c2=20;b=20;a=80;d=40;(*Values of hyber parameters*)

sc=1;ns=1000;n=60;m=30;k=20;realα=2;realβ=1;T2=1.5;T3=2.5;T1=0.5;T=T3;
nmcmc=500;nburn=200;h=0.5; c1=0.5;q=0.5;Xα2=0;Xβ2=0;Xα1=0;t=10;Xβ1=0;XS1=0;XH1=0;realS=N[(((1+(t^(realβ))))^(-realα))];realH=N[realα  realβ (t^(realβ-1 ))(((1+(t^(realβ))))^(-1))];XS2=0;Xα3=0;Xβ3=0;XS3=0;XH3=0;XH2=0;

Do[Label[repeat];c2=20;b=20;a=80;d=40;(*Values of hyber parameters*);R={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,30};
(*R={2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0};*)w=RandomVariate[UniformDistribution[],m];
Do[v[i]=(((w[[i]]))^(1/(i+(∑_(j=0)^(i-1))R[[m-j]]))),{i,1,m}];
Do[u[i]=1-(∏_(j=0)^(i-1))v[m-j],{i,1,m}];
Do[x[i]=((((((1-u[i]))^(-(1/(realα))))-1))^(1/(realβ))),{i,1,m}];
Do[If[x[i]<T,J=i,],{i,1,m}];RT=0;
If[J< k,D1=k;c=(((1+(((x[J+1]))^(realβ))))^(realα));u1=RandomVariate[UniformDistribution[],n-(∑_(i=1)^J)R[[i]]-J-1];xx=Sort[((((((((1-u1)/c)))^(-(1/(realα))))-1))^(1/(realβ)))];Do[x[i]=xx[[1]];xx=Delete[xx,1],{i,J+2,D1}];Do[R[[i]]=0,{i,J+1,k-1}];R[[k]]=n-k-(∑_(i=1)^J)R[[i]],If[k≤ J<m,D1=J;RT=n-J-(∑_(i=1)^J)R[[i]],D1=m]];
L=D1 (Log[β]+Log[α])+(β-1) (∑_(i=1)^D1)Log[x[i]]-(∑_(i=1)^D1)Log[1+(((x[i]))^β)]-α((∑_(i=1)^D1)(1+R[[i]])Log[1+(((x[i]))^β)]+RT Log[1+(T^β)]);
αM[jj]=α/.FindRoot[{(∂_α) L==0,(∂_β) L==0},{α,realα},{β,realβ}];
βM[jj]=β/.FindRoot[{(∂_α) L==0,(∂_β) L==0},{α,realα},{β,realβ}];
SM[jj]=(((1+(t^(βM[jj]))))^(-αM[jj]));HM[jj]=αM[jj] βM[jj] (t^(βM[jj]-1 ))(((1+(t^(βM[jj]))))^(-1));
If[αM[jj]<0,Goto[repeat], ];
f11[β_,α_]=-D[L,α,α];
f22[β_,α_]=-D[L,β,β];
f21[β_,α_]=-D[L,β,α];
f12[β_,α_]=-D[L,α,β];
m1=Inverse[{{f11[βM[jj],αM[jj]],f12[βM[jj],αM[jj]]},{f21[βM[jj],αM[jj]],f22[βM[jj],αM[jj]]}}];
MatrixForm[m1];(*If[m1[[2,2]]<0, Goto[repeat],Goto[end1]];Label[end1];*)
Lα1[jj]=αM[jj]-1.96*(m1[[1,1]])^0.5; Uα1[jj]=αM[jj]+1.96*m1[[1,1]]^0.5; Aα1[jj]=Uα1[jj]-Lα1[jj];If[Lα1[jj]<realα<Uα1[jj],Xα1=Xα1+1,Xα1];
Lβ1[jj]=βM[jj]-1.96*m1[[2,2]]^0.5; Uβ1[jj]=βM[jj]+1.96*m1[[2,2]]^0.5;Aβ1[jj]=Uβ1[jj]-Lβ1[jj];If[Lβ1[jj]<realβ<Uβ1[jj],Xβ1=Xβ1+1,Xβ1];
(******************************** 95% Confidence Interval for S(t) and H(t)***********************************)
G1=(({{-(((1+(t^(βM[jj]))))^(-αM[jj]))Log[1+(t^(βM[jj]))], -αM[jj](t^(βM[jj]))(((1+(t^(βM[jj]))))^(-αM[jj]-1))Log[t]}}));
G2=(({{βM[jj] (t^(βM[jj]-1))(((1+(t^(βM[jj]))))^(-1)), αM[jj]((1+(t^(βM[jj])))((t^(βM[jj]-1))+βM[jj](t^(βM[jj]-1)) Log[t])-βM[jj](t^(2βM[jj]-1))Log[t])(((1+(t^(βM[jj]))))^(-2))}}));
VS=G1.m1.Transpose[G1];VH=G2.m1.Transpose[G2];
LS1[jj]=SM[jj]-1.96*(VS[[1,1]])^0.5; US1[jj]=SM[jj]+1.96*(VS[[1,1]])^0.5; AS1[jj]=US1[jj]-LS1[jj];If[LS1[jj]<realS<US1[jj],XS1=XS1+1,XS1];
