PORTAL ESTADÍSTICA APLICADA

 

DISTRIBUCIÓN PROBABILIDAD CHI-CUADRADO

 

Para n > 30 la variable

n

a

0.995

0.99

0.98

0.975

0.95

0.90

0.10

0.05

0.025

0.02

0.01

1

0,04393

0,03157

0,03628

0,03982

0,00393

0,0158

2,706

3,841

5,024

5,412

6,635

2

0,0100

0,0201

0,0404

0,0506

0,103

0,211

4,605

5,991

7,378

7,824

9,210

3

0,0717

0,115

0,185

0,216

0,352

0,584

6,251

7,815

9,348

9,837

11,345

4

0,207

0,297

0,429

0,484

0,711

1,064

7,779

9,488

11,143

11,668

13,277

5

0,412

0,554

0,752

0,831

1,145

1,610

9,236

11,070

12,832

13,388

15,086

6

0,676

0,872

1,134

1,237

1,635

2,204

10,645

12,592

14,449

15,033

16,812

7

0,989

1,239

1,564

1,690

2,167

2,833

12,017

14,067

16,013

16,622

18,475

8

1,344

1,646

2,032

2,180

2,733

3,490

13,362

15,507

17,535

18,168

20,090

9

1,735

2,088

2,532

2,700

3,325

4,168

14,684

16,919

19,023

19,679

21,666

10

2,156

2,558

3,059

3,247

3,940

4,865

15,987

18,307

20,483

21,161

23,209

11

2,603

3,053

3,609

3,816

4,575

5,578

17,275

19,675

21,920

22,618

24,725

12

3,074

3,571

4,178

4,404

5,226

6,304

18,549

21,026

23,337

24,054

26,217

13

3,565

4,107

4,765

5,009

5,892

7,042

19,812

22,362

24,736

25,472

27,688

14

4,075

4,660

5,368

5,629

6,571

7,790

21,064

23,685

26,119

26,873

29,141

15

4,601

5,229

5,985

6,262

7,261

8,547

22,307

24,996

27,488

28,259

30,578

16

5,142

5,812

6,614

6,908

7,962

10,312

23,542

26,296

28,845

29,633

32,000

17

5,697

6,408

7,255

7,564

8,672

10,085

24,769

27,587

30,191

30,995

33,409

18

6,265

7,015

7,906

8,231

9,390

10,865

25,989

28,869

31,526

32,346

34,805

19

6,844

7,633

8,567

8,907

10,117

11,651

27,204

30,144

32,852

33,687

36,191

20

7,434

8,260

9,237

9,591

10,851

12,443

28,412

31,410

34,170

35,020

37,566

21

8,034

8,897

9,915

10,283

11,591

13,240

29,615

32,671

35,479

36,343

38,932

22

8,643

9,542

10,600

10,982

12,338

14,041

30,813

33,924

36,781

37,659

40,289

23

9,260

10,196

11,293

11,668

13,091

14,848

32,007

35,172

38,076

38,968

41,638

24

9,886

10,856

11,992

12,401

13,848

15,659

33,196

36,415

39,364

40,270

42,980

25

10,520

11,524

12,697

13,120

14,611

16,473

34,382

37,652

40,646

41,566

44,314

26

11,160

12,198

13,409

13,844

15,379

17,292

35,563

38,885

41,923

42,856

45,642

27

11,808

12,879

14,125

14,573

16,151

18,114

36,741

40,113

43,194

44,140

46,963

28

12,461

13,565

14,847

15,308

16,928

18,939

37,916

41,337

44,461

45,419

48,278

29

13,121

14,256

15,574

16,407

17,708

19,768

39,087

42,557

45,722

46,693

49,588

30

13,787

14,953

16,306

16,791

18,493

20,599

40,256

43,773

46,979

47,962

50,892

Distribución c 2 de Pearson

 

Sean n variables aleatorias N(0, 1) independientes entre sí . La variable

 

 

recibe el nombre de c 2 (chi-cuadrado) de Pearson con 'n' grados de libertad. Su función de densidad es:

 

 

en donde, para p > 0, se define la función Gamma:

 

 

con lo cual,

 

 

 

 

   

 

PREMIO NOBEL DE ECONOMÍA (1969-2016)

 

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