Simulacion Promodel Ejercicios Unidad 3

8/22/2019 Simulacion Promodel Ejercicios Unidad 3

1/125

0.022 i Oi Ei ((Ei-Oi)^2)/Ei

0.119 1 0 - 2 23 10 16.9

0.154 2 2. -4 26 10 25.6

0.202 3 4.-6 17 10 4.90.433 4 6. -8 14 10 1.6

0.569 5 8. -10 6 10 1.6

0.818 6 10. - 12 5 10 2.5

0.843 7 12. -14 3 10 4.9

0.877 8 14 -16 2 10 6.4

1.182 9 16 -18 3 10 4.9

1.264 10 18- 20 1 10 8.1

1.29 100 100 77.4

1.392

1.395 Viendo en tablas

1.422

1.453

1.486

1.495 Distribucion Lognormal

1.53

1.578

1.611

1.781

1.816

2.007

2.0522.072

2.103

2.155

2.333

2.381

2.44

2.498

2.547

2.63

2.637

2.717

2.945

3.032

3.043

3.078

3.151

3.28

3.384

1. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 90%,

qu tipo de distribucin siguen los datos.

Conclusion como: 77.4


2/125

3.461

3.528

3.69

3.708

3.791

3.957

4.0784.214

4.301

4.313

4.661

4.714

4.767

4.772

4.793

4.891

5.244

5.285

5.3

5.901

5.924

5.959

5.977

6.001

6.412

6.443

6.72

6.9667.088

7.094

7.281

7.378

7.489

7.552

7.728

7.766

7.822

8.11

8.115

8.121

8.281

8.477

9.269

10.177

10.369

10.451

10.87


3/125

11.094

12.171

12.877

13.602

14.344

15.733

16.67717.066

17.392

19.867


4/125


5/125

i Oi Ei ((Ei-Oi)^2)/Ei

9.69 1 0 - 3 0 10 10

11.266 2 3. -6 0 10 1011.528 3 6.-9 0 10 10

12.612 4 9. -12 3 10 4.9

12.901 5 12. -15 11 10 0.1

13.03 6 15. - 18 20 10 10

13.238 7 18 -21 27 10 28.9

13.55 8 21 -24 21 10 12.1

13.764 9 24 -27 11 10 0.1

13.914 10 27- 30 6 10 1.6

14.223 99 100 87.7

14.513

14.881

14.889


15.537

15.653

15.781


16.089

16.241

16.307

16.35616.611

16.64

16.715

16.905

17.054

17.239

17.38

17.386

17.454

17.728

17.905

17.947

18.187

18.284

18.384

18.475

18.519

18.538

2. A partir de la prueba Chi-cuadrada determine, con un nivel de confianza de 90%,

qu tipo de distribucin siguen los datos.



6/125

18.548

18.692

18.709

18.755

18.799

19.036

19.06319.255

19.659

19.662

19.87

19.898

20.008

20.112

20.289

20.452

20.526

20.539

20.555

20.854

20.977

21.291

21.777

21.815

21.867

21.949

22.156

22.23122.383

22.472

22.554

22.701

22.776

22.845

23.03

23.031

23.313

23.319

23.448

23.463

23.498

23.609

24.38

24.445

24.793

24.953

25.106


7/125

25.216

25.371

25.775

25.791

26.646

26.933

27.53927.676

27.889

28.778

28.823

29.503


8/125

es


9/125

9.526

9.695 i Oi Ei ((Ei-Oi)^2)/Ei

9.766 1 0 - 2 0 10 1010.118 2 2. -4 0 10 10

10.412 3 4.-6 0 10 10

10.441 4 6. -8 0 10 10

10.452 5 8. -10 3 10 4.9

10.475 6 10. - 12 51 10 168.1

10.522 7 12. -14 42 10 102.4

10.634 8 14 -16 4 10 3.6

10.653 9 16 -18 0 10 10

10.671 10 18- 20 0 10 10

10.771 100 100 339

10.883

10.893

10.902


11.002

11.019

11.052


11.252

11.264

11.30911.346

11.363

11.369

11.381

11.399

11.61

11.617

11.65

11.654

11.664

11.665

11.689

11.728

11.743

11.765

11.769

11.792

11.793

3. Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los

datos utilice la prueba Chi-Cuadrada.

Conclusion como: 339


10/125

11.836

11.843

11.845

11.854

11.855

11.866

11.87311.931

11.931

11.936

11.985

11.991

12.038

12.074

12.131

12.146

12.157

12.161

12.204

12.212

12.247

12.273

12.286

12.299

12.316

12.347

12.357

12.36312.437

12.48

12.503

12.533

12.548

12.556

12.566

12.571

12.656

12.659

12.66

12.683

12.763

12.809

12.863

12.957

13.013

13.049

13.172


11/125

13.271

13.317

13.577

13.598

13.61

13.83

13.9414.086

14.116

14.121

14.374


12/125

4. Emplee la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 95%, qu

distribucin siguen los datos. Compruebe con la herramienta Stat::Fit de ProModel.

0.003

0.046

0.0810.121

0.123

0.151 i Oi Ei

0.156 1 0 - 1 41 10

0.161 2 1 - 2. 26 10

0.223 3 2. - 3 20 10

0.234 4 3. - 4 6 10

0.235 5 4. - 5 2 10

0.256 6 5. - 6 1 10

0.28 7 6. - 7 1 10

0.347 8 7. - 8 2 10

0.355 9 8. - 9 1 10

0.382 10 9. - 10 0 10

0.412 100 100

0.464

0.468

0.486

0.494 Viendo en tab

0.504

0.504

0.5180.531 Distribucion Lognormal

0.561

0.585

0.598

0.635

0.654

0.667

0.684

0.699

0.754

0.754

0.761

0.776

0.831

0.904

0.922

0.951

1.019



13/125

1.182

1.182

1.187

1.202

1.228

1.229

1.2431.337

1.38

1.383

1.419

1.424

1.427

1.45

1.458

1.506

1.525

1.597

1.613

1.639

1.662

1.679

1.78

1.876

1.962

2.06

2.087

2.1982.258

2.294

2.312

2.327

2.393

2.451

2.516

2.606

2.628

2.66

2.7

2.756

2.771

2.775

2.815

2.898

2.933

3.141

3.192


14/125

3.258

3.399

3.582

3.591

4.518

4.923

5.7156.985

7.145

7.66

8.055


15/125

tipo de

((Ei-Oi)^2)/Ei

96.1

25.6

10

1.6

6.4

8.1

8.1

6.4

8.1

10

180.4

las

ri como uniformes


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dgitos; emplee la prueba de Kolmogorov-Smirnov.

0.189

0.891 i Oi Ei ((Ei-Oi)^2)/Ei1.313 1 0 - 3 10 10

1.368 2 3 - 6. 10 10

1.544 3 6. - 9 10 10

1.669 4 9. - 12 10 10

1.784 5 12. - 15 10 10

1.992 6 15. - 18 10 10

2.005 7 18 - 21 10 10

2.5 8 21 - 24 10 10

2.549 9 24 - 27 10 10

2.695 10 27 - 30 10 10

2.831 13 0 100 100

3.14

3.178

3.186


3.643

3.706

3.724


3.779

4.0574.367

4.449

4.594

4.688

4.688

5.078 13

5.271 19

5.542 18

5.599 19 18

6.265 9

6.62 13

6.645 6

6.934 1

7.058 3

7.103

7.16

7.419

7.422



17/125

7.508

7.603

7.805

7.844

8.185

8.231

8.3228.423

8.936 18

9.049

9.051

9.579

10.165

10.212

10.257

10.317

10.335

10.663

10.745

10.784

10.962

11.118

11.143

11.157

11.475

11.555

11.963 18

12.08212.299

12.561

12.831

13.234

13.26

13.528

14.405

14.624 9

15.154

15.33

15.334

15.497

15.584

15.696

16.143

16.256

16.432

16.675

16.877


18/125

17.583

17.901 13

18.993

19.171

19.204

20.599

21.12721.5 6

24.93 1

25.998

27.334

31.066 3


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6, Determine, con un nivel de confianza de 90%, qu tipo de distribu