LH1[jj]=HM[jj]-1.96*(VH[[1,1]])^0.5; UH1[jj]=HM[jj]+1.96*(VH[[1,1]])^0.5;AH1[jj]=UH1[jj]-LH1[jj];If[LH1[jj]<realH<UH1[jj],XH1=XH1+1,XH1];
(***********************************MCMC method for Informative priros**********************************************************)
W1[β_]:=(∑_(i=1)^D1)(1+R[[i]])Log[1+(((x[i]))^β)]+RT Log[1+(T^β)]+β d;
(*conditonal posterior distn of alpha*)

α2[0]=αM[jj];β2[0]=βM[jj];
Do[   g1[α_,β_]:=(β^(D1+a+c2-1))(E^(-β b-α W1[β]))((∏_(i=1)^D1)((((x[i]))^(β-1))/(1+(((x[i]))^β))));
βstar1=-1;
While[βstar1<0,βstar1=RandomReal[NormalDistribution[β2[o-1],m1[[2,2]]^0.5]]];
r1=Min[1,g1[α2[o-1],βstar1]/g1[α2[o-1],β2[o-1]]];
If[RandomReal[]≤r1, β2[o]=βstar1, β2[o]= β2[o-1]];
α2[o]=RandomReal[GammaDistribution[(D1+a),1/W1[β2[o]]]]
,{o,1,nmcmc}];
alpha2=Table[α2[i],{i,nburn,nmcmc}];alpha22=Sort[alpha2];beta2=Table[β2[i],{i,nburn,nmcmc}];beta22=Sort[beta2];
Lα2[jj]=alpha22[[Ceiling[(nmcmc-nburn)*0.025]]];Uα2[jj]=alpha22[[Ceiling[(nmcmc-nburn)*0.975]]];Aα2[jj]=Uα2[jj]-Lα2[jj];If[Lα2[jj]<realα<Uα2[jj],Xα2=Xα2+1,Xα2];
Lβ2[jj]=beta22[[Ceiling[(nmcmc-nburn)*0.025]]];Uβ2[jj]=beta22[[Ceiling[(nmcmc-nburn)*0.975]]];Aβ2[jj]=Uβ2[jj]-Lβ2[jj];If[Lβ2[jj]<realβ<Uβ2[jj],Xβ2=Xβ2+1,Xβ2];
Do[S2[i]=N[(((1+(t^(β2[i]))))^(-α2[i]))];H2[i]=N[α2[i]  β2[i] (t^(β2[i]-1 ))(((1+(t^(β2[i]))))^(-1))],{i,1,nmcmc}];Stable=Sort[Table[S2[i],{i,nburn,nmcmc}]];Htable=Sort[Table[H2[i],{i,nburn,nmcmc}]];
LS2[jj]=Stable[[Ceiling[(nmcmc-nburn)*0.025]]];US2[jj]=Stable[[Ceiling[(nmcmc-nburn)*0.975]]];AS2[jj]=US2[jj]-LS2[jj];If[LS2[jj]<realS<US2[jj],XS2=XS2+1,XS2];
LH2[jj]=Htable[[Ceiling[(nmcmc-nburn)*0.025]]];UH2[jj]=Htable[[Ceiling[(nmcmc-nburn)*0.975]]];AH2[jj]=UH2[jj]-LH2[jj];If[LH2[jj]<realH<UH2[jj],XH2=XH2+1,XH2];
αmc2[jj]=((∑_(i=nburn+1)^nmcmc)α2[i])/(nmcmc-nburn);                                                                                                                                                     
βmc2[jj]=((∑_(i=nburn+1)^nmcmc)β2[i])/(nmcmc-nburn);
αlB2[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  α2[i])))/(nmcmc-nburn)];                                                                                                                                                     
βlB2[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  β2[i])))/(nmcmc-nburn)];     
αeB2[jj]=(((((∑_(i=nburn+1)^nmcmc)(((α2[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));                                                                                                                                                     
