Таблица А.57
Оптимальные граничные точки интервалов группирования при проверке сложных гипотез по критериям типа c 2 (при оценивании масштабного и основного параметров гамма-распределения в зависимости от значений основного параметра q 0) и соответствующие значения относительной асимптотической информации A
|
k |
ti |
q 0 |
|||||||||||||
|
0,1 |
0,25 |
0,5 |
0,75 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|||
|
3 |
t1 |
0,0002 |
0,0001 |
0,0174 |
0,0674 |
0,1465 |
0,6326 |
1,2531 |
1,9397 |
2,6678 |
3,4243 |
4,1991 |
5,0000 |
5,5684 |
|
|
t2 |
0,7690 |
1,3001 |
1,3958 |
1,7831 |
2,1616 |
3,6024 |
4,9530 |
6,2482 |
7,5171 |
8,7554 |
9,9722 |
11,0000 |
11,5683 |
||
|
A |
0,2935 |
0,4295 |
0,4235 |
0,4191 |
0,4160 |
0,4108 |
0,4090 |
0,4082 |
0,4078 |
0,4076 |
0,4074 |
0,4066 |
0,3959 |
||
|
4 |
t1 |
0,0001 |
0,0009 |
0,0141 |
0,0547 |
0,1192 |
0,5255 |
1,0651 |
1,6535 |
2,3099 |
3,0485 |
3,8332 |
4,4721 |
5,1905 |
|
|
t2 |
0,1050 |
0,4420 |
0,7205 |
0,9295 |
1,1408 |
2,0195 |
2,9542 |
3,7846 |
4,7349 |
5,9786 |
7,0038 |
7,7331 |
8,5822 |
||
|
t3 |
1,0554 |
1,6647 |
2,1525 |
2,5459 |
2,9273 |
4,3900 |
5,7928 |
7,0557 |
8,3627 |
9,8297 |
11,0038 |
12,1919 |
13,3510 |
||
|
A |
0,3907 |
0,5375 |
0,5533 |
0,5528 |
0,5522 |
0,5519 |
0,5516 |
0,5518 |
0,5520 |
0,5519 |
0,5518 |
0,5522 |
0,5522 |
||
|
5 |
t1 |
0,0001 |
0,0001 |
0,0022 |
0,0163 |
0,0489 |
0,3372 |
0,7833 |
1,3162 |
1,9088 |
2,5400 |
3,2076 |
3,8879 |
4,5914 |
|
|
t2 |
0,0067 |
0,0069 |
0,0562 |
0,1567 |
0,2866 |
0,9477 |
1,7049 |
2,5067 |
3,3384 |
4,1833 |
5,0516 |
5,9108 |
6,7911 |
||
|
t3 |
0,4719 |
0,4976 |
0,9018 |
1,2211 |
1,5380 |
2,7990 |
4,0007 |
5,1861 |
6,3503 |
7,4937 |
8,6378 |
9,7492 |
10,8738 |
||
|
t4 |
1,6365 |
1,7707 |
2,3241 |
2,8083 |
3,2629 |
4,9736 |
6,4906 |
7,9494 |
9,3623 |
10,7201 |
12,0696 |
13,3731 |
14,6632 |
||
|
A |
0,4606 |
0,6722 |
0,6873 |
0,6863 |
0,6854 |
0,6843 |
0,6831 |
0,6829 |
0,6828 |
0,6827 |
0,6827 |
0,6827 |
0,6827 |
||
|
6 |
t1 |
0,0001 |
0,0001 |
0,0015 |
0,0117 |
0,0359 |
0,2749 |
0,6666 |
1,1605 |
1,7122 |
2,3025 |
2,9247 |
3,5934 |
4,2563 |
|
|
t2 |
0,0084 |
0,0081 |
0,0395 |
0,1075 |
0,1994 |
0,7283 |
1,3734 |
2,0974 |
2,8583 |
3,6306 |
4,4208 |
5,2755 |
6,0669 |
||
|
t3 |
0,3965 |
0,4143 |
0,5026 |
0,6546 |
0,8360 |
1,7532 |
2,6992 |
3,7061 |
4,7238 |
5,7019 |
6,6737 |
7,7638 |
8,6866 |
||
|
t4 |
1,0052 |
1,1842 |
1,4058 |
1,7072 |
2,0307 |
3,3927 |
4,6776 |
5,9657 |
7,2088 |
8,4152 |
9,5909 |
