Jadval-2
“O‘zbekiston temir yo‘llari” AJ eksport yuklarini tashish hajmi bo‘yicha ma `lumotning
tahlili
Jadval-2 ma’lumotlari bo‘yicha, quyidagi miqdorlarni
1
2
3
4
5
6
7
N п/п
йиллар
Минг тонна
t
t
2
1
2013
7 424 160
-4
16
-29 696 640
118 786 560
2
2014
6 550 076
-3
9
-19 650 228
58 950 684
3
2015
5 269 100
-2
4
-10 538 200
21 076 400
4
2016
6 114 334
-1
1
-6 114 334
6 114 334
5
2017
8 007 353
0
0
0
0
6
2018
8 479 203
1
1
8 479 203
8 479 203
7
2019
8 762 317
2
4
17 524 634
35 049 268
8
2020
10 412 320
3
9
31 236 960
93 710 880
9
2021
11 901 340
4
16
47 605 360
190 421 440
10
2022
10 892 392
5
25
54 461 960
272 309 800
сумма
83 812 595
5
85
93 308 715
804 898 569
t
t
t
Y
Y
Y
−
=
+
1
t
t
t
Y
Y
Y
−
=
+
1
2
t
t
t
Y
Y
Y
2
1
2
3
−
=
+
t
t
t
Y
Y
Y
−
=
+
1
t
t
t
Y
Y
Y
−
=
+
1
2
t
t
t
Y
Y
Y
2
1
2
3
−
=
+
1
2
3
4
5
6
7
8
9
10
N п/п
Годы
наблюде
ний
Y
t
2
ΔY
t
ΔY
t
2
Δ
2
Y
t
Δ
2
Y
t
2
Δ
3
Y
t
Δ
3
Y
t
2
1
2013
7 424 160,0
55 118 151 705 600,0
2
2014
6 550 076,0
42 903 495 605 776,0
-874 084,0
764 022 839 056,0
3
2015
5 269 100,0
27 763 414 810 000,0
-1 280 976,0
1 640 899 512 576,0
-406 892,0
165 561 099 664,0
4
2016
6 114 334,0
37 385 080 263 556,0
845 234,0
714 420 514 756,0
2 126 210,0
4 520 768 964 100,0
2 533 102,0
6 416 605 742 404,0
5
2017
8 007 353,0
64 117 702 066 609,0
1 893 019,0
3 583 520 934 361,0
1 047 785,0
1 097 853 406 225,0
-1 078 425,0
1 163 000 480 625,0
6
2018
8 479 203,0
71 896 883 515 209,0
471 850,0
222 642 422 500,0
-1 421 169,0
2 019 721 326 561,0
-2 468 954,0
6 095 733 854 116,0
7
2019
8 762 317,0
76 778 199 208 489,0
283 114,0
80 153 536 996,0
-188 736,0
35 621 277 696,0
1 232 433,0
1 518 891 099 489,0
8
2020
10 412 320,0 108 416 407 782 400,0
1 650 003,0
2 722 509 900 009,0
1 366 889,0
1 868 385 538 321,0
1 555 625,0
2 419 969 140 625,0
9
2021
11 901 340,0 141 641 893 795 600,0
1 489 020,0
2 217 180 560 400,0
-160 983,0
25 915 526 289,0
-1 527 872,0
2 334 392 848 384,0
10
2022
10 892 392,0 118 644 203 481 664,0
-1 008 948,0
1 017 976 066 704,0
-2 497 968,0
6 239 844 129 024,0
-2 336 985,0
5 461 498 890 225,0
Сумма
83 812 595,0 744 665 432 234 903,0 3 468 232,0 12 963 326 287 358,0
-134 864,0
15 973 671 267 880,0
-2 091 076,0
25 410 092 055 868,0
392
, 𝑘 = 1,2,3
qiymatlarini hisoblaganimizda, chekli ayirmalarning variatsiya koeffitsienlarini qiymatlarini o‘zaro
taqriban tengligini ko‘ramiz
𝑉
1
≈
𝑉
2
≈ 𝑉
3
. Bu o‘rganilayotgan dinamik qatorning trend qismini
chiziqli bog‘lanishga ega ekanligini, ya’ni yuqorida to‘g‘ri trend model tanlanganini tasdiqlaydi.
Vaqtli qatorni xususiyatlarini o‘rganishda avtokorrelyasiya koeffitsienti muhim ahamiyatga ega.
Avtokorrelyasiya koeffitsientini hisoblash uchun statistik ma’lumotlar yordamida quyidagi jadval-3
ni tuzamiz.