βeB2[jj]=(((((∑_(i=nburn+1)^nmcmc)(((β2[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));  
(*αB2[jj]=((∑_(i=nburn+1)^nmcmc)(((α2[i]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((α2[i]))^c1));
βB2[jj]=((∑_(i=nburn+1)^nmcmc)(((β2[i]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((β2[i]))^c1));
*)
Smc2[jj]=((∑_(i=nburn+1)^nmcmc)S2[i])/(nmcmc-nburn);                                                                                                                                                     
Hmc2[jj]=((∑_(i=nburn+1)^nmcmc)H2[i])/(nmcmc-nburn);
SlB2[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  S2[i])))/(nmcmc-nburn)];                                                                                                                                                     
HlB2[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  H2[i])))/(nmcmc-nburn)];     
SeB2[jj]=(((((∑_(i=nburn+1)^nmcmc)(((S2[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));                                                                                                                                                     
HeB2[jj]=(((((∑_(i=nburn+1)^nmcmc)(((H2[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));
(*SB2[jj]=((∑_(i=nburn+1)^nmcmc)(((Stable[[i]]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((Stable[[i]]))^c1));
HB2[jj]=((∑_(i=nburn+1)^nmcmc)(((Htable[[i]]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((Htable[[i]]))^c1))*)
(***********************************MCMC method for Non-Informative priros**********************************************************)
c2=0;b=0;a=0 ; d=0;
W1[β_]:=(∑_(i=1)^D1)(1+R[[i]])Log[1+(((x[i]))^β)]+RT Log[1+(T^β)]+β d;
(*conditonal posterior distn of alpha*)

α3[0]=αM[jj];β3[0]=βM[jj];
Do[   g1[α_,β_]:=(β^(D1+a+c2-1))(E^(-β b-α W1[β]))((∏_(i=1)^D1)((((x[i]))^(β-1))/(1+(((x[i]))^β))));
βstar1=-1;
While[βstar1<0,βstar1=RandomReal[NormalDistribution[β3[o-1],m1[[2,2]]^0.5]]];
r1=Min[1,g1[α3[o-1],βstar1]/g1[α3[o-1],β3[o-1]]];
If[RandomReal[]≤r1, β3[o]=βstar1, β3[o]= β3[o-1]];
α3[o]=RandomReal[GammaDistribution[(D1+a),1/W1[β3[o]]]]
,{o,1,nmcmc}];
alpha3=Table[α3[i],{i,nburn,nmcmc}];alpha33=Sort[alpha3];beta3=Table[β3[i],{i,nburn,nmcmc}];beta33=Sort[beta3];
Lα3[jj]=alpha33[[Ceiling[(nmcmc-nburn)*0.025]]];Uα3[jj]=alpha33[[Ceiling[(nmcmc-nburn)*0.975]]];Aα3[jj]=Uα3[jj]-Lα3[jj];If[Lα3[jj]<realα<Uα3[jj],Xα3=Xα3+1,Xα3];
Lβ3[jj]=beta33[[Ceiling[(nmcmc-nburn)*0.025]]];Uβ3[jj]=beta33[[Ceiling[(nmcmc-nburn)*0.975]]];Aβ3[jj]=Uβ3[jj]-Lβ3[jj];If[Lβ3[jj]<realβ<Uβ3[jj],Xβ3=Xβ3+1,Xβ3];