emplee la prueba de Kolmogorov-Smirnov. Compruebe con la herra

17.574 16.257 13.345 22.863

18.338 23.217 15.495 17.403

2.69 20.232 21.411 21.107Media= 18.9699 21.427 14.581 23.523 19.87

Varianza = 0.2863 15.305 21.17 16.155 22.88

21.151 14.817 14.702 27.014

14.24 24.154 19.501 16.238

18.739 14.206 17.471 18.59

22.658 22.24 19.916 16.537

24.477 17.673 22.422 13.373

i Ri i/n i-1/n (i/n)-ri ri-(i-1/n) D+ D-

1 9.784 0.0333 0.0000 -9.7507 9.7840 -9.7507

2 10.279 0.0667 0.0333 -10.2123 10.2457

3 12.858 0.1000 0.0667 -12.7580 12.7913

4 15.907 0.1333 0.1000 -15.7737 15.8070

5 16.032 0.1667 0.1333 -15.8653 15.8987

6 16.452 0.2000 0.1667 -16.2520 16.2853

7 16.463 0.2333 0.2000 -16.2297 16.2630

8 16.677 0.2667 0.2333 -16.4103 16.4437

9 16.713 0.3000 0.2667 -16.4130 16.4463

10 16.939 0.3333 0.3000 -16.6057 16.6390

11 17.487 0.3667 0.3333 -17.1203 17.1537

12 17.532 0.4000 0.3667 -17.1320 17.1653

13 17.926 0.4333 0.4000 -17.4927 17.5260

14 18.436 0.4667 0.4333 -17.9693 18.0027

15 18.515 0.5000 0.4667 -18.0150 18.0483

16 18.825 0.5333 0.5000 -18.2917 18.3250

17 19.209 0.5667 0.5333 -18.6423 18.6757

18 19.301 0.6000 0.5667 -18.7010 18.7343

19 19.364 0.6333 0.6000 -18.7307 18.7640

20 20.169 0.6667 0.6333 -19.5023 19.5357

21 20.346 0.7000 0.6667 -19.6460 19.6793

22 21.073 0.7333 0.7000 -20.3397 20.373023 21.878 0.7667 0.7333 -21.1113 21.1447

24 22.029 0.8000 0.7667 -21.2290 21.2623

25 22.208 0.8333 0.8000 -21.3747 21.4080

26 23.479 0.8667 0.8333 -22.6123 22.6457

27 23.787 0.9000 0.8667 -22.8870 22.9203

28 24.076 0.9333 0.9000 -23.1427 23.1760

29 26.853 0.9667 0.9333 -25.8863 25.9197

30 28.501 1.0000 0.9667 -27.5010 27.5343 27.5343


20/125

En tablas 0.220

Como 0.22


21/125

in siguen los datos;

ienta Stat::Fit de ProModel.

12.846 15.557 16.526

22.671 17.469 18.489

14.238 20.098 19.88116.021 18.107 13.315

20.774 14.255 12.478

12.165 16.597 21.404

20.795 25.924 18.874

18.587 19.929 25.354

23.96 14.417 18.338

21.971 20.549 24.509

D

27.5343


22/125

os

en una distribucion lognormal y uniforme


23/125

7. Determine, con un nivel de confianza de 90%, qu tipo de distribucin

siguen los datos usando la prueba de Kolmogorov-Smirnov, Compruebe con Stat::Fit.

1.979 6.097 3.823 5.52 4.203

5.53 6.891 5.997 6.64 6.376

3.863 1.738 2.913 5.171 6.856

7.228 6.03 6.184 7.6 5.7164.72 5.771 4.521 3.715 5.368

6.176 5.059 5.325 6.478 4.229

6.459 3.083 6.199 2.59 7.407

4.364 8.986 4.195 2.952 3.59

6.101 2.625 4.463 7.9 3.715

6.739 7.049 5.743 5.448 3.958


1 4.548 0.0333 0.0000 -4.5147 4.5480

2 3.242 0.0667 0.0333 -3.1753 3.2087

3 6.303 0.1000 0.0667 -6.2030 6.2363

4 5.225 0.1333 0.1000 -5.0917 5.1250

5 5.307 0.1667 0.1333 -5.1403 5.1737

6 6.536 0.2000 0.1667 -6.3360 6.3693

7 4.769 0.2333 0.2000 -4.5357 4.5690

8 3.154 0.2667 0.2333 -2.8873 2.9207

9 5.427 0.3000 0.2667 -5.1270 5.1603

10 3.404 0.3333 0.3000 -3.0707 3.104011 5.366 0.3667 0.3333 -4.9993 5.0327

12 5.919 0.4000 0.3667 -5.5190 5.5523

13 8.503 0.4333 0.4000 -8.0697 8.1030

14 4.743 0.4667 0.4333 -4.2763 4.3097

15 6.093 0.5000 0.4667 -5.5930 5.6263

16 3.822 0.5333 0.5000 -3.2887 3.3220

17 2.938 0.5667 0.5333 -2.3713 2.4047

18 6.316 0.6000 0.5667 -5.7160 5.7493

19 6.532 0.6333 0.6000 -5.8987 5.9320

20 2.917 0.6667 0.6333 -2.2503 2.2837 -2.2503

21 3.136 0.7000 0.6667 -2.4360 2.4693

22 4.705 0.7333 0.7000 -3.9717 4.0050

23 6.476 0.7667 0.7333 -5.7093 5.7427

24 5.966 0.8000 0.7667 -5.1660 5.1993

25 8.546 0.8333 0.8000 -7.7127 7.7460 7.746

26 8.441 0.8667 0.8333 -7.5743 7.6077

27 4.484 0.9000 0.8667 -3.5840 3.6173

28 3.546 0.9333 0.9000 -2.6127 2.6460


24/125

29 3.431 0.9667 0.9333 -2.4643 2.4977

30 5.769 1.0000 0.9667 -4.7690 4.8023

En tablas 0.220

Como 0.22


25/125

4.972 8.429

6.86 5.991

5.665 3.396

5.781 4.4651.871 1.629

5.619 4.062

7.001 8.501

7.356 6.269

4.881 7.41

6.632 7.036

D


26/125

ucion lognormal y exponencial


27/125

8. Utilice la prueba de Anderson-Darling para determinar, con un

qu tipo de distribucin siguen los datos. Compruebe con S

-1.413 0.066

-0.618 -1.425

1.542 0.27

-1.152 0.512-0.93 0.121

-0.418 1.317

1.567 -1.717

0.913 -0.697

0.01 -0.429

1.077 0.2

i Yi Y 50+1-i 2*i-1 PEA(Yi) 1-PEA(Y50+1-i) Ln (PEA(Yi))

1 0.889 -1.525 1 0.143 0.0123 -1.9449106

2 -1.553 -1.691 3 0.0332 0.0241 -3.4052054

3 -0.204 -2.477 5 0.0433 0.0586 -3.1396026

4 0.436 -3.541 7 0.888 0.0786 -0.1187835

5 1.672 -5.343 9 0.089 0.0962 -2.4191189

6 -1.638 -4.12 11 0.0978 0.1098 -2.3248307

7 0.431 -5.983 13 0.1174 0.111 -2.1421684

8 0.564 -7.965 15 0.1252 0.1227 -2.0778428

9 1.24 -7.373 17 0.1256 0.1484 -2.074653

10 1.219 -7.528 19 0.1931 0.1707 -1.6445471

11 -0.056 -11.631 21 0.2207 0.1787 -1.51095112 1.51 -11.104 23 0.232 0.184 -1.4610179

