tabla chi cuadrado

DISTRIBUCION JI CUADRADO
Jorge M. Galbiati
Funci´
on de densidad:
f (x) =

1
xk/2−1 e−x/2
k/2
2 Γ(k/2)

Grados de libertad k ∈ {1, 2, 3, ...}

Espacio param´
etrico:
Valor esperado:
Varianza:

si x > 0

k

2k
1
1−2t

Funci´
on generadora de momentos:

k/2

para t < 1/2

TABLA DE DISTRIBUCION JI CUADRADO
La tabla entrega valores de la cuantila z para valores dados de probabilidad acumux
lada F (x)= 0 f (y)dy.
Los valores de probabilidad acumulada son 0.0005; 0.001; 0.0025; 0.005; 0.010; 0.025;
desde 0.050 hasta 0.950, variando en 0.050; 0.975; 0.990; 0.995; 0.998; 0.999; 0.9995.
Los valores de los grados de libertad son: De 1 a 30; de 35 a 100 variando en 5; 110;
120; 200.
f(y)

F(x)
0

x

y

APROXIMACION NORMAL DE LA JI-CUADRADO.
Si una variable aleatoria X tiene distribuci´onji-cuadrado con k grados de libertad,
tiene distribuci´on aproximada
entonces si k es grande la variable aleatoria Z = √X−k
(2k)
normal standard.
En la pr´actica, si k es grande, si se requiere la probabilidad acumulada F (x) con
F distribuci´on ji-cuadrado, se puede obtener su valor aproximado buscando en la
tabla normal
x−k
FN √
(2k)
andar. Se puede utilizar, como criterio, la
en que FN es ladistribuci´on normal est´
condici´on k > 200.

TABLA DE DISTRIBUCION JI - CUADRADO
Grados de
Libertad
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
200

0.0005
0.000
0.001
0.015
0.064
0.158
0.299
0.485
0.710
0.972
1.265
1.587
1.934
2.305
2.697
3.108
3.536
3.980
4.439
4.912
5.398
5.896
6.404
6.924
7.453
7.991
8.538
9.0939.656
10.23
10.80
13.79
16.91
20.14
23.46
26.87
30.34
33.88
37.47
41.11
44.79
48.52
52.28
56.07
59.90
67.63
75.47
140.7

Probabilidad acumulada
0.001
0.000
0.002
0.024
0.091
0.210
0.381
0.598
0.857
1.152
1.479
1.834
2.214
2.617
3.041
3.483
3.942
4.416
4.905
5.407
5.921
6.447
6.983
7.529
8.085
8.649
9.222
9.803
10.39
10.99
11.59
14.69
17.92
21.25
24.67
28.17
31.74
35.36
39.04
42.76
46.52
50.32
54.1658.02
61.92
69.79
77.76
143.8

0.0025
0.000
0.005
0.045
0.145
0.307
0.527
0.794
1.104
1.450
1.827
2.232
2.661
3.112
3.582
4.070
4.573
5.092
5.623
6.167
6.723
7.289
7.865
8.450
9.044
9.646
10.26
10.87
11.50
12.13
12.76
16.03
19.42
22.90
26.46
30.10
33.79
37.54
41.33
45.17
49.04
52.95
56.89
60.86
64.86
72.92
81.07
148.4

0.005
0.000
0.010
0.072
0.207
0.412
0.676
0.989
1.344
1.735
2.156
2.603
3.0743.565
4.075
4.601
5.142
5.697
6.265
6.844
7.434
8.034
8.643
9.260
9.886
10.52
11.16
11.81
12.46
13.12
13.79
17.19
20.71
24.31
27.99
31.73
35.53
39.38
43.28
47.21
51.17
55.17
59.20
63.25
67.33
75.55
83.85
152.2

0.010
0.000
0.020
0.115
0.297
0.554
0.872
1.239
1.646
2.088
2.558
3.053
3.571
4.107
4.660
5.229
5.812
6.408
7.015
7.633
8.260
8.897
9.542
10.20
10.86
11.52
12.20
12.88
13.56
14.26
14.9518.51
22.16
25.90
29.71
33.57
37.48
41.44
45.44
49.48
53.54
57.63
61.75
65.90
70.06
78.46
86.92
156.4

0.025
0.001
0.051
0.216
0.484
0.831
1.237
1.690
2.180
2.700
3.247
3.816
4.404
5.009
5.629
6.262
6.908
7.564
8.231
8.907
9.591
10.28
10.98
11.69
12.40
13.12
13.84
14.57
15.31
16.05
16.79
20.57
24.43
28.37
32.36
36.40
40.48
44.60
48.76
52.94
57.15
61.39
65.65
69.92
74.22
82.87
91.57
162.7

0.050
0.0040.103
0.352
0.711
1.145
1.635
2.167
2.733
3.325
3.940
4.575
5.226
5.892
6.571
7.261
7.962
8.672
9.390
10.12
10.85
11.59
12.34
13.09
13.85
14.61
15.38
16.15
16.93
17.71
18.49
22.47
26.51
30.61
34.76
38.96
43.19
47.45
51.74
56.05
60.39
64.75
69.13
73.52
77.93
86.79
95.70
168.3

0.100
0.016
0.211
0.584
1.064
1.610
2.204
2.833
3.490
4.168
4.865
5.578
6.304
7.042
7.790
8.547
9.312
10.09
10.86
11.6512.44
13.24
14.04
14.85
15.66
16.47
17.29
18.11
18.94
19.77
20.60
24.80
29.05
33.35
37.69
42.06
46.46
50.88
55.33
59.79
64.28
68.78
73.29
77.82
82.36
91.47
100.6
174.8

0.150
0.036
0.325
0.798
1.366
1.994
2.661
3.358
4.078
4.817
5.570
6.336
7.114
7.901
8.696
9.499
10.31
11.12
11.95
12.77
13.60
14.44
15.28
16.12
16.97
17.82
18.67
19.53
20.39
21.25
22.11
26.46
30.86
35.29
39.75
44.24
48.76
53.29...