Do[S3[i]=N[(((1+(t^(β3[i]))))^(-α3[i]))];H3[i]=N[α3[i]  β3[i] (t^(β3[i]-1 ))(((1+(t^(β3[i]))))^(-1))],{i,1,nmcmc}];Stable3=Sort[Table[S3[i],{i,nburn,nmcmc}]];Htable3=Sort[Table[H3[i],{i,nburn,nmcmc}]];
LS3[jj]=Stable3[[Ceiling[(nmcmc-nburn)*0.025]]];US3[jj]=Stable3[[Ceiling[(nmcmc-nburn)*0.975]]];AS3[jj]=US3[jj]-LS3[jj];If[LS3[jj]<realS<US3[jj],XS3=XS3+1,XS3];
LH3[jj]=Htable3[[Ceiling[(nmcmc-nburn)*0.025]]];UH3[jj]=Htable3[[Ceiling[(nmcmc-nburn)*0.975]]];AH3[jj]=UH3[jj]-LH3[jj];If[LH3[jj]<realH<UH3[jj],XH3=XH3+1,XH3];
αmc3[jj]=((∑_(i=nburn+1)^nmcmc)α3[i])/(nmcmc-nburn);                                                                                                                                                     
βmc3[jj]=((∑_(i=nburn+1)^nmcmc)β3[i])/(nmcmc-nburn);
αlB3[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  α3[i])))/(nmcmc-nburn)];                                                                                                                                                     
βlB3[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  β3[i])))/(nmcmc-nburn)];     
αeB3[jj]=(((((∑_(i=nburn+1)^nmcmc)(((α3[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));                                                                                                                                                     
βeB3[jj]=(((((∑_(i=nburn+1)^nmcmc)(((β3[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));  
(*αB2[jj]=((∑_(i=nburn+1)^nmcmc)(((α2[i]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((α2[i]))^c1));
βB2[jj]=((∑_(i=nburn+1)^nmcmc)(((β2[i]))^(c1+1)))/((∑_(i=nburn+1)^nmcmc)(((β2[i]))^c1));
*)
Smc3[jj]=((∑_(i=nburn+1)^nmcmc)S3[i])/(nmcmc-nburn);                                                                                                                                                     
Hmc3[jj]=((∑_(i=nburn+1)^nmcmc)H3[i])/(nmcmc-nburn);
SlB3[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  S3[i])))/(nmcmc-nburn)];                                                                                                                                                     
HlB3[jj]=((-1)/h)Log[((∑_(i=nburn+1)^nmcmc)(E^(-h  H3[i])))/(nmcmc-nburn)];     
SeB3[jj]=(((((∑_(i=nburn+1)^nmcmc)(((S3[i]))^(-q)))/(nmcmc-nburn)))^(-1/q));                                                                                                                                                     
HeB3[jj]=(((((∑_(i=nburn+1)^nmcmc)(((H3[i]))^(-q)))/(nmcmc-nburn)))^(-1/q))
,{jj,1,ns}];
(*********************************MLE Estimates  *****************************)
αML=Round[(1/ns)*(∑_(i=1)^ns)αM[i],0.0001];βML=Round[(1/ns)*(∑_(i=1)^ns)βM[i],0.0001];