Jadval-3
“O‘zbekiston temir yo‘llari” AJ eksport yuklarini tashish hajmi bo‘yicha ma `lumotning
tahlili
Jadval-3 asosida, quyidagi formula bilan, avtokorrelyasiya koeffitsientlarini hisoblaymiz
([1]-[5]):
(4)
R
L
ning
𝑅
2
, ...,
𝑅
5
qiymatlarini L yilga (L-lag ya’ni yillarni L=1,2,3,4,5 ga so‘rib
hisoblashlar ko‘rsatadiki, ularning barcha qiymatlari noldan farqli. Demak, dinamik qator sifatida
O’zbekiston Respublikasining temir yo’l transporti aksionerlik jamiyati tomonidan tashilgan eksport
yuklari hajmini, avtokorrelyasion bog‘lanishga ega ekanligini tasdiqlaydi.
Bu gipotezani yani avtokorrelyasion bog‘lanishga ega ekanligini quyidagi Darbin-Vatson
kriteriyasi bilan tekshirganimizda ham:
𝑑
𝑘𝑢𝑧
= ∑(𝑌
𝑡+1
− 𝑌
𝑡
)
2
/
𝑇−1
𝑡=1
∑ 𝑌
𝑡
2
.
𝑇
𝑡=1
barcha
𝑑
𝑘𝑢𝑧
- qiymatlarini, maxsus jadvaldan[1]-[5] topilgan,
𝑑
𝑘𝑟𝑖𝑡
= 1. 04
kritik qiymatidan
kichik
𝑑
𝑘𝑢𝑧
< 𝑑
𝑘𝑟𝑖𝑡
ekanligini ko‘ramiz. Demak, 95% li kafolat bilan, o’rganilayotgan tasodifiy
jarayon avtokorrelyasion
t
t
t
y
y
+
=
−
1
,
=Cov (y
t
, y
t+1
) bog‘lanishga ega. Ya’ni bu yilda
O’zbekiston Respublikasining temir yo’l transporti jamiyati tomonidan tashilgan eksport yuklari
(
)
(
)
C
k
k
T
k
t
t
k
k
k
T
y
V
2
2
−
=
=
2
3
4
6
7
N п/п
Годы
наблюдений
Минг тонна
1
2013
7 424 160,0
2
2014
6 550 076,0
48 628 812 236 160,0
3
2015
5 269 100,0
34 513 005 451 600,0
39 118 641 456 000,0
4
2016
6 114 334,0
32 217 037 279 400,0
40 049 352 389 384,0
45 393 793 909 440,0
5
2017
8 007 353,0
48 959 630 697 902,0
42 191 543 692 300,0
52 448 770 708 828,0
59 447 869 848 480,0
6
2018
8 479 203,0
67 895 971 579 659,0
51 844 679 195 802,0
44 677 768 527 300,0
55 539 424 069 428,0
62 950 959 744 480,0
7
2019
8 762 317,0
74 297 464 593 351,0
70 162 965 316 901,0
53 575 732 751 878,0
46 169 524 504 700,0
57 393 842 286 092,0
8
2020
10 412 320,0
91 236 048 545 440,0
88 288 174 980 960,0
83 375 121 788 960,0
63 664 402 194 880,0
54 863 555 312 000,0
9
2021
11 901 340,0
123 920 560 508 800,0
104 283 313 804 780,0
100 913 877 832 020,0
95 298 230 553 020,0
72 768 767 807 560,0
10
2022
10 892 392,0
129 634 060 605 280,0
113 415 071 069 440,0
95 442 591 592 264,0
92 358 802 923 576,0
87 219 227 758 376,0
Сумма
83 812 595,0 651 302 591 497 592,0 549 353 741 905 567,0 475 827 657 110 690,0 412 478 254 094 084,0 335 196 352 908 508,0
−
−
−
−
−
−
=
+
=
+
=
−
=
−
=
−
=
−
=
+
=
+
N
L
t
N
L
t
t
t
L
N
t
L
N
t
t
t
L
N
t
L
N
t
N
L
t
t
t
L
t
t
L
L
N
Y
Y
L
N
Y
Y
L
N
Y
Y
Y
Y
R
1
2
1
2
1
2
1
2
1
1
1
393
hajmi, o‘tgan yillarda tashilgan eksport yuklari hajmiga bog‘liq bo‘lgan murakkab tasodifiy jarayon
ekan.