13 -2.067 -12.281 25 0.2389 0.2887 -1.4317102

14 -0.869 -13.952 27 0.2529 0.2943 -1.3747611

15 -1.293 -14.296 29 0.2741 0.3012 -1.2942623

16 -1.018 -14.717 31 0.2865 0.3021 -1.2500167

17 -1.322 -15.635 33 0.314 0.3033 -1.1583623

18 2.295 -15.267 35 0.3205 0.3543 -1.137873

19 -1.108 -18.86 37 0.3214 0.3593 -1.1350688

20 0.095 -18.11 39 0.3756 0.3624 -0.9792305

21 1.583 -20.354 41 0.4029 0.3721 -0.9090669

22 0.824 -20.317 43 0.4203 0.4194 -0.8667865

23 1.905 -19.79 45 0.4392 0.4425 -0.8228004

24 -0.112 -21.03 47 0.4514 0.4494 -0.7954014

25 -0.559 -24.289 49 0.4871 0.4521 -0.7192858

26 -0.289 -25.559 51 0.5479 0.5129 -0.6016625

27 1.97 -26.112 53 0.5506 0.5486 -0.5967467

28 2.21 -25.095 55 0.5575 0.5608 -0.5842928

29 0.683 -27.176 57 0.5806 0.5797 -0.5436932

30 -0.354 -27.417 59 0.6279 0.5971 -0.4653744


28/125

31 0.89 -29.905 61 0.6376 0.6244 -0.4500442

32 -0.86 -32.108 63 0.6407 0.6786 -0.445194

33 1.733 -29.705 65 0.6457 0.6795 -0.4374203

34 0.365 -34.322 67 0.6967 0.686 -0.3614004

35 0.283 -35.018 69 0.6979 0.7135 -0.3596795

36 -0.296 -36.293 71 0.6988 0.7259 -0.3583907

37 -0.952 -36.869 73 0.7057 0.7471 -0.348565138 -0.281 -39.067 75 0.7113 0.7611 -0.340661

39 -0.104 -36.49 77 0.816 0.768 -0.2033409

40 -1.631 -39.056 79 0.8213 0.7793 -0.1968668

41 1.472 -38.781 81 0.8293 0.8069 -0.1871733

42 0.627 -39.76 83 0.8516 0.8744 -0.1606383

43 -0.965 -41.436 85 0.8773 0.8748 -0.1309063

44 0.017 -42.569 87 0.889 0.8826 -0.117658

45 0.88 -45.638 89 0.8902 0.9022 -0.1163091

46 -1.343 -43.328 91 0.9038 0.911 -0.1011472

47 -0.541 -45.564 93 0.9232 0.9112 -0.0799094

48 -0.477 -47.204 95 0.9414 0.9567 -0.0603872

49 -0.691 -49.553 97 0.9759 0.9668 -0.0243952

50 -1.525 -48.111 99 0.9877 0.9857 -0.0123763

Los datos sigu


29/125

nivel de confianza de 90%,

ai::Fit.

-0.423 -0.174 -1.139

0.061 0.7 -0.078

2.293 -0.889 0.099

2.324 0.654 -1.2810.595 0.597 -0.185

0.249 0.937 -0.67

0.125 -0.608 1.027

-0.145 -1.088 0.137

-1.42 -0.07 1.517

-0.959 -0.144 -1.169

Ln(1-PEA(Y50+1-i)) (2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i)))

-4.398156017 -6.343066665

-3.725543438 -21.39224652

-2.837020582 -29.88311613

-2.54338358 -18.63516981

-2.341325921 -42.84400348

-2.20909475 -49.87317997

-2.198225078 -56.42511484

-2.098012927 -62.63783621

-1.907843948 -67.70244854

-1.767847649 -64.83550004

-1.722046857 -67.89295427-1.692819521 -72.53826086

-1.242367192 -66.85193542

-1.223155624 -70.14375222

-1.199980783 -72.3330487

-1.196997191 -75.85743194

-1.193032864 -77.59604019

-1.037611267 -76.14194944

-1.023597585 -79.87065719

-1.015006705 -77.77525222

-0.988592644 -77.80404075

-0.868930161 -74.63581799

-0.815314815 -73.71518415

-0.799841919 -74.97643669

-0.793851885 -74.14374842

-0.667674385 -64.73618063

-0.6003857 -63.4480165

-0.578390943 -63.94760454

-0.545244551 -62.06945335

-0.515670675 -57.88165714


30/125

-0.47096409 -56.18150275

-0.387723427 -52.47379475

-0.386398045 -53.54819111

-0.376877651 -49.46462789

-0.337572842 -48.11040836

-0.320343015 -48.19009379

-0.291556234 -46.72885453-0.272990524 -46.02386407

-0.263965546 -35.98259818

-0.249359198 -35.25185608

-0.214555534 -32.54003617

-0.134217342 -24.47302211

-0.13375999 -22.4966321

-0.124883182 -21.10108663

-0.102919054 -19.5113077

-0.093212382 -17.6867203

-0.092992867 -16.07990926

-0.044265416 -9.9419938

-0.03376363 -5.641402338

-0.01440323 -2.651170637

en uns distribucion lognormal y una distribucion uniforme


31/125

9. Determine, con un nivel de confianza de 90%r

qu tipo de distribucin siguen los datos; utilice la prueba de Kolmogorov-Smirnov.

21.92 7.902 10.824 22.258 13.343

11.536 10.187 11.442 13.396 13.07

24.956 5.442 12.996 5.073 13.62

5.481 2.959 7.503 4.159 23.4666.08 9.053 5.178 18.7 9.056

2.491 10.123 3.244 9.433 11.774

25.237 7.588 1.152 8.059 26.399

9.888 13.798 15.255 20.507 11.147

2.898 20.041 10.228 9.553 19.87

6.848 7.197 12.156 1.674 8.582


1 7.982 0.0333 0.0000 -7.9487 7.9820

2 18.951 0.0667 0.0333 -18.8843 18.9177

3 6.361 0.1000 0.0667 -6.2610 6.2943

4 3.382 0.1333 0.1000 -3.2487 3.2820

5 37.134 0.1667 0.1333 -36.9673 37.0007

6 17.684 0.2000 0.1667 -17.4840 17.5173

7 6.839 0.2333 0.2000 -6.6057 6.6390

8 3.274 0.2667 0.2333 -3.0073 3.0407 -3.0073

9 22.836 0.3000 0.2667 -22.5360 22.5693

10 12.427 0.3333 0.3000 -12.0937 12.1270

11 40.122 0.3667 0.3333 -39.7553 39.7887 39.788712 12.348 0.4000 0.3667 -11.9480 11.9813

13 6.405 0.4333 0.4000 -5.9717 6.0050

14 14.387 0.4667 0.4333 -13.9203 13.9537

15 21.099 0.5000 0.4667 -20.5990 20.6323

16 8.814 0.5333 0.5000 -8.2807 8.3140

17 7.073 0.5667 0.5333 -6.5063 6.5397

18 7.325 0.6000 0.5667 -6.7250 6.7583

19 14.432 0.6333 0.6000 -13.7987 13.8320

20 11.811 0.6667 0.6333 -11.1443 11.1777

21 5.862 0.7000 0.6667 -5.1620 5.1953

22 8.725 0.7333 0.7000 -7.9917 8.0250

23 34.45 0.7667 0.7333 -33.6833 33.7167

24 10.037 0.8000 0.7667 -9.2370 9.2703

25 9.021 0.8333 0.8000 -8.1877 8.2210

26 22.939 0.8667 0.8333 -22.0723 22.1057

27 10.708 0.9000 0.8667 -9.8080 9.8413

28 10.046 0.9333 0.9000 -9.1127 9.1460

29 14.65 0.9667 0.9333 -13.6833 13.7167


32/125

30 24.699 1.0000 0.9667 -23.6990 23.7323

En tablas 0.220

Como 0.22


33/125

11.045 23.603

13.668 7.954

11.02 11.729

5.219 11.7136.647 5.767

3.271 10.39

29.285 22.35

19.691 7.711

8.52 26.182

16.293 16.126

D

39.7887


34/125

10. A partir de la prueba de Kolmogorov-Smirnov, determine con un nivel de co

de 90% qu tipo de distribucin siguen los datos.

