A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit
Table 2
Simulated expected lengths of 95% UPL that contain at least l of m future observations at each of r locations from Weibull distribution for sample sizes , 10, 20 using GV, CNPT, and BCKL methods*.
GV
CNPT
BCKL
GV
CNPT
BCKL
GV
CNPT
BCKL
, ,
0.1
0.5
0.38
0.37
0.37
0.25
0.25
0.25
0.19
0.18
0.18
1
0.18
0.18
0.18
0.15
0.15
0.15
0.13
0.13
0.13
3
0.12
0.12
0.12
0.11
0.11
0.11
0.11
0.11
0.11
1
0.5
3.80
3.76
3.77
2.50
2.47
2.46
1.85
1.79
1.78
1
1.79
1.78
1.78
1.51
1.50
1.49
1.33
1.31
1.30
3
1.19
1.19
1.19
1.13
1.13
1.13
1.09
1.09
1.09
5
0.5
19.10
18.63
18.71
12.53
12.31
12.28
9.25
9.00
8.93
1
9.00
8.90
8.91
7.55
7.48
7.46
6.64
6.54
6.51
3
5.96
5.94
5.94
5.67
5.65
5.65
5.46
5.44
5.43
50
0.5
190.16
186.02
186.79
124.82
123.47
123.08
92.75
89.95
89.25
1
90.03
88.84
89.00
75.45
74.85
74.73
66.36
65.44
65.18
3
59.64
59.40
59.44
56.70
56.54
56.51
54.62
54.39
54.32
100
0.5
383.79
374.67
376.24
251.24
247.09
246.32
184.91
180.11
178.70
1
179.98
178.41
178.72
151.07
149.92
149.66
132.80
130.95
130.43
3
119.27
118.77
118.83
113.40
113.11
113.04
109.24
108.74
108.59
, ,
0.1
0.5
0.27
0.27
0.26
0.18
0.18
0.18
0.14
0.13
0.13
1
0.15
0.15
0.15
0.13
0.13
0.13
0.11
0.11
0.11
3
0.11
0.11
0.11
0.11
0.11
0.11
0.10
0.10
0.10
1
0.5
2.66
2.64
2.63
1.82
1.79
1.78
1.38
1.34
1.32
1
1.51
1.50
1.50
1.29
1.27
1.27
1.14
1.13
1.12
3
1.13
1.12
1.12
1.08
1.07
1.07
1.04
1.03
1.03
5
0.5
13.34
13.20
13.16
9.11
8.96
8.88
6.91
6.68
6.60
1
7.55
7.50
7.49
6.43
6.39
6.36
5.74
5.63
5.60
3
5.63
5.61
5.61
5.38
5.36
5.36
5.20
5.17
5.16
50
0.5
133.95
132.56
130.91
91.13
89.64
88.90
69.09
66.84
66.04
1
75.44
75.21
74.90
64.36
63.77
63.47
57.36
56.35
56.00
3
56.31
56.16
56.11
53.78
53.59
53.56
51.98
51.72
51.63
100
0.5
266.35
263.65
264.21
182.16
178.70
177.11
138.26
133.44
132.09
1
151.03
149.96
149.92
128.62
127.63
127.06
114.74
112.72
112.11
3
112.63
112.38
112.23
107.49
107.24
107.02
104.02
103.40
103.22
, ,
0.1
0.5
1.65
1.41
1.46
0.75
0.71
0.73
0.49
0.47
0.47
1
0.36
0.33
0.33
0.26
0.25
0.25
0.22
0.21
0.21
3
0.15
0.14
0.15
0.14
0.13
0.13
0.13
0.13
0.13
1
0.5
16.54
14.00
14.60
7.55
7.13
7.26
4.87
4.64
4.67
1
3.56
3.28
3.34
2.59
2.51
2.54
2.15
2.10
2.11
3
1.48
1.44
1.45
1.35
1.34
1.34
1.28
1.27
1.27
5
0.5
82.85
70.44
73.11
37.77
35.69
36.25
24.36
23.18
23.40
1
17.79
16.52
16.75
12.93
12.54
12.67
10.73
10.47
10.53
3
7.40
7.22
7.26
6.77
6.70
6.73
6.41
6.36
6.37
50
0.5
830.35
710.92
733.32
376.12
355.27
362.96
242.46
232.30
234.39
1
177.94
164.84
166.79
129.32
125.54
127.11
107.39
104.72
105.50
3
74.12
72.18
72.67
67.71
67.05
67.21
64.11
63.63
63.68
100
0.5
1650.20
1408.03
1456.67
754.87
713.90
725.43
485.52
464.88
467.82
1
356.26
328.69
334.60
258.73
251.05
252.98
214.54
209.88
210.49
3
148.20
144.36
145.19
135.32
134.11
134.56
128.23
127.21
127.43
*Results are obtained assuming unknown scale and shape parameters .
