14 ma'ruza Eksperiment natijalarini empirik taqsimlashni tasdiqlash

R / S nisbatining muhim chegaralari 

Namuna hajmi n	Pastki chegara				Yuqori chegara
	Xato ehtimoli
	0,01	0,025	0,05	0.10	0.10	0,05	0,025	0,01
3 to'rt besh 6 7 8 9 o'n o'n bir 12 o'n uch 14 15 16 17 o'n sakkiz 19 20 25 o'ttiz 35 40 45 ellik	1,737 1.87 2.02 2.15 2.26 2.35 2.44 2.51 2.58 2.64 2.70 2.75 2.80 2.84 2.88 2.92 2.96 2.99 3.15 3.27 3.38 3.47 3.55 3.62	1,745 1.93 2.09 2.22 2.33 2.43 2.51 2.59 2.66 2.72 2.78 2.83 2.88 2.93 2.97 3.01 3.05 3.09 3.24 3.37 3.48 3.57 3.66 3.73	1.758 1.98 2.15 2.28 2.40 2.50 2.59 2.67 2.74 2.80 2.86 2.92 2.97 3.01 3.06 3.10 3.14 3.18 3.34 3.47 3.58 3.67 3.75 3.83	1,782 2.04 2.22 2.37 2.49 2.59 2.68 2.76 2.84 2.90 2.96 3.02 3.07 3.12 3.17 3.21 3.25 3.29 3.45 3.59 3.70 3.79 3.88 3.95	1.997 2.409 2,712 2,449 3.143 3.308 3.449 3.57 3.68 3.78 3.87 3.95 4.02 4.09 4.15 4.21 4.27 4.32 4.53 4.70 4.84 4.96 5.06 5.14	1.999 2.429 2.753 3.012 3.222 3.399 3.552 3.685 3.80 3.91 4,00 4.09 4.17 4.24 4.31 4.37 4.43 4.49 4.71 4.89 5.04 5.16 5.26 5.35	2000 2,439 2.782 3.056 3.282 3.471 3.634 3.777 3.903 4.02 4.12 4.21 4.29 4.37 4.44 4.51 4.57 4.63 4.87 5.06 5.21 5.34 5.45 5.54	2000 2.445 2.803 3.095 3.338 3.543 3.720 3.875 4.012 4.134 4,244 4.34 4.44 4.52 4.60 4.67 4.74 4.80 5.06 5.26 5.42 5.56 5.67 5.77

 

Bu shuni anglatadiki, tebranish usulidan foydalanish, shuningdek, Jadvalda keltirilgan eksperimental natijalarning empirik taqsimoti degan ilgari xulosani tasdiqlaydi. 14 . 1ni taxminan oddiy taqsimot deb hisoblash mumkin.

 

              Tajriba natijalari bilan namunaning nisbatan katta tanlanganligi ( n > 100) bo'lgan holda, empirik taqsimotni normal taqsimot ekanligini tekshirish uchun boshqa usullar ishlab chiqilgan. Ushbu usullardan biri bukish va kurtozni tekshirish usuli .

              Bunday holda, tajriba natijalari guruhlarga bo'linadi. Bunday holda, boshida ularning diapazoni R aniqlanadi . Quyidagi formuladan foydalanib, R oralig'ini ajratish kerak bo'lgan intervallar sonini aniqlash tavsiya etiladi :

                                           ...                      ( 14.5 )

H oraliq uzunligi   formula bilan aniqlanadi

                                                  ...                                ( 14.6 )

Shundan so'ng, quyidagi formulalar bo'yicha eksperimentning "guruhlangan" natijalari asosida o'rtacha arifmetik  va dispersiyaning qiymati s ² aniqlanadi :

                                             ,                           ( 14.7 )

                                '( 14.8 )

Sheppardning tuzatishi qaerda   , tajriba natijalarini guruhlashda yuzaga kelishi mumkin bo'lgan xatolarni hisobga oladi.

              Bundan tashqari, formula bo'yicha aniqlash talab qilinadi

                             (14.9)

uchinchi tartib m ₃ va formula bo'yicha moment

                             (14.10)

m ₄ to'rtinchi tartib momenti  . Ikkinchi tartibli momentning qiymati m ₂ = s ² ( 14.8 ) formula bo'yicha aniqlanadi .

Asimmetriya indeksini quyidagi formula aniqlaydi

   ...         ( 14.11 )

Nosimmetrik taqsimot uchun m ₃ = 0 va A = 0.

Ampirik taqsimot va normal taqsimotni taqqoslashni osonlashtirish uchun kurtozning ko'rsatkichi sifatida quyidagi qiymat aniqlanadi:

                                                                                                                                                                                                                                                          ( 14.12 ).

Shakl. 14 .1 assimetriya va kurtoz ko'rsatkichlariga qarab taqsimlash funktsiyasidagi o'zgarishlarni ko'rsatadi.

Asimmetriya indikatori uchun standart og'ishning qiymati quyidagi formula bilan aniqlanadi

                                 ...              ( 14.13 )

 

 

 

 

 

 

 

 

 

 

 

 

 

Shakl: 14 . 1. Asimmetriya va kurtoz indekslariga qarab eksperimental natijalarni taqsimlash funktsiyalari:

               A - assimetriya indeksiga qarab o'zgartirish;

               B - kurtoz tezligiga qarab o'zgaradi ;

               (------) – normal taqsimot grafigi;

               () - empirik taqsimot grafigi.

 

Kurtoz indeksi uchun standart og'ishning qiymati quyidagi formula bo'yicha aniqlanadi

 ...             ( 14.14 )

Sharoitda bo'lsa      ( 14 . 1 5 ) va        ( 4 . 1 6 ), biz eksperimental natijalar empirik tarqatish oddiy tarqatish, deb taxmin mumkin.