3.366 12.233 5.725 9.186 8.232

2.91 8.391 2.288 4.582 6.114

11.892 14.542 9.851 11.088 6.301

3.171 7.782 5.682 9.587 12.51910.263 5.367 3.059 6.341 3.613

5.582 4.836 8.663 6.975 8.441

9.799 7.825 9.464 7.799 6.929

4.141 2.972 14.575 2.248 6.565

9.264 14.575 6.742 5.551 5.313

4.028 6.515 9.474 6.817 10.19


1 5.091 0.0333 0.0000 -5.0577 5.0910

2 6.752 0.0667 0.0333 -6.6853 6.7187

3 11.584 0.1000 0.0667 -11.4840 11.5173

4 9.595 0.1333 0.1000 -9.4617 9.4950

5 7.558 0.1667 0.1333 -7.3913 7.4247

6 4.179 0.2000 0.1667 -3.9790 4.0123

7 13.47 0.2333 0.2000 -13.2367 13.2700

8 9.71 0.2667 0.2333 -9.4433 9.4767

9 14.135 0.3000 0.2667 -13.8350 13.8683 13.8683

10 12.436 0.3333 0.3000 -12.1027 12.1360

11 11.319 0.3667 0.3333 -10.9523 10.9857

12 10.64 0.4000 0.3667 -10.2400 10.273313 13.333 0.4333 0.4000 -12.8997 12.9330

14 13.784 0.4667 0.4333 -13.3173 13.3507

15 8.12 0.5000 0.4667 -7.6200 7.6533

16 10.035 0.5333 0.5000 -9.5017 9.5350

17 1.512 0.5667 0.5333 -0.9453 0.9787 -0.9453

18 5.259 0.6000 0.5667 -4.6590 4.6923

19 5.937 0.6333 0.6000 -5.3037 5.3370

20 8.153 0.6667 0.6333 -7.4863 7.5197

21 3.274 0.7000 0.6667 -2.5740 2.6073

22 7.242 0.7333 0.7000 -6.5087 6.5420

23 10.081 0.7667 0.7333 -9.3143 9.3477

24 4.867 0.8000 0.7667 -4.0670 4.1003

25 6.451 0.8333 0.8000 -5.6177 5.6510

26 5.599 0.8667 0.8333 -4.7323 4.7657

27 11.317 0.9000 0.8667 -10.4170 10.4503

28 8.086 0.9333 0.9000 -7.1527 7.1860

29 2.954 0.9667 0.9333 -1.9873 2.0207

30 5.418 1.0000 0.9667 -4.4180 4.4513


35/125

En tablas 0.220

Como 0.22


36/125

fianza

6.545 6.481

9.965 10.643

5.35 3.465

9.964 1.2983.068 7.291

2.064 5.147

8.915 8.007

13.418 5.238

6.348 5.723

4.961 13.263

D

13.8683


37/125

11. Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen

los datos; utilice la prueba de Kolmogorov-Smirnov.

0.102 0.285 0.725 5.567 6.773

3.661 3.072 5.193 0.329 2.721

0.664 6.032 0.093 3.856 1.779

2.342 2.954 0.883 1.79 3.8472.35 3.983 1.517 0.695 3.564

3.986 2.416 0.577 0.617 1.494

0.852 4.342 0.064 0.299 0.214

4.276 0.371 4.52 0.408 0.113

2.859 0.799 4.718 8.664 0.339

2.852 0.04 1.86 0.716 3.551

i Ri i/n i-1/n (i/n)-ri ri-(i-1/n) D+

1 1.338 0.0333 0.0000 0.3380 0.9667 0.3380

2 1.198 0.0667 0.0333 -0.8020 1.9333

3 1.852 0.1000 0.0667 -1.1480 2.9000

4 3.05 0.1333 0.1000 -0.9500 3.8667

5 1.003 0.1667 0.1333 -3.9970 4.8333

6 0.286 0.2000 0.1667 -5.7140 5.8000

7 2.283 0.2333 0.2000 -4.7170 6.7667

8 0.388 0.2667 0.2333 -7.6120 7.7333

9 0.095 0.3000 0.2667 -8.9050 8.7000

10 0.265 0.3333 0.3000 -9.7350 9.6667

11 0.58 0.3667 0.3333 -10.4200 10.6333

12 0.294 0.4000 0.3667 -11.7060 11.600013 1.586 0.4333 0.4000 -11.4140 12.5667

14 4.117 0.4667 0.4333 -9.8830 13.5333

15 1.645 0.5000 0.4667 -13.3550 14.5000

16 0.395 0.5333 0.5000 -15.6050 15.4667

17 0.483 0.5667 0.5333 -16.5170 16.4333

18 2.156 0.6000 0.5667 -15.8440 17.4000

19 1.355 0.6333 0.6000 -17.6450 18.3667

20 7.487 0.6667 0.6333 -12.5130 19.3333

21 0.53 0.7000 0.6667 -20.4700 20.3000

22 0.049 0.7333 0.7000 -21.9510 21.2667

23 1.426 0.7667 0.7333 -21.5740 22.2333

24 4.688 0.8000 0.7667 -19.3120 23.2000

25 0.46 0.8333 0.8000 -24.5400 24.1667

26 1.581 0.8667 0.8333 -24.4190 25.1333

27 0.774 0.9000 0.8667 -26.2260 26.1000

28 0.429 0.9333 0.9000 -27.5710 27.0667

29 2.267 0.9667 0.9333 -26.7330 28.0333

30 2.032 1.0000 0.9667 -27.9680 29.0000


38/125

En tablas 0.220

Como 0.22


39/125

0.101 5.549

0.988 0.716

1.729 1.456

2.659 3.6220.573 0.204

0.468 1.037

3.294 0.345

0.24 2.923

1.892 1.262

0.493 0.269

D- D

29


40/125

12. Determine, con un nivel de confianza de 95%, qu Tipo de distribucin siguen los datos;

emplee la prueba de Kolmogorov-Smirnov. Compruebe con Stat :Fit.

18.39 19.825 23.279 23.206 19.351

24.364 19.2 21.265 16.905 27.313

22.105 25.105 22.137 27.514 15.766

15.625 16.168 29.769 18.158 18.29319.743 24.525 18.112 26.259 19.466

25.275 24.56 22.09 19.608 15.447

22.189 20.807 27.339 22.556 24.059

29.122 27.19 26.915 26.844 19.573

24.007 28.127 25.213 19.964 27.141

24.985 17.717 19.063 29.986 24.074


1 26.739 0.0333 0.0000 -26.7057 26.7390

2 23.396 0.0667 0.0333 -23.3293 23.3627

3 21.326 0.1000 0.0667 -21.2260 21.2593

4 17.539 0.1333 0.1000 -17.4057 17.4390

5 26.421 0.1667 0.1333 -26.2543 26.2877

6 20.931 0.2000 0.1667 -20.7310 20.7643

7 28.013 0.2333 0.2000 -27.7797 27.8130

8 25.57 0.2667 0.2333 -25.3033 25.3367

9 22.518 0.3000 0.2667 -22.2180 22.2513

10 29.791 0.3333 0.3000 -29.4577 29.4910 29.491

11 22.607 0.3667 0.3333 -22.2403 22.2737

12 28.553 0.4000 0.3667 -28.1530 28.186313 15.138 0.4333 0.4000 -14.7047 14.7380

14 19.921 0.4667 0.4333 -19.4543 19.4877

15 18.044 0.5000 0.4667 -17.5440 17.5773

16 18.562 0.5333 0.5000 -18.0287 18.0620

17 26693 0.5667 0.5333 -26692.4333 26692.4667

18 18.746 0.6000 0.5667 -18.1460 18.1793

19 18.883 0.6333 0.6000 -18.2497 18.2830

20 17.89 0.6667 0.6333 -17.2233 17.2567

21 19.584 0.7000 0.6667 -18.8840 18.9173

22 24.449 0.7333 0.7000 -23.7157 23.7490

23 21.15 0.7667 0.7333 -20.3833 20.4167

24 22.216 0.8000 0.7667 -21.4160 21.4493

25 25.744 0.8333 0.8000 -24.9107 24.9440

26 26.714 0.8667 0.8333 -25.8473 25.8807

27 29.751 0.9000 0.8667 -28.8510 28.8843

28 16.818 0.9333 0.9000 -15.8847 15.9180

29 26.128 0.9667 0.9333 -25.1613 25.1947

30 15.515 1.0000 0.9667 -14.5150 14.5483 -14.515


41/125

En tablas 0.240

Como 0.24>-14.515 No se aceptan los numeros


42/125

15.24 15.792

18.097 20.233

22.029 25.164

15.858 25.11126.276 25.948

29.631 28.821

15.724 21.614

26.853 17.053

25.458 26.06

23.517 20.733

D

29.491


43/125

Los datos no siguen ninguna distribucion


44/125

13. Determine, don un nivel de confianza de 90%, qu tipo de distribucin liguen los

datos usando la prueba de Anderson-Darling. Compruebe con Stat :Fit

7.717 7.971 5.261 5.994 7.215 6.1 6.876

6.377 6.155 7.512 7.936 7.96 6.157 5.7966.15 5.983 6.061 7.492 6.974 5.386 6.347

6.174 5.962 6.153 6.838 5.741 5.478 5.471

7.814 6.238 7.484 6.15 7.561 7.734 5.595

7.354 5.826 5.858 5.316 7.081 6.476 7.394

7.99 5.793 5.057 5.245 6.246 7.538 7.314

7.495 6.004 7.374 7.071 5.549 6.932 6.262

5.021 6.8 7.322 7.84 5.547 5.601 6.524

6.351 6.438 7.76 7.771 7.118 5.5 5.901

i Yi Y50+1-i 2*i-1 PEA(Yi) 1-PEA(Y50+1-i) Ln (PEA(Yi))

