Tsu-2011 - ieeetsu
Tsu-2011 - ieeetsu
Tsu-2011 - ieeetsu
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s t a t i s t i k a<br />
Tavi I<br />
wertilovani da intervaluri Sefasebebi. ndobis<br />
intervali saSualosaTvis<br />
Sefasebis amocana: n moculobis X ( X1,..., X n<br />
) SerCevis safuZvelze<br />
gavakeToT daskvnebi generaluri erTobliobis ucnobi parametris Sesaxeb.<br />
SerCevis nebismier Tn ( X) Tn ( X1,..., Xn)<br />
funqcias statistika (Sefaseba)<br />
ewodeba. wertilovani Sefasebis amocanaa moiZebnos iseTi statistika<br />
Tn( X1,..., X<br />
n)<br />
, romlis SerCeviTi mniSvneloba Tn( x1,..., x<br />
n)<br />
, garkveuli azriT,<br />
SeiZleba CaiTvalos ucnobi parametris WeSmariti (realuri) mniSvnelobis<br />
miaxloebad (Sefasebad) da gamoyenebuli iqnas mis nacvlad. aseT<br />
statistikas (Sefasebas) wertilovani statistika (Sefaseba) ewodeba.<br />
Tn ( X) Tn ( X1,..., Xn)<br />
Sefasebas ewodeba Caunacvlebeli (anu gadauadgilebadi),<br />
Tu E<br />
T( X)<br />
.<br />
T ( X) T ( X ,..., X ) Sefasebas ewodeba Zalmosili (anu Zaldebuli),<br />
n n 1 n<br />
P <br />
Tu Tn<br />
( T n<br />
albaTobiT krebadia -sken), roca n.<br />
Caunacvlebel Sefasebas ewodeba optimaluri (anu efeqturi), Tu<br />
mas sxva Caunacvlebel Sefasebebs Sori gaaCnia umciresi dispersia.<br />
Tu n moculobis SerCeva warmodgenilia variaciuli mwkrivis saxiT,<br />
maSin SerCeviTi saSualo ewodeba sidides:<br />
x1n 1<br />
x2n2 ...<br />
xknk n1 n2<br />
nk<br />
x x1 x2<br />
...<br />
.<br />
n n n n<br />
Tu SerCevidan miRebuli mniSvnelobebi ara dajgufebuli, maSin SerCeviTi<br />
saSualo<br />
1<br />
n<br />
x x i .<br />
n i1<br />
SerCeviTi saSualo warmoadgens ucnobi maTematikuri lodinis Caunacvlebel<br />
da Zalmosil Sefasebas.<br />
SerCeviTi dispersia ewodeba sidides:<br />
k<br />
n<br />
2<br />
2 ni<br />
1<br />
2<br />
s xi<br />
x xi<br />
x<br />
.<br />
i1 n n i1<br />
Sesworebuli SerCeviTi dispersia ewodeba sidides:<br />
n<br />
' n<br />
2 2 1<br />
s s x <br />
2<br />
i<br />
x .<br />
n1 n1<br />
i1<br />
Sesworebuli SerCeviTi dispersia warmoadgens ucnobi dispersiis<br />
Caunacvlebel da Zalmosil Sefasebas.<br />
SerCeviTi standartuli gadaxra (Sesabamisad, Sesworebuli SerCevi-<br />
Ti standartuli gadaxra) ewodeba ariTmetikul kvadratul fesvs SerCev-<br />
94
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