,19,10,43,9,17,42,2,22,6,
14,0,59,9,11,5,11,37,15,26,
57,8,16,22,5,13,19,12,34,8,28,35,13,11,59,
8,7,20,36,39,14,31,18,32,30,
29,9,2,5,3,19,27,76,4,32,
24,13,3,13,24,41,20,0,13,26,
0,23,19,10,14,14,13,15,18,29,
29,0,20,0,22,13,17,12,29,0,
0,16,55,11,19,9,2,9,32,16,
55,10,59,8,65,39,1,8,2,7,
37,8,0,5,8,0,7,0,20,10,
11,3,0,7,31,14,18,3,4,34,
32,4,9,9,8,36,44,0,9,27,28,55,72,12,1,
9,0,32,0,0,2,15,5,6,17,
63,61,9,15,15,0,2)
#########goal is found unique maximum for 5-parameter function with usingÂ
"maxLik" function
#####the function in latex commands is as following:
 \begin{eqnarray*}
&&\ell(\xi,\omega,\nu,\lambda_1,\lambda_2)=n\log2-n\log\omega+n\log\Gamma(\frac{\nu+1}{2})-\frac{n}{2}\log(\nu\pi)\\
&-&n\log\Gamma(\frac{\nu}{2})-\frac{\nu+1}{2}\sum_{i=1}^{n}\log(1+\frac{(x_i-\xi)^2}{\omega^2\nu})+\sum_{i=1}^{n}\log\Phi(\lambda_1\frac{(x_i-\xi)}{\sqrt{\omega^2+\lambda_2(x_i-\xi)^2}})
\end{eqnarray*}
##############
G2StNV178<-function(a){
require(maxLik)
II=0
nu<-(a[1])
lambda1<-a[2]
lambda2<-a[3]
ksi<-a[4]
omega<-a[5]
II<-log(prod((2*dt((x-ksi)/omega,nu)*pnorm((lambda1*(x-ksi)/omega)/sqrt(1+lambda2*((x-ksi)/omega)^2)))/omega))
II
}
########definition of gradient function
gradlik<- function(a){
nu<-a[1]
lambda1<-a[2]
lambda2<-a[3]
ksi<-a[4]
omega<-a[5]Â
#*******#
h<-c(f1=n*digamma((nu+1)/2)-n/(2*nu)-n*digamma(nu/2)-1/2*sum(log(1+(x-ksi)^2/(omega^2nu)))+(nu+1)/2*sum((x-ksi)^2/(omege^2*nu^2+nu*(x-ksi)^2)),
f2=sum((x-ksi)*dnorm(lambda1*(x-ksi)/sqrt(omega^2+lambda2*(x-ksi)^2))/(sqrt(omega^2+lambda2*(x-ksi)^2)*pnorm(lambda1*(x-ksi)/sqrt(omega^2+lambda2*(x-ksi))))),
f3=sum((lambda1*(x-ksi)^3*dnorm(lambda1*(x-ksi)/sqrt(omega^2+lambda2*(x-ksi)^2)))/(
2*omega^3*pnorm(lambda1*(x-ksi)/sqrt(omega^2+lambda2*(x-ksi)^2))
*sqrt((1+lambda2*(x-ksi)^2/omega^2 )^3))),
f4=(nu+1)*sum((x-ksi)/(omega^2*nu+(x-ksi)^2))-sum((lambda1*dnorm((lambda1*(x-ksi))/(omega^2+lambda2*(x-ksi)^2)))/(omega*sqrt(1+lambda2*(x-ksi)^2/(omega^2))
*pnorm(lambda1*(x-ksi)/(sqrt(omega^2+lambda2*(x-ksi)^2))))),
f5=-n/omega+(nu+1)*n*sum((x-ksi)^2/(nu*omega^3+omega*(x-ksi)^2))-sum((lambda1*(x-ksi)*omega*dnorm(lambda1*(x-ksi)/(sqrt(omega^2+lambda2*(x-ksi)^2))
/(pnorm(lambda1*(x-ksi)/(sqrt(omega^2+lambda2*(x-ksi)^2))*sqrt((omega^2+lambda2*(x-ksi)^2)^3)))))))
}
n<- length(x) # the final command is :
res<- maxLik(G2StNV178,grad=gradlik,start=c(4.666484 ,4603.399055 ,
4603.399055Â Â ,-0.016674 ,19.055865),tol=1e-16,iterlim =3000)
summary(res)
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