Математика \ Математическое моделирование физических процессов

Математическое моделирование в среде MATLAB компьютерный эксперимент на основе бутстреп – подхода (метода), страница 6

3.1997 -20.4687 6.6853 161.9111

2.8117 -20.9482 6.5279 162.1779

3.1664 -21.0637 6.3374 162.7393

2.7864 -20.2575 6.8158 162.4358

2.4984 -20.6846 6.7082 162.0099

3.0913 -20.5642 6.6328 161.9037

2.6621 -20.6901 6.2052 162.4883

2.5905 -20.8337 6.4628 162.3770

Yall =

6.0719 -19.1491 9.8373 165.2897

5.2901 -19.6243 8.5404 164.1257

5.4039 -21.1021 8.6097 163.6705

3.2741 -17.1903 12.8710 164.6585

6.6158 -18.2346 9.0057 166.7196

6.7152 -19.0349 9.2901 165.9242

3.4051 -15.8481 8.4309 164.4530

8.7645 -14.7943 10.9563 165.1408

7.2246 -20.3398 7.5563 167.1481

7.9144 -15.5130 10.0093 166.7199

6.1805 -18.1420 10.1556 166.0201

7.1599 -16.9574 7.4808 165.2733

3.5461 -16.7282 10.2308 164.6781

6.0613 -18.3470 9.5969 165.0340

4.9115 -16.8629 8.4037 163.7214

4.6745 -15.2243 12.5411 166.0598

2.8145 -20.4888 6.8743 162.1732

2.7300 -20.6144 6.3793 162.2295

2.5351 -20.7744 6.5124 162.6791

2.4826 -20.8751 6.2126 161.9913

2.4795 -20.4030 6.5088 162.1066

2.5271 -21.0645 6.6315 162.3103

3.2640 -20.5948 6.8780 162.3172

2.6547 -20.3785 6.6731 162.0635

3.1997 -20.4687 6.6853 161.9111

2.8117 -20.9482 6.5279 162.1779

3.1664 -21.0637 6.3374 162.7393

2.7864 -20.2575 6.8158 162.4358

2.4984 -20.6846 6.7082 162.0099

3.0913 -20.5642 6.6328 161.9037

2.6621 -20.6901 6.2052 162.4883

2.5905 -20.8337 6.4628 162.3770

MeanYB =

2.7684 -20.6690 6.5653 162.2446

MeanYall =

4.2971 -19.1811 8.0800 163.7672

Количество, когда Q_M > Q_MB:

sq_m =

Оценки параметров базовой модели, рассчитанные взвешенным МНК

Q_M =

5.8258

-4.2481

-2.9002

0.4920

Оценки параметров модели с учетом данных, сгенерированных бутстреп-методом, рассчитанные взвешенным МНК :

Q_MB =

4.2971

-4.2188

-2.9064

0.4923

3.3. По сгенерированным данным (п.1)

sigma = 1.5;

Q=[6 -4 -3 0.5];

N = 16;

X1=[0:0.1:10];

rnd=[];

Ysred=[];

k_intrv=5;

KB=100;

YB=[];

Yall=[];

MeanYall=[];

MeanYB=[];

PLAN=[

0 N;

2.765 N;

7.235 N;

10 N;

];

sq_m=0;

for l=1:KB

random = randn(N+1,4)*sigma;

Ysred = mean(Ymodel);

for i=1:N

for j=1:4

YB(i,j)=Ysred(j)+random(i,j);

end

Yall = [Ymodel;YB];

MeanYB = mean(YB);

MeanYall = mean(Yall);

Q_M=inv(F'*F)*F'*Ysred';

k=4;

D_MB=[];

for i= 1: k

sum = 0;

for j= 1: 2*N

sum = sum + (Yall(j,i)-MeanYall(i))^2;

end

D_MB(i) = (1/((2*N)*(2*N-1)))*sum;

end

D = diag(D_MB);

M = F'*inv(D)*F;

Q_MB=inv(M)*F'*inv(D)*MeanYall';

sqm=0;

sqmb=0;

for i= 1: k

sqm = sqm + (Q(i)-Q_M(i))^2;

sqmb = sqmb + (Q(i)-Q_MB(i))^2;

end

if sqm > sqmb

sq_m=sq_m+1;

end

Ymodel

Ysred

Yall

MeanYB

MeanYall

sq_m

Q_M

Q_MB

Результаты

Ymodel =

8.5444 -16.7598 9.8265 166.9943

7.0834 -18.9879 9.7658 166.1934

3.6379 -18.0983 9.1599 164.3775

4.3880 -16.7007 10.3927 166.5148

4.9292 -16.7954 8.8020 165.7917

7.4852 -15.9975 7.7978 166.7088

5.8611 -17.5693 12.0178 165.5934

7.1259 -17.5272 7.4251 166.5637

6.6186 -17.0837 12.4536 165.3449

6.4305 -15.5659 8.8766 165.8230

6.2121 -15.9700 10.1831 164.1200

6.3538 -16.3374 8.5878 166.9151

5.9857 -18.3566 7.3265 167.9977

6.1652 -19.3342 9.5829 165.5141

7.2786 -18.7227 9.6440 165.0974

8.1598 -17.9350 9.0559 164.5018

Ysred =

6.3912 -17.3588 9.4311 165.8782

YB =

3.5732 -19.3066 9.1647 167.7800

8.1687 -18.4595 12.7524 166.4022

8.0079 -15.7426 9.4738 166.9310

9.3369 -16.8263 10.6946 166.5361

5.3775 -18.4514 9.7028 165.9238

6.0888 -16.2601 10.9819 163.5222

5.1197 -17.1408 7.8966 166.5034

7.7729 -18.0997 8.9014 163.9780

5.3096 -17.2352 7.6208 166.4093

7.9773 -18.2365 10.7248 168.8782

4.1397 -17.3032 10.2841 164.6787

7.4922 -17.7366 9.0004 166.5097

6.9227 -16.5932 7.5252 165.0259

5.5793 -18.2443 7.6788 165.0293

3.9445 -15.5803 8.0816 170.7771

5.5234 -16.6379 9.8836 164.6498