10,8271 |
11,9504 |
||
|
t5 |
2,1652 |
2,4989 |
2,8500 |
3,2836 |
3,7235 |
5,4747 |
7,0410 |
8,5901 |
10,0180 |
11,4056 |
12,7849 |
14,1612 |
15,4369 |
||
|
A |
0,4971 |
0,7353 |
0,7537 |
0,7547 |
0,7550 |
0,7562 |
0,7552 |
0,7553 |
0,7553 |
0,7554 |
0,7554 |
0,7554 |
0,7554 |
||
Продолжение таблицы А.57
|
k |
ti |
q 0 |
|||||||||||||
|
0,1 |
0,25 |
0,5 |
0,75 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|||
|
7 |
t1 |
0,0001 |
0,0001 |
0,0004 |
0,0057 |
0,0221 |
0,2167 |
0,5653 |
1,0141 |
1,5232 |
2,0821 |
2,6677 |
3,2932 |
3,9406 |
|
|
t2 |
0,0038 |
0,0025 |
0,0108 |
0,0500 |
0,1166 |
0,5478 |
1,1131 |
1,7702 |
2,4536 |
3,1743 |
3,9123 |
4,6777 |
5,4648 |
||
|
t3 |
0,1797 |
0,0410 |
0,0925 |
0,2284 |
0,3912 |
1,1407 |
1,9393 |
2,8270 |
3,6910 |
4,5783 |
5,4600 |
6,3671 |
7,3013 |
||
|
t4 |
0,5288 |
0,4646 |
0,6828 |
0,9915 |
1,2954 |
2,4686 |
3,5748 |
4,7415 |
5,8355 |
6,9445 |
8,0213 |
9,1131 |
10,2077 |
||
|
t5 |
1,0436 |
1,1561 |
1,5670 |
2,0188 |
2,4198 |
3,9694 |
5,3077 |
6,6860 |
7,9718 |
9,2499 |
10,4796 |
11,7240 |
12,9476 |
||
|
t6 |
2,2397 |
2,4021 |
2,9833 |
3,5832 |
4,0461 |
5,9991 |
7,5653 |
9,1629 |
10,6299 |
12,0854 |
13,4560 |
14,8718 |
16,2321 |
||
|
A |
0,5114 |
0,7667 |
0,8105 |
0,8109 |
0,8108 |
0,8119 |
0,8102 |
0,8102 |
0,8102 |
0,8102 |
0,8102 |
0,8102 |
0,8102 |
||
|
8 |
t1 |
0,0001 |
0,0001 |
0,0003 |
0,0040 |
0,0159 |
0,1844 |
0,4977 |
0,9170 |
1,3943 |
1,9240 |
2,5077 |
3,0919 |
3,7563 |
|
|
t2 |
0,0027 |
0,0022 |
0,0084 |
0,0348 |
0,0826 |
0,4551 |
0,9594 |
1,5625 |
2,2038 |
2,8839 |
3,6103 |
4,3191 |
5,1373 |
||
|
t3 |
0,0957 |
0,0328 |
0,0705 |
0,1502 |
0,2602 |
0,8978 |
1,5950 |
2,3867 |
3,1820 |
4,0075 |
4,8728 |
5,6906 |
6,6741 |
||
|
t4 |
0,3263 |
0,3834 |
0,4798 |
0,5781 |
0,7609 |
1,7715 |
2,6854 |
3,7086 |
4,6920 |
5,6847 |
6,7305 |
7,6677 |
8,9040 |
||
|
t5 |
0,6101 |
0,9448 |
1,1839 |
1,3564 |
1,6561 |
3,0194 |
4,1947 |
5,4260 |
6,6012 |
7,7777 |
8,9631 |
10,0664 |
11,4006 |
||
|
t6 |
1,2780 |
1,7712 |
2,1530 |
2,3744 |
2,7596 |
4,4362 |
5,8189 |
7,2285 |
8,5823 |
9,8976 |
11,2079 |
12,4406 |
13,8668 |
||
|
t7 |
2,3017 |
3,1466 |
3,6705 |
3,9163 |
4,4165 |
6,4500 |
8,0196 |
9,6251 |
11,1743 |
12,6288 |
14,0809 |
15,4715 |
16,9779 |
||
|
A |
0,5196 |
0,7959 |
0,8453 |
0,8468 |
0,8470 |
0,8491 |
0,8471 |
0,8472 |
0,8472 |
0,8472 |
0,8472 |
0,8472 |
0,8471 |
||
Окончание таблицы А.57
|
k |
ti |
q 0 |
||||||||||||
|
0,1 |
0,25 |
0,5 |
0,75 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