1 5.021 7.99 1 0.143 0.0123 -1.9449

2 5.057 6.99 3 0.0332 0.0241 -3.4052

3 5.245 5.99 5 0.0433 0.0586 -3.1396

4 5.261 4.99 7 0.888 0.0786 -0.1188

5 5.316 3.99 9 0.089 0.0962 -2.4191

6 5.547 2.99 11 0.0978 0.1098 -2.3248

7 5.549 1.99 13 0.1174 0.111 -2.1422

8 5.741 0.99 15 0.1252 0.1227 -2.07789 5.793 -0.01 17 0.1256 0.1484 -2.0747

10 5.826 -1.01 19 0.1931 0.1707 -1.6445

11 5.858 -2.01 21 0.2207 0.1787 -1.5110

12 5.962 -3.01 23 0.232 0.184 -1.4610

13 5.983 -4.01 25 0.2389 0.2887 -1.4317

14 5.994 -5.01 27 0.2529 0.2943 -1.3748

15 6.004 -6.01 29 0.2741 0.3012 -1.2943

16 6.061 -7.01 31 0.2865 0.3021 -1.2500

17 6.15 -8.01 33 0.314 0.3033 -1.1584

18 6.15 -9.01 35 0.3205 0.3543 -1.1379

19 6.153 -10.01 37 0.3214 0.3593 -1.1351

20 6.155 -11.01 39 0.3756 0.3624 -0.9792

21 6.174 -12.01 41 0.4029 0.3721 -0.9091

22 6.238 -13.01 43 0.4203 0.4194 -0.8668

23 6.246 -14.01 45 0.4392 0.4425 -0.8228

24 6.351 -15.01 47 0.4514 0.4494 -0.7954

25 6.377 -16.01 49 0.4871 0.4521 -0.7193

26 6.438 -17.01 51 0.5479 0.5129 -0.6017


45/125

27 6.8 -18.01 53 0.5506 0.5486 -0.5967

28 6.838 -19.01 55 0.5575 0.5608 -0.5843

29 6.974 -20.01 57 0.5806 0.5797 -0.5437

30 7.071 -21.01 59 0.6279 0.5971 -0.4654

31 7.081 -22.01 61 0.6376 0.6244 -0.4500

32 7.118 -23.01 63 0.6407 0.6786 -0.4452

33 7.215 -24.01 65 0.6457 0.6795 -0.437434 7.322 -25.01 67 0.6967 0.686 -0.3614

35 7.354 -26.01 69 0.6979 0.7135 -0.3597

36 7.374 -27.01 71 0.6988 0.7259 -0.3584

37 7.484 -28.01 73 0.7057 0.7471 -0.3486

38 7.492 -29.01 75 0.7113 0.7611 -0.3407

39 7.495 -30.01 77 0.816 0.768 -0.2033

40 7.512 -31.01 79 0.8213 0.7793 -0.1969

41 7.561 -32.01 81 0.8293 0.8069 -0.1872

42 7.717 -33.01 83 0.8516 0.8744 -0.1606

43 7.76 -34.01 85 0.8773 0.8748 -0.1309

44 7.771 -35.01 87 0.889 0.8826 -0.1177

45 7.814 -36.01 89 0.8902 0.9022 -0.1163

46 7.84 -37.01 91 0.9038 0.911 -0.1011

47 7.936 -38.01 93 0.9232 0.9112 -0.0799

48 7.96 -39.01 95 0.9414 0.9567 -0.0604

49 7.971 -40.01 97 0.9759 0.9668 -0.0244

50 7.99 -41.01 99 0.9877 0.9857 -0.0124


46/125

Los datos siguen una distribucion uniforme


47/125

7.514 6.409 6.679

7.579 6.45 6.7195.053 5.129 5.922

7.745 5.057 5.548

7.587 5.235 7.872

5.304 5.175 6.499

5.909 6.215 6.949

5.531 6.335 5.271

6.169 5.484 6.823

5.104 7.633 6.074

Ln(1-PEA(Y50+1-i))

(2*i-1)*(Ln(PEA(Yi))+

Ln(1-PEA(Y50+1-i)))i)))

-4.3982 -1.9326

-3.7255 -10.1433

-2.8370 -15.4050

-2.5434 -0.2813

-2.3413 -20.9063

-2.2091 -24.3653

-2.1982 -26.4052

-2.0980 -29.3271-1.9078 -32.7463

-1.7678 -28.0031

-1.7220 -27.9773

-1.6928 -29.3714

-1.2424 -28.5753

-1.2232 -29.1725

-1.2000 -28.7988

-1.1970 -29.3854

-1.1930 -28.2171

-1.0376 -27.4251

-1.0236 -28.7034

-1.0150 -24.0564

-0.9886 -22.0156

-0.8689 -19.2376

-0.8153 -17.1135

-0.7998 -16.2621

-0.7939 -13.0921

-0.6677 -4.5269


48/125

-0.6004 -2.5518

-0.5784 -1.2921

-0.5452 2.0524

-0.5157 7.7718

-0.4710 10.6357

-0.3877 14.7046

-0.3864 15.7352-0.3769 21.7482

-0.3376 24.4136

-0.3203 26.0932

-0.2916 29.0931

-0.2730 31.5329

-0.2640 43.4787

-0.2494 46.0122

-0.2146 50.1979

-0.1342 59.2422

-0.1338 63.2310

-0.1249 66.5500

-0.1029 69.9443

-0.0932 73.6966

-0.0930 77.3100

-0.0443 85.1497

-0.0338 91.4133

-0.0144 96.3590


49/125


50/125

60.197 14. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confianz

60.659 qu tipo de distribucin siguen los datos. Compruebe con Siat::Fit.