MαML=Round[(1/ns)*(∑_(i=1)^ns)(αM[i]-realα)^2,0.00001];
MβML=Round[(1/ns)*(∑_(i=1)^ns)(βM[i]-realβ)^2,0.00001];
BαML=Round[(Abs[αML-realα]),0.0001];BβML=Round[(Abs[βML-realβ]),0.0001];
(*********************************Bayesian Estimates (SEL) For Informative Priros  *****************************)
αBs=Round[(1/ns)*(∑_(i=1)^ns)αmc2[i],0.0001];βBs=Round[(1/ns)*(∑_(i=1)^ns)βmc2[i],0.0001];
MαBs=Round[(1/ns)*(∑_(i=1)^ns)(αmc2[i]-realα)^2,0.00001];
MβBs=Round[(1/ns)*(∑_(i=1)^ns)(βmc2[i]-realβ)^2,0.00001];
BαBs=Round[(Abs[αBs-realα]),0.0001];BβBs=Round[(Abs[βBs-realβ]),0.0001];
SBs=Round[(1/ns)*(∑_(i=1)^ns)Smc2[i],0.00001];HBs=Round[(1/ns)*(∑_(i=1)^ns)Hmc2[i],0.00001];
MSBs=Round[(1/ns)*(∑_(i=1)^ns)(Smc2[i]-realS)^2,0.000001];
MHBs=Round[(1/ns)*(∑_(i=1)^ns)(Hmc2[i]-realH)^2,0.000001];
BSBs=Round[(Abs[SBs-realS]),0.000001];BHBs=Round[(Abs[HBs-realH]),0.000001];
(********************************Bayesian under Linex For Informative Priors***********************************)
αBl=Round[(1/ns)*(∑_(i=1)^ns)αlB2[i],0.0001];βBl=Round[(1/ns)*(∑_(i=1)^ns)βlB2[i],0.0001];
MαBl=Round[(1/ns)*(∑_(i=1)^ns)(αlB2[i]-realα)^2,0.00001];
MβBl=Round[(1/ns)*(∑_(i=1)^ns)(βlB2[i]-realβ)^2,0.00001];
BαBl=Round[(Abs[αBl-realα]),0.0001];BβBl=Round[(Abs[βBl-realβ]),0.0001];
SBl=Round[(1/ns)*(∑_(i=1)^ns)SlB2[i],0.00001];HBl=Round[(1/ns)*(∑_(i=1)^ns)HlB2[i],0.00001];
MSBl=Round[(1/ns)*(∑_(i=1)^ns)(SlB2[i]-realS)^2,0.000001];
MHBl=Round[(1/ns)*(∑_(i=1)^ns)(HlB2[i]-realH)^2,0.000001];
BSBl=Round[(Abs[SBl-realS]),0.000001];BHBl=Round[(Abs[HBl-realH]),0.000001];

(********************************Bayesian under G Entropy  For Informative priors***********************************)
αBe=Round[(1/ns)*(∑_(i=1)^ns)αeB2[i],0.0001];βBe=Round[(1/ns)*(∑_(i=1)^ns)βeB2[i],0.0001];
MαBe=Round[(1/ns)*(∑_(i=1)^ns)(αeB2[i]-realα)^2,0.00001];
MβBe=Round[(1/ns)*(∑_(i=1)^ns)(βeB2[i]-realβ)^2,0.00001];
BαBe=Round[(Abs[αBe-realα]),0.0001];BβBe=Round[(Abs[βBe-realβ]),0.0001];
SBe=Round[(1/ns)*(∑_(i=1)^ns)SeB2[i],0.0001];HBe=Round[(1/ns)*(∑_(i=1)^ns)HeB2[i],0.0001];
MSBe=Round[(1/ns)*(∑_(i=1)^ns)(SeB2[i]-realS)^2,0.000001];
MHBe=Round[(1/ns)*(∑_(i=1)^ns)(HeB2[i]-realH)^2,0.000001];
BSBe=Round[(Abs[SBe-realS]),0.00001];BHBe=Round[(Abs[HBe-realH]),0.00001];


(*(*********************************Bayesian  Estimates based on Al-Bayatti  loss function c1=0.5*****************************)
αBB=Round[(1/ns)*(∑_(i=1)^ns)αB2[i],0.0001];βBB=Round[(1/ns)*(∑_(i=1)^ns)βB2[i],0.0001];
MαBB=Round[(1/ns)*(∑_(i=1)^ns)(αB2[i]-realα)^2,0.00001];MβBB=Round[(1/ns)*(∑_(i=1)^ns)(βB2[i]-realβ)^2,0.00001];
BαBB=Round[(Abs[αBB-realα]),0.0001];BβBB=Round[(Abs[βBB-realβ]),0.0001];