||
|
9 |
t1 |
0,0001 |
0,0001 |
0,0002 |
0,0022 |
0,0117 |
0,1574 |
0,4415 |
0,8250 |
1,2787 |
1,8036 |
2,3310 |
2,9325 |
3,5049 |
|
t2 |
0,0036 |
0,0018 |
0,0037 |
0,0189 |
0,0595 |
0,3801 |
0,8363 |
1,3799 |
1,9839 |
2,6636 |
3,3046 |
4,0472 |
4,7203 |
|
|
t3 |
0,1629 |
0,0233 |
0,0294 |
0,0782 |
0,1800 |
0,7206 |
1,3446 |
2,0408 |
2,7845 |
3,6131 |
4,3498 |
5,2235 |
5,9677 |
|
|
t4 |
0,4542 |
0,2630 |
0,1561 |
0,2537 |
0,4663 |
1,3046 |
2,1024 |
2,9543 |
3,8605 |
4,8731 |
5,6929 |
6,7298 |
7,5272 |
|
|
t5 |
0,8449 |
0,6803 |
0,7006 |
0,8015 |
1,1711 |
2,3623 |
3,3756 |
4,4160 |
5,5171 |
6,7275 |
7,6700 |
8,8737 |
9,8149 |
|
|
t6 |
1,3601 |
1,2444 |
1,4308 |
1,5324 |
2,0444 |
3,5295 |
4,7341 |
5,9506 |
7,2053 |
8,5518 |
9,6244 |
10,9257 |
11,9962 |
|
|
t7 |
2,0236 |
2,0557 |
2,4709 |
2,4940 |
3,1377 |
4,8994 |
6,2737 |
7,6705 |
9,0544 |
10,5335 |
11,7263 |
13,1211 |
14,3026 |
|
|
t8 |
3,2912 |
3,3968 |
4,0759 |
3,9852 |
4,7460 |
6,9403 |
8,4320 |
9,9701 |
11,5363 |
13,1888 |
14,4967 |
15,9995 |
17,3478 |
|
|
A |
0,5331 |
0,8132 |
0,8731 |
0,8746 |
0,8752 |
0,8777 |
0,8750 |
0,8751 |
0,8751 |
0,8751 |
0,8752 |
0,8751 |
0,8752 |
|
|
10 |
t1 |
0,0001 |
0,0001 |
0,0001 |
0,0017 |
0,0088 |
0,1354 |
0,4037 |
0,7710 |
1,2056 |
1,7008 |
2,2056 |
2,7623 |
3,3874 |
|
t2 |
0,0014 |
0,0011 |
0,0015 |
0,0148 |
0,0445 |
0,3236 |
0,7554 |
1,2761 |
1,8522 |
2,4850 |
3,1019 |
3,7698 |
4,5270 |
|
|
t3 |
0,0258 |
0,0105 |
0,0114 |
0,0599 |
0,1314 |
0,5997 |
1,1925 |
1,8495 |
2,5594 |
3,3033 |
4,0198 |
4,7890 |
5,6411 |
|
|
t4 |
0,1769 |
0,0813 |
0,0537 |
0,1839 |
0,3195 |
1,0272 |
1,7976 |
2,6008 |
3,4385 |
4,3011 |
5,1228 |
5,9921 |
6,9987 |
|
|
t5 |
0,4189 |
0,3690 |
0,2154 |
0,5363 |
0,7622 |
1,7846 |
2,7624 |
3,7386 |
4,7390 |
5,7567 |
6,6818 |
7,6452 |
8,7656 |
|
|
t6 |
0,7642 |
0,7764 |
0,6807 |
1,1571 |
1,4768 |
2,7934 |
3,9800 |
5,1491 |
6,3872 |
7,4632 |
8,5358 |
9,6020 |
10,8348 |
|
|
t7 |
1,2344 |
1,3290 |
1,3022 |
1,9077 |
2,3108 |
3,8955 |
5,2602 |
6,5860 |
7,9069 |
9,1388 |
10,3168 |
11,5153 |
12,8376 |
|
|
t8 |
1,9812 |
2,1251 |
2,1657 |
2,9083 |
3,3819 |
5,2597 |
6,7736 |
8,2430 |
9,6771 |
11,0173 |
12,3097 |
13,6369 |
15,0781 |
|
|
t9 |
3,1510 |
3,4573 |
3,5785 |
4,4672 |
5,0088 |
7,3134 |
8,9003 |
10,5600 |
12,2411 |
13,5436 |
15,0178 |
16,4962 |
18,0356 |
|
|
A |
0,5362 |
0,8245 |
0,8936 |
0,8956 |
0,8958 |
0,8990 |
0,8957 |
0,8958 |
0,8956 |
0,8958 |
0,8959 |
0,8959 |
0,8959 |
|