60.747

61.771

62.614 i Oi Ei

62.686 1 60-64 12 10

62.849 2 64-68 3 1063.185 3 68-72 13 10

63.391 4 72-76 11 10

63.479 5 76-80 10 10

63.499 6 80-84 10 10

63.766 7 84-88 5 10

64.31 8 88-92 14 10

65.272 9 92-96 9 10

66.832 10 96-100 13 10

68.147 100 100

68.18

68.181

68.51 La distribucion que se siguen en estos dat

68.775

69.235

69.346

69.716

69.933

70.205

70.569

70.684

71.6872.537

72.55

73.105

73.495

73.711

73.864

74.473

75.107

75.425

75.734

75.734

76.159

76.248

76.276

76.753

77.024

77.148

77.388

77.588


51/125

79.007

79.56

80.042

80.15

81.057

81.149

81.93182.187

82.416

83.537

83.704

83.945

84.366

86.06

86.162

86.478

86.95

88.371

88.431

88.819

89.36

89.607

90.108

90.591

90.697

90.854

91.051

91.26291.325

91.54

91.917

92.229

92.978

93.2

93.535

93.645

95.076

95.181

95.804

95.882

96.594

96.829

96.893

96.937

97.305

97.491

97.58


52/125

97.844

97.891

97.926

98.002

98.783

99.813


53/125

a de 95%

((Ei-Oi)^2)/Ei

0.4

4.90.9

0.1

0

0

2.5

1.6

0.1

0.9

11.4

s es uniforme


54/125


datos Emplee Ia prueba Chi-Cuadrada y compruebe con Stat::Fit

H0: Binomial

H1: Otra Distribucion

1.316

1.34 i Oi Ei ((Ei-Oi)^2)/Ei

1.443 1 0-1 9 16.6 3.47951.556 2 1-2. 22 16.6 1.7566

1.677 3 2-3. 28 16.6 7.8289

1.689 4 3-4. 26 16.6 5.3229

1.806 5 4-5. 11 16.6 1.8892

1.81 6 5-6. 4 16.6 9.5639

1.874 100 99.6 29.8410

2.076

2.171 1.61 Viendo en tablas

2.173

2.225

2.246

2.33 H0:

2.369 Distribucion Binomial2.37

2.37 Intervalo p(x) Ei=50*p(x)

2.499 0-4 0.1521 7.605

2.639 5 0.2091 10.455

2.649 6 0.273 13.65

2.682 7 0.2292 11.462.727 8.-9 0.1366 6.83

2.744

2.749 Total 1 50

2.782

2.804

2.848

2.912

2.919

2.949

3.009

3.018

3.028

3.046

3.049

3.137

3.2

3.206

3.292

10

50



55/125

3.309

3.347

3.351

3.361

3.408

3.449

3.5013.572

3.587

3.722

3.724

3.775

3.786

3.796

3.82

3.899

3.903

3.953

3.964

4.035

4.043

4.057

4.075

4.098

4.102

4.111

4.123

4.1424.164

4.328

4.339

4.344

4.347

4.374

4.375

4.398

4.463

4.574

4.606

4.87

4.879

4.907

4.951

4.968

4.993

5.006

5.08


56/125

5.187

5.246

5.329

5.331

5.337

5.444

5.6175.813

5.828

6.351

6.385

6.43

6.767


57/125

(Ei-Oi)2/Ei

0.7537

0.2023

0.009

1.73451.4698

4.1693


58/125


59/125

16. Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los datos;

utilice la prueba de Anderson-Darling. Compruebe con Stat;:Fit.

198.912 193.496 198.169 186.553 186.699 189.485 197.916

186.72 175.625 193.319 208.652 180.861 189.234 179.564

186.615 191.5 191.643 201.017 187.908 180.002 192.118191.445 184.243 185.089 194.686 188.845 194.979 203.149

183.463 193.388 193.112 194.638 184.73 188.484 194.847

191.088 178.781 199.534 191.382 173.618 193.244 185.665

176.583 187.396 198.267 181.183 186.406 192.473 193.006

193.267 192.581 195.991 200.364 188.597 188.87 191.077

198.414 174.54 194.575 184.283 194.842 186.476 196.176

203.231 192.099 177.14 172.582 188.939 183.386 180.174

H0: Normal H0: Los datos siguen la distribucion Normal

H1: Otra distribucion

i Yi Y50+1-i 2*i-1 PEA(Yi) 1-PEA(Y50+1-i) Ln (PEA(Yi))

1 172.582 191.077 1 0.143 0.0123 -1.9449

2 172.773 190.077 3 0.0332 0.0241 -3.4052

3 173.618 189.077 5 0.0433 0.0586 -3.1396

4 174.54 188.077 7 0.888 0.0786 -0.1188

5 175.524 187.077 9 0.089 0.0962 -2.4191

6 175.625 186.077 11 0.0978 0.1098 -2.3248

7 176.583 185.077 13 0.1174 0.111 -2.14228 176.613 184.077 15 0.1252 0.1227 -2.0778

9 177.14 183.077 17 0.1256 0.1484 -2.0747

10 178.781 182.077 19 0.1931 0.1707 -1.6445

11 179.564 181.077 21 0.2207 0.1787 -1.5110

12 179.576 180.077 23 0.232 0.184 -1.4610

13 180.002 179.077 25 0.2389 0.2887 -1.4317

14 180.174 178.077 27 0.2529 0.2943 -1.3748

15 180.861 177.077 29 0.2741 0.3012 -1.2943

16 181.175 176.077 31 0.2865 0.3021 -1.2500

17 181.183 175.077 33 0.314 0.3033 -1.1584

18 181.189 174.077 35 0.3205 0.3543 -1.1379

19 182.241 173.077 37 0.3214 0.3593 -1.1351

20 183.386 172.077 39 0.3756 0.3624 -0.9792

21 183.463 171.077 41 0.4029 0.3721 -0.9091

22 183.73 170.077 43 0.4203 0.4194 -0.8668

23 184.097 169.077 45 0.4392 0.4425 -0.8228

24 184.243 168.077 47 0.4514 0.4494 -0.7954

25 184.283 167.077 49 0.4871 0.4521 -0.7193

26 184.548 166.077 51 0.5479 0.5129 -0.6017


60/125

27 184.73 165.077 53 0.5506 0.5486 -0.5967

28 185.089 164.077 55 0.5575 0.5608 -0.5843

29 185.665 163.077 57 0.5806 0.5797 -0.5437

30 185.913 162.077 59 0.6279 0.5971 -0.4654

31 186.406 161.077 61 0.6376 0.6244 -0.4500

32 186.476 160.077 63 0.6407 0.6786 -0.4452

33 186.553 159.077 65 0.6457 0.6795 -0.437434 186.615 158.077 67 0.6967 0.686 -0.3614

35 186.699 157.077 69 0.6979 0.7135 -0.3597

36 186.72 156.077 71 0.6988 0.7259 -0.3584

37 187.396 155.077 73 0.7057 0.7471 -0.3486

38 187.85 154.077 75 0.7113 0.7611 -0.3407

39 187.908 153.077 77 0.816 0.768 -0.2033

40 188.484 152.077 79 0.8213 0.7793 -0.1969

41 188.597 151.077 81 0.8293 0.8069 -0.1872

42 188.845 150.077 83 0.8516 0.8744 -0.1606

43 188.87 149.077 85 0.8773 0.8748 -0.1309

44 188.939 148.077 87 0.889 0.8826 -0.1177

45 189.234 147.077 89 0.8902 0.9022 -0.1163

46 189.485 146.077 91 0.9038 0.911 -0.1011

47 189.795 145.077 93 0.9232 0.9112 -0.0799

48 190.21 144.077 95 0.9414 0.9567 -0.0604

49 190.292 143.077 97 0.9759 0.9668 -0.0244

50 191.077 142.077 99 0.9877 0.9857 -0.0124


61/125


62/125

184.548 176.613 194.656

200.401 206.452 185.913

200.353 197.755 190.21202.014 179.576 181.175

199.871 172.773 181.189

192.927 175.524 189.795

192.881 182.241 187.85

206.708 190.292 198.489

183.73 197.7 184.097

195.355 193.626 206.255

Ln(1-PEA(Y50+1-i))

(2*i-1)*(Ln(PEA(Yi))+

Ln(1-PEA(Y50+1-i)))i)))

-4.3982 -1.9326

-3.7255 -10.1433

-2.8370 -15.4050

-2.5434 -0.2813

-2.3413 -20.9063

-2.2091 -24.3653

-2.1982 -26.4052-2.0980 -29.3271

-1.9078 -32.7463

-1.7678 -28.0031

-1.7220 -27.9773

-1.6928 -29.3714

-1.2424 -28.5753

-1.2232 -29.1725

-1.2000 -28.7988

-1.1970 -29.3854

-1.1930 -28.2171

-1.0376 -27.4251

-1.0236 -28.7034

-1.0150 -24.0564

-0.9886 -22.0156

-0.8689 -19.2376

-0.8153 -17.1135

-0.7998 -16.2621

-0.7939 -13.0921

-0.6677 -4.5269


63/125

-0.6004 -2.5518

-0.5784 -1.2921

-0.5452 2.0524

-0.5157 7.7718

-0.4710 10.6357

-0.3877 14.7046

-0.3864 15.7352-0.3769 21.7482

-0.3376 24.4136

-0.3203 26.0932

-0.2916 29.0931

-0.2730 31.5329

-0.2640 43.4787

-0.2494 46.0122

-0.2146 50.1979

-0.1342 59.2422

-0.1338 63.2310

-0.1249 66.5500

-0.1029 69.9443

-0.0932 73.6966

-0.0930 77.3100

-0.0443 85.1497

-0.0338 91.4133

-0.0144 96.3590

Distribucion Normal


64/125


65/125

17, Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los datos.

