[Retracted] Comparison of Five Methods to Estimate the Parameters for the Three-Parameter Lindley Distribution with Application to Life Data

Code 1

clc

clear

%Number of Trials (10000).

m=1;M=zeros(3,5);MSE=zeros(3,5);MAE=zeros(3,5);MRE=zeros(3,5);

for j=1:m

%Size of sample, theta's, alpha's and beta's Values, you can change them.

P=[10 1 3 2]; %[n T A B]

n=P(1); %Size of sample

T=P(2); %theta

A=P(3); %alpha

B=P(4); %beta

for i=1:n

end

x=round(x',4);

z=sort(x);

syms T A B

%Initial

y0=[P(2) P(3) P(4)];

%MLE

S1=0;S2=0;S3=0;

for i=1:n

S1=S1+x(i)/n;

S2=S2+log((x(i)));

S3=S3+x(i)^2/n;

end

;

F=@(y) double(LL(y(1),y(2),y(3)));

[TAB,fval,exitflag1]=fminunc(F,y0);

T_ML=TAB(1);

A_ML=TAB(2);

B_ML=TAB(3);

%OLE.

S=0;

for i=1:n

;

end

S(T,A,B)=S;

F=@(y) double(S(y(1),y(2),y(3)));

[TAB,fval,exitflag2]=fminunc(F,y0);

T_LS=TAB(1);

A_LS=TAB(2);

B_LS=TAB(3);

%WLS.

S=0;

for i=1:n

;

;

end

S(T,A,B)=S;

F=@(y) double(S(y(1),y(2),y(3)));

[TAB,fval,exitflag3]=fminunc(F,y0);

T_WLS=TAB(1);

A_WLS=TAB(2);

B_WLS=TAB(3);

%MPS

syms u

;

;

S=0;

y(1)=0;z(n+1)=inf;

for i=1:n+1.

y(i+1)=z(i);

D(i)=CF(y(i+1))-CF(y(i));

if D(i)==0

S=S+log(pdf(y(i)));

else

S=S+log(D(i));

end

end

S(T,A,B)=-S/(n+1);

F=@(y) double(S(y(1),y(2),y(3)));

[TAB,fval,exitflag4]=fminunc(F,y0);

T_MPS=TAB(1);

A_MPS=TAB(2);

B_MPS=TAB(3);

%CVM

S=0;

for i=1:n

;

end

S(T,A,B)=S+1/(n);

F=@(y) double(S(y(1),y(2),y(3)));

[TAB,fval,exitflag5]=fminunc(F,y0);

T_CVM=TAB(1);

A_CVM=TAB(2);

B_CVM=TAB(3);

E=[P(2) T_ML T_LS T_WLS T_MPS T_CVM;P(3) A_ML A_LS A_WLS A_MPS A_CVM;P(4) B_ML B_LS B_WLS B_MPS B_CVM];%Real MLE,OLS,WLS,MPS,CVM.

E_ML=(E(:,2)-E(:,1));

E_LS=(E(:,3)-E(:,1));

E_WLS=(E(:,4)-E(:,1));

E_MPS=(E(:,5)-E(:,1));

E_CVM=(E(:,6)-E(:,1));

%if max(abs(sum(E(:,2:6),2)/5-P(:,2:4)'))<sum(P(:,2:4))

(exitflag1+exitflag2+exitflag3+exitflag4+exitflag5)

if (exitflag1+exitflag2+exitflag3+exitflag4+exitflag5)>=5

M=M+E(:,2:6)

MSE=MSE+[E_ML E_LS E_WLS E_MPS E_CVM].^2

MAE=MAE+abs([E_ML E_LS E_WLS E_MPS E_CVM])

end

end

M=M/m;

MSE=MSE/m;

MAE=MAE/m;