*)
(********************* 95% Credible intervals for α, β based on informative priors******************)
AVGα2=Round[(1/ns)*(∑_(i=1)^ns)Aα2[i],0.0001];GPα2=Round[N[Xα2/ns],0.0001]; 
AVGβ2=Round[(1/ns)*(∑_(i=1)^ns)Aβ2[i],0.0001];GPβ2=Round[N[Xβ2/ns],0.0001];
(********************* 95% Credible intervals for S, H based on informative priors******************)
AVGS2=Round[(1/ns)*(∑_(i=1)^ns)AS2[i],0.0001];GPS2=Round[N[XS2/ns],0.0001]; 
AVGH2=Round[(1/ns)*(∑_(i=1)^ns)AH2[i],0.0001];GPH2=Round[N[XH2/ns],0.0001];
(********************* 95% Asymptotic confidence intervals for α, β ******************)
AVGα1=Round[(1/ns)*(∑_(i=1)^ns)Aα1[i],0.0001];GPα1=Round[N[Xα1/ns],0.001]; 
AVGβ1=Round[(1/ns)*(∑_(i=1)^ns)Aβ1[i],0.0001];GPβ1=Round[N[Xβ1/ns],0.001];
(*********************************MLE Estimates for S and H  *****************************)
SML=Round[(1/ns)*(∑_(i=1)^ns)SM[i],0.0001];HML=Round[(1/ns)*(∑_(i=1)^ns)HM[i],0.0001];
MSML=Round[(1/ns)*(∑_(i=1)^ns)(SM[i]-realS)^2,0.00001];
MHML=Round[(1/ns)*(∑_(i=1)^ns)(HM[i]-realH)^2,0.00001];
BSML=Round[(Abs[SML-realS]),0.0001];BHML=Round[(Abs[HML-realH]),0.0001];
(********************* 95% Asymptotic confidence intervals for S, H ******************)
AVGS1=Round[(1/ns)*(∑_(i=1)^ns)AS1[i],0.00001];GPS1=Round[N[XS1/ns],0.0001]; 
AVGH1=Round[(1/ns)*(∑_(i=1)^ns)AH1[i],0.00001];GPH1=Round[N[XS1/ns],0.0001];
(*********************************Bayesian Estimates (SEL) For Non-Informative Priros  *****************************)
αBs3=Round[(1/ns)*(∑_(i=1)^ns)αmc3[i],0.001];βBs3=Round[(1/ns)*(∑_(i=1)^ns)βmc3[i],0.0001];
MαBs3=Round[(1/ns)*(∑_(i=1)^ns)(αmc3[i]-realα)^2,0.0001];
MβBs3=Round[(1/ns)*(∑_(i=1)^ns)(βmc3[i]-realβ)^2,0.0001];
BαBs3=Round[(Abs[αBs3-realα]),0.00001];BβBs3=Round[(Abs[βBs3-realβ]),0.00001];
SBs3=Round[(1/ns)*(∑_(i=1)^ns)Smc3[i],0.00001];HBs3=Round[(1/ns)*(∑_(i=1)^ns)Hmc3[i],0.00001];
MSBs3=Round[(1/ns)*(∑_(i=1)^ns)(Smc3[i]-realS)^2,0.0001];
MHBs3=Round[(1/ns)*(∑_(i=1)^ns)(Hmc3[i]-realH)^2,0.0001];
BSBs3=Round[(Abs[SBs3-realS]),0.00001];BHBs3=Round[(Abs[HBs3-realH]),0.00001];
(********************************Bayesian under Linex For Non-Informative Priors***********************************)
αBl3=Round[(1/ns)*(∑_(i=1)^ns)αlB3[i],0.0001];βBl3=Round[(1/ns)*(∑_(i=1)^ns)βlB3[i],0.0001];
MαBl3=Round[(1/ns)*(∑_(i=1)^ns)(αlB3[i]-realα)^2,0.0001];
MβBl3=Round[(1/ns)*(∑_(i=1)^ns)(βlB3[i]-realβ)^2,0.0001];
BαBl3=Round[(Abs[αBl3-realα]),0.00001];BβBl3=Round[(Abs[βBl3-realβ]),0.00001];
SBl3=Round[(1/ns)*(∑_(i=1)^ns)SlB3[i],0.00001];HBl3=Round[(1/ns)*(∑_(i=1)^ns)HlB3[i],0.00001];
MSBl3=Round[(1/ns)*(∑_(i=1)^ns)(SlB3[i]-realS)^2,0.0001];