Emplee la prueba Chi-Cuadrada y compruebe con Stat;Fit

18.089 14.601 12.091 17.516 12.258

13.025 18.482 19.439 15.032 10.81616.93 18.475 18.064 16.39 15.989

18.917 18.737 13.028 13.534 14.233

17.552 18.398 10.877 13.538 13.217

14.954 17.131 11.747 16.26 17.652

17.15 17.12 13.871 15.645 17.293

16.648 19.48 16.416 18.18 19.408

17.803 14.342 18.055 14.458 15.287

12.777 15.501 17.047 11.436 16.925

11.144 i Oi Ei ((Ei-Oi)^2)/Ei

11.779 1 10.-11 0 5 5

12.082 2 11.-12 2 5 1.8

13.163 3 12.-13 1 5 3.2

13.435 4 13-14 3 5 0.8

13.536 5 14-15 6 5 0.2

14.257 6 15-16 9 5 3.2

14.257 7 16-17 7 5 0.8

14.504 8 17-18 14 5 16.2

14.517 9 18-19 7 5 0.8

14.658 10 19-20 1 5 3.2

14.77215.188

15.21

15.235

15.281

15.663

15.845

15.881

15.959

15.967

16.082

16.162

16.651

16.733

16.751

16.766

16.805

17.02

17.175

17.206


66/125

17.211

17.223

17.239

17.264

17.264 La distribucion que siguen estos datos es lognormal

17.497

17.5117.52

17.551

17.579

17.77

18.129

18.145

18.168

18.345

18.476

18.58

18.93

19.787


67/125


68/125


69/125

18. Utilice la prueba de Kolmogorov-Smirnov para determinar, con u n nivel de confianza de 90%,

qu tipo de distribucin siguen los datos. Compruebe con Stat::Fit.

2.865 4.419 3.681 6.502 1.141 2.773 2.299 4.589

2.336 2.201 1.186 3.61 0.753 2.653 3.574 3.588

3.42 1.123 3.264 2.219 1.962 2.915 4.282 4.835

1.242 3.725 4.317 1.694 3.286 3.698 3.208 1.628

3.117 1.283 3.821 0.943 1.713 4.715 1.74 2.769

1.904 3.144 3.541 1.494 5.983 1.649 4.02 1.475

1.304 2.151 2.953 1.06 7.8 7.621 2.872 1.474

5.632 2.941 2.274 1.841 1.651 4.009 2.54 2.669

2.285 4.579 3.631 6.574 1.941 3.255 1.372 2.284

2.819 3.47 3.158 2.194 1.524 2.105 2.806 4.819


1 1.123 0.0333 0.0000 -1.0897 1.1230 -1.0897

2 1.186 0.0667 0.0333 -1.1193 1.1527

3 1.242 0.1000 0.0667 -1.1420 1.1753

4 1.283 0.1333 0.1000 -1.1497 1.1830

5 1.304 0.1667 0.1333 -1.1373 1.1707

6 1.904 0.2000 0.1667 -1.7040 1.7373

7 2.151 0.2333 0.2000 -1.9177 1.9510

8 2.201 0.2667 0.2333 -1.9343 1.96779 2.274 0.3000 0.2667 -1.9740 2.0073

10 2.285 0.3333 0.3000 -1.9517 1.9850

11 2.336 0.3667 0.3333 -1.9693 2.0027

12 2.819 0.4000 0.3667 -2.4190 2.4523

13 2.865 0.4333 0.4000 -2.4317 2.4650

14 2.941 0.4667 0.4333 -2.4743 2.5077

15 2.953 0.5000 0.4667 -2.4530 2.4863

16 3.117 0.5333 0.5000 -2.5837 2.6170

17 3.144 0.5667 0.5333 -2.5773 2.6107

18 3.158 0.6000 0.5667 -2.5580 2.591319 3.264 0.6333 0.6000 -2.6307 2.6640

20 3.42 0.6667 0.6333 -2.7533 2.7867

21 3.47 0.7000 0.6667 -2.7700 2.8033

22 3.541 0.7333 0.7000 -2.8077 2.8410

23 3.631 0.7667 0.7333 -2.8643 2.8977

24 3.681 0.8000 0.7667 -2.8810 2.9143

25 3.725 0.8333 0.8000 -2.8917 2.9250

26 3.821 0.8667 0.8333 -2.9543 2.9877


70/125

27 4.317 0.9000 0.8667 -3.4170 3.4503

28 4.419 0.9333 0.9000 -3.4857 3.5190

29 4.579 0.9667 0.9333 -3.6123 3.6457

30 5.632 1.0000 0.9667 -4.6320 4.6653 4.6653

En tablas 0.220

Como 0.22


71/125

7.142 1.783

3.128 3.1

3.057 1

3.704 1.02

2.877 3.956

1.802 1.569

2.18 2.395

1.539 1.917

4.499 4.037

1.946 3.197

D


72/125

4.6653

s


73/125

19, Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los datos usando

la pruebo do Kolmogorov-Smirnov. Compruebe con Stat::Fit.

174.847 402.174 282.143 859.252 36.146 164.428 116.195 432.915119.609 107.279 38.269 271.768 21.4 151.421 266.496 268.621

244.874 35.337 223.936 108.878 87.316 180.701 378.203 479.587

40.973 288.761 384.365 67.65 226.819 284.664 216.767 63.229

205.085 43.048 303.22 27.863 68.959 456.507 70.826 164.015

82.842 208.481 261.858 54.809 989.3 64.625 334.56 53.719

44.148 102.905 185.161 32.573 1231.86 1176.46 175.667 53.632

647.174 183.747 113.87 78.092 64.731 332.889 139.595 153.12

114.911 431.138 274.864 877.946 85.668 222.815 47.822 114.754

169.609 251.844 210.369 106.671 56.651 98.984 168.127 476.397


1 35.337 0.0333 0.0000 -35.3037 35.3370 -35.3037

2 38.269 0.0667 0.0333 -38.2023 38.2357

3 40.973 0.1000 0.0667 -40.8730 40.9063

4 43.048 0.1333 0.1000 -42.9147 42.9480

5 44.148 0.1667 0.1333 -43.9813 44.0147

6 82.842 0.2000 0.1667 -82.6420 82.6753

7 102.905 0.2333 0.2000 -102.6717 102.7050

8 107.279 0.2667 0.2333 -107.0123 107.04579 113.87 0.3000 0.2667 -113.5700 113.6033

10 114.911 0.3333 0.3000 -114.5777 114.6110

11 119.609 0.3667 0.3333 -119.2423 119.2757

12 169.609 0.4000 0.3667 -169.2090 169.2423

13 174.847 0.4333 0.4000 -174.4137 174.4470

14 183.747 0.4667 0.4333 -183.2803 183.3137

15 185.161 0.5000 0.4667 -184.6610 184.6943

16 205.085 0.5333 0.5000 -204.5517 204.5850

17 208.481 0.5667 0.5333 -207.9143 207.9477

18 210.369 0.6000 0.5667 -209.7690 209.802319 223.936 0.6333 0.6000 -223.3027 223.3360

20 244.874 0.6667 0.6333 -244.2073 244.2407

21 251.844 0.7000 0.6667 -251.1440 251.1773

22 261.858 0.7333 0.7000 -261.1247 261.1580

23 274.864 0.7667 0.7333 -274.0973 274.1307

24 282.143 0.8000 0.7667 -281.3430 281.3763

25 288.761 0.8333 0.8000 -287.9277 287.9610

26 303.22 0.8667 0.8333 -302.3533 302.3867


74/125

27 384.365 0.9000 0.8667 -383.4650 383.4983

28 402.174 0.9333 0.9000 -401.2407 401.2740

29 431.138 0.9667 0.9333 -430.1713 430.2047

30 647.174 1.0000 0.9667 -646.1740 646.2073 646.2073

En tablas 0.220

Como 0.22


75/125

1034.5 73.83206.518 203.016

197.647 30.094

285.525 30.911

176.297 324.298

75.188 59.444

105.45 125.164

57.566 83.781

416.533 337.344

86.082 215.32

D


76/125

646.2073

ros

Los fatos siguen una distribucion

lognormal y exponencial.


77/125

20. A partir de la prueba de Kolmogorov-Smirnov, determine con un nivel de confianza de

90% qu tipo de distribucin siguen los datos. Compruebe con Stat::Fit.