Tasodifiy jarayonlarni sonli xarakteristikalariga intervalli statistik baho qurishda normal
taqsimot muhim rol o‘ynaydi. Aksariyat holda, diyarli bir xil sharoitda, bir-biridan katta farq
qilmaydigan tasodifiy miqdorlarning yig’indisi, ehtimollar nazariyasining markaziy limit
teoremasiga asosan
𝑦(𝑡)
̅̅̅̅̅̅
normal taqsimotga ega bo‘ladi.
Bizni misolda, O’zbekiston Respublikasining temir yo’l transporti jamiyati tomonidan har yili
o’rtacha tashilgan eksport yuklari hajmi, normal taksimoga ega degan
𝐻
0
(5) asosiy statistik
gipotezani
, normal taqsimotga ega emas degan
𝐻
1
alternativ shartda Shapiro-Vilkokson, Pirson
xamda parametrik kriteriyalar yordamida bilan tekshirganimizda:
𝐻
0
:
𝑃(𝑋 < 𝑥)
=
𝐹
𝑎,𝜎
(𝑥) ,
𝐻
1
:
𝑃(𝑋 < 𝑥) ≠ 𝐹
𝑎,𝜎
(𝑥)
(5)
95% li kafolat asosiy
𝐻
0
gipoteza qobul qilinadi(Jadval-4 ga qarang).
EHMning 7x va “Exsel” programmalaridan foydalanib, O’zbekiston Respublikasining temir
yo’l transporti jamiyati tomonidan, har yili o’rtacha tashilgan eksport yuklari hajmining muhim sonli
xarakteristikalarini hisoblaymiz (Jadval-4):
Jadval-4
Temir yo’lda tashilgan eksport yuklari
hajmining tanlanma xarakteristikalari
Temir yo’lda tashilgan eksport yuklari hajmining
tanlanma xarakteristikalarini sta-tistik baholari
O‘rtacha har yili tashilgan yk
y̅
T
−
ming tonna
8381259,5
Tanlanma dispersiyasi
𝐷
𝑇
469003,0
Tanlanma o‘rtacha kvadratik chetlanish
𝜎
𝑇
684,84
Asimmetriya A
0,26
Ekssessa
𝐸
𝐾
-0,94
Tanlanma o‘rtacha
𝑦̅
𝑇
qiymatini xatosi m
u
m
u
=
𝜎
𝑢
√𝑛
=
684,84
√10
= 216,72
Limitik xato
𝑚
𝑢
′
m’
u
= t m
u
= 2,31
∙ 216
,72 = 500,62
Intervalli statistik baho (95% li)
𝑦̅
𝑇
± t m
u
𝑦̅
𝑇
± t m
u
= 8381259,5 ± 500,62 ,
(8380758,88; 8381760,12) ming tonna
Statistik gipotezalar:
𝐻
0
: 𝑃(𝑦̅
T
< 𝑥) = F
a,𝜎
(x)
𝐻
0
: 𝑃(𝑦̅
T
< 𝑥) ≠ F
a,𝜎
(x)
95% li kafolat bilan
𝐻
0
qobil qilinadi
Bu tasdiq asosida,
𝛼 = 0,05
qiymatdorlik darajasi bilan ( ya’ni 95% li kafolat bilan) intervalli
statistik baho qurilgan (8380758,88; 8381760,12) ming tonna (jadval - 4 ga qarang).
O’zbekiston Respublikasining temir yo’l transporti aksioner jamiyati tomonidan, 2013-2022
yillarda tashilgan eksport yuklari hajmini, diskret {Y
t
, t
T} turg’in dinamik qator sifatida qilingan
statistik tahlillar asosida, quyidagicha xulosalar chiqarish mumkin:
1) o’rtacha yillik, O’zbekiston Respublikasining temir yo’l transporti aksioner jamiyati
tomonidan tashilgan eksport yuklari hajmi, diskret {Y
t
, t
T} dinamik qator tashkil etadi;
2) O’zbekiston Respublikasining temir yo’l transporti aksioner jamiyati tomonidan, tashilgan
eksport yuklari hajminini bosh yo’nalishini xarakterlovchi trend qismi quyidagicha chiziqli
bog‘lanishga ega
𝒚(𝒕) = 𝟏𝟎𝟗𝟕𝟕𝟒𝟗, 𝟔𝒕 +
𝟖𝟑𝟖𝟏𝟐𝟓𝟗, 𝟓
;
3) yillik o’rtacha tashilgan eksport yuklari hajmi
𝑦(𝑡)
̅̅̅̅̅̅
=
𝟖𝟑𝟖𝟏𝟐𝟓𝟗, 𝟓
ming tonnani tashkil
etadi, uning intervalli statistic bahosi 95% kafolat bilan
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