MHBl3=Round[(1/ns)*(∑_(i=1)^ns)(HlB3[i]-realH)^2,0.0001];
BSBl3=Round[(Abs[SBl3-realS]),0.00001];BHBl3=Round[(Abs[HBl3-realH]),0.00001];
(********************************Bayesian under G Entropy  For Non-Informative priors***********************************)
αBe3=Round[(1/ns)*(∑_(i=1)^ns)αeB3[i],0.0001];βBe3=Round[(1/ns)*(∑_(i=1)^ns)βeB3[i],0.0001];
MαBe3=Round[(1/ns)*(∑_(i=1)^ns)(αeB3[i]-realα)^2,0.0001];
MβBe3=Round[(1/ns)*(∑_(i=1)^ns)(βeB3[i]-realβ)^2,0.0001];
BαBe3=Round[(Abs[αBe3-realα]),0.00001];BβBe3=Round[(Abs[βBe3-realβ]),0.00001];
SBe3=Round[(1/ns)*(∑_(i=1)^ns)SeB3[i],0.0001];HBe3=Round[(1/ns)*(∑_(i=1)^ns)HeB3[i],0.0001];
MSBe3=Round[(1/ns)*(∑_(i=1)^ns)(SeB3[i]-realS)^2,0.0001];
MHBe3=Round[(1/ns)*(∑_(i=1)^ns)(HeB3[i]-realH)^2,0.0001];
BSBe3=Round[(Abs[SBe3-realS]),0.00001];BHBe3=Round[(Abs[HBe3-realH]),0.00001];
(********************* 95% Credible intervals for α, β based on Non-Informative priors******************)
AVGα3=Round[(1/ns)*(∑_(i=1)^ns)Aα3[i],0.0001];GPα3=Round[N[Xα3/ns],0.00001]; 
AVGβ3=Round[(1/ns)*(∑_(i=1)^ns)Aβ3[i],0.0001];GPβ3=Round[N[Xβ3/ns],0.00001];
(********************* 95% Credible intervals for S, H based on Non-Informative priors******************)
AVGS3=Round[(1/ns)*(∑_(i=1)^ns)AS3[i],0.0001];GPS3=Round[N[XS3/ns],0.00001]; 
AVGH3=Round[(1/ns)*(∑_(i=1)^ns)AH3[i],0.0001];GPH3=Round[N[XH3/ns],0.00001];


(***************************************Table of Data************************************)
Print[Style[Grid[{{"ns","T","n","m","k","Sch","realα","realβ","nmcmc","nburn","a","b","c2","d"},{ns,T,n ,m,k,sc ,realα,realβ , 
nmcmc, nburn  ,   a,b, c2,d}},Dividers->All,ItemSize->Automatic,Background->{{Pink},{Yellow},None}],FontSize->18]];
Print[Style[Grid[{{"Parameter","","MLE","BS(IP)","BS(NIP)","BL(IP)","BL(NIP)","BE(IP)","BE(NIP)",Grid[{{"ACI"},{"AL"}}],Grid[{{"ACI"},{"CP"}}],Grid[{{"BCI(IP)"},{"AL"}}],Grid[{{"BCI(IP)"},{"CP"}}],Grid[{{"BCI(NIP)"},{"AL"}}],Grid[{{"BCI(NIP)"},{"CP"}}]},
{"α","EB",BαML,BαBs,BαBs3,BαBl,BαBl3,BαBe,BαBe3,AVGα1,GPα1,AVGα2,GPα2,AVGα3,GPα3},
{" ","MSE",MαML,MαBs,MαBs3,MαBl,MαBl3,MαBe,MαBe3,,,,,,},
{"β","EB",BβML,BβBs,BβBs3,BβBl,BβBl3,BβBe,BβBe3,AVGβ1,GPβ1,AVGβ2,GPβ2,AVGβ3,GPβ3},
{" ","MSE",MβML,MβBs,MβBs3,MβBl,MβBl3,MβBe,MβBe3,,,,,,},
{"S(t)","EB",BSML,BSBs,BSBs3,BSBl,BSBl3,BSBe,BSBe3,AVGS1,GPS1,AVGS2,GPS2,AVGS3,GPS3},
{" ","MSE",MSML,MSBs,MSBs3,MSBl,MSBl3,MSBe,MSBe3,,,,,,},
{"H(t)","EB",BHML,BHBs,BHBs3,BHBl,BHBl3,BHBe,BHBe3,AVGH1,GPH1,AVGH2,GPH2,AVGH3,GPH3},
{" ","MSE",MHML,MHBs,MHBs3,MHBl,MHBl3,MHBe,MHBe3,,,,,,}
},
Dividers->All,ItemSize->Automatic,Background->{{Pink},{Yellow},None}],FontSize->16]];