0.488 0.116 0.731 0.094 0.684 0.093 0.368 0.09

0.995 0.908 0.183 0.146 0.633 0.567 0.058 0.507

0.088 0.382 0.707 0.413 0.581 0.254 0.44 0.447

0.149 0.427 0.743 0.434 0.26 0.738 0.3 0.3020.731 0.313 0.908 0.845 0.937 0.607 0.025 0.302

0.591 0.781 0.85 0.048 0.58 0.346 0.723 0.787

0.745 0.005 0.256 0.845 0.445 0.777 0.896 0.245

0.307 0.692 0.905 0.046 0.128 0.766 0.366 0.513

0.084 0.08 0.16 0.028 0.714 0.454 0.913 0.666

0.967 0.28 0.333 0.531 0.285 0.504 0.837 0.681


1 0.005 0.0333 0.0000 0.0283 0.0050

2 0.08 0.0667 0.0333 -0.0133 0.0467

3 0.084 0.1000 0.0667 0.0160 0.0173

4 0.088 0.1333 0.1000 0.0453 -0.0120

5 0.116 0.1667 0.1333 0.0507 -0.0173

6 0.149 0.2000 0.1667 0.0510 -0.0177

7 0.16 0.2333 0.2000 0.0733 -0.0400

8 0.183 0.2667 0.2333 0.0837 -0.0503

9 0.256 0.3000 0.2667 0.0440 -0.0107

10 0.28 0.3333 0.3000 0.0533 -0.0200

11 0.307 0.3667 0.3333 0.0597 -0.0263

12 0.313 0.4000 0.3667 0.0870 -0.0537

13 0.333 0.4333 0.4000 0.1003 -0.0670 0.1003

14 0.382 0.4667 0.4333 0.0847 -0.0513

15 0.427 0.5000 0.4667 0.0730 -0.0397

16 0.488 0.5333 0.5000 0.0453 -0.0120

17 0.591 0.5667 0.5333 -0.0243 0.0577

18 0.692 0.6000 0.5667 -0.0920 0.1253 0.1253

19 0.707 0.6333 0.6000 -0.0737 0.1070

20 0.731 0.6667 0.6333 -0.0643 0.0977

21 0.731 0.7000 0.6667 -0.0310 0.064322 0.743 0.7333 0.7000 -0.0097 0.0430

23 0.745 0.7667 0.7333 0.0217 0.0117

24 0.781 0.8000 0.7667 0.0190 0.0143

25 0.85 0.8333 0.8000 -0.0167 0.0500

26 0.905 0.8667 0.8333 -0.0383 0.0717

27 0.908 0.9000 0.8667 -0.0080 0.0413

28 0.908 0.9333 0.9000 0.0253 0.0080

29 0.967 0.9667 0.9333 -0.0003 0.0337


78/125

30 0.995 1.0000 0.9667 0.0050 0.0283

En tablas 0.220

Como 0.22


79/125

0.761 0.42

0.78 0.139

0.251 0.87

0.314 0.4230.608 0.078

0.535 0.61

0.335 0.194

0.302 0.833

0.213 0.373

0.209 0.626

D

0.1253


80/125

s


81/125

21. Determine, con un nivel de confianza de 90%, si la variable aleatoria representada por la

siguiente tabla de frecuencia sigue una distribucin exponencial con media 1.

Intervalo Frecuencia0--1 29

1--2 18

2--3 18

3--4 12

4--5 8

5--6 3

6--7 2

7--8 5

8--9 3

9--10 0

10--? 2

H0: Exponencial

H1: Otra Distribucion

Intervalo Oi Poi POAi PEAi [POAi - PEAi]0--1 29 0.29 0.29 0.6321 0.3421

1--2 18 0.18 0.47 0.8647 0.3947

2--3 18 0.18 0.65 0.9502 0.3002

3--4 12 0.12 0.77 0.9817 0.2117

4--5 8 0.08 0.85 0.9933 0.1433

5--6 3 0.03 0.88 0.9975 0.1175

6--7 2 0.02 0.9 0.9991 0.0991

7--8 5 0.05 0.95 0.9997 0.0497

8--9 3 0.03 0.98 0.9999 0.0199

9--10 0 0 0.98 1 0.02

10--? 2 0.02 1 1 0

Total 100 1 C 0.3947

El valor estadistico es C=0.3947

D0.1,100 = 0.1220

0

5

10

15

20

25

30

35

0--1 1--2 2--3 3--4 4--5 5--6 6--7


82/125

Se rechaza la hipotesis de que los numeros siguen una distribucion Exponencial.


83/125

7--8 8--9 9--10 10--?

Series1


84/125


datos; emplee la prueba de Anderson-Darling y compruebe con Stat::Fit.

Intervalo Frecuencia

?-12 312.0-12.5 4

12.5-13.0 3

13.0-13.5 6

13.5-14.0 8

14.0-14.5 15

14.5-15.0 12

15.0-15.5 13

15.5-16.0 7

16.0-16.5 16

16.5-17.0 7

17.0-? 6

0

2

4

6

8

10

12

14

16

18


85/125


86/125

Series1


87/125


88/125

23. Determine, con un nivel de confianza de 95%, qu tipo de distribucin

siguen los datos. Utilice la prueba Chi-Cuadrada,


?--150 0150--151 13

151--152 8

152--153 11

153--154 15

154--155 7

155--156 8

156--157 9

157--158 11

158--159 10

159--160 8

160--? 0


1 ?--150 0 8.33 8.330

2 150--151 13 8.33 2.618

3 151--152 8 8.33 0.013

4 152--153 11 8.33 0.8565 153--154 15 8.33 5.341

6 154--155 7 8.33 0.212

7 155--156 8 8.33 0.013

8 156--157 9 8.33 0.054

9 157--158 11 8.33 0.856

10 158--159 10 8.33 0.335

11 159--160 8 8.33 0.013

12 160--? 0 8.33 8.330

Total 100 99.96 26.971

En tablas 4.575 con grados de libertad de 11 y con un 95% de confiabilidad.

Por lo tanto como 4.575


89/125


90/125

24. Determinecon un nivel de confianza de 90%rqu tipo de distribucin

siguen los datos; emplee la prueba Chi-Cuadrada.


0--2 392--4 57

4--6 47

6--8 23

8--10 18

10--12 9

12--14 2

14--16 3

16--18 1

18--20 1

20--22 0

200


1 0--2 39 18.18 23.843

2 2--4 57 8.33 284.366

3 4--6 47 8.33 179.516

4 6--8 23 8.33 25.835

5 8--10 18 8.33 11.2266 10--12 9 8.33 0.054

7 12--14 2 8.33 4.810

8 14--16 3 8.33 3.410

9 16--18 1 8.33 6.450

10 18--20 1 8.33 6.450

11 20--22 0 8.33 8.330

Total 200 101.48 554.291


91/125

Los datos siguen una distribucion lognormal.


92/125

25. Utilice la prueba de Kolmogorov-Smirnov para determinar con un nivel de confianza de 95% q

4 5 3 5 5 4 3 2 4 3

4 6 4 3 5 2 2 3 3 4

4 4 3 3 3 2 2 3 2 3

3 4 5 2 3 4 3 3 5 3

2 5 3 4 4 1 4 5 4 5

7 2 4 4 2 4 1 5 4 4

5 5 5 2 4 4 5 4 4 1

6 4 6 6 2 4 4 2 2 2

3 3 2 5 3 5 1 3 2 4

1 2 5 2 3 1 5 3 2 5

No: 100

Oi Poi POAi PEAi

0 - 1 6 0.06 0.06 0.097922 - 3 43 0.43 0.49 0.37459

4 - 5 46 0.46 0.95 0.61319

6 - 5 0.05 1.00 1.00000

100 1.00 c=

Tomando como base: 0.136

: 1.38

: 5.19

MEDIA MUESTRAL

VARIANZA

0.4143

0.3368

0.0000

Intervalos POAi - PEAi

-0.03790.1154


93/125

tipo de distribucin siguen los datos.

3.49

1.7676

0

5

10

15

20

25

30

35

40

45

50

1 3 5

- - - -

0 2 4 6


94/125

26. Determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los datos usando l

1 0 0 1 0 0 1 0 0 0 Intervalo Oi POi POAi PEAi

0 0 0 1 0 0 0 0 0 0 0 56 0.56 0.56 0.6005

0 0 1 0 0 0 0 0 1 1 1 37 0.37 0.93 0.90671 0 1 2 1 1 1 0 0 0 2 7 0.07 1 0.9848

1 0 1 2 0 0 1 1 0 1 c

0 1 1 0 0 1 1 2 1 0

1 2 0 1 1 1 0 1 0 1

1 0 1 2 0 0 1 2 1 0

1 0 0 0 0 0 0 0 1 0

0 0 0 1 0 1 2 1 0 0

5

Documents

Simulacion Promodel Ejercicios Unidad 3