Page 394 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV

laxfr] vufHkufr] n{krk vkSj i;kZIrrk ,d vPNs vkx.kd osQ izeq[k vfHky{k.k gSaA

;Fks"Vrkμ;g Li"V gS fd og vkx.kd fdlh izkpy gsrq ;Fks"V dgyk,xk ;fn mlesa izkpy ls lacafèkr U;kn'kZ
dh leLr egÙoiw.kZ tkudkjh gksA fdlh caVu osQ fy, ;Fks"V vpy dh vko';d 'krZ xq.ku[k.M izes; }kjk
nh tkrh gS] ftlosQ vuqlkj T = f(x) izkpy θ gsrq ;Fks"V gksxk ;fn vkSj osQoy ;fn U;kn'kZ ekuksa dk la;qDr ?kuRo
iQyu L bl izdkj gksrk gS fd
L =g [f(x)]. h(x)
θ
tcfd g [f(x)] dk eku θ vkSj x ij fuHkZj gksrk gS tcfd h(x) dk eku θ ij vkèkkfjr ugha gksrkA
θ
;Fks"Vrk osQ xq.kèkeZ
(i) ;fn T izkpy θ gsrq ,d ;Fks"V vkx.kd gS rks Ψ(f), T dk ,d ls ,d iQyu Ψ(f), Ψ(θ) gsrq ;Fks"V
gksrk gSA ;g i;kZIr vkx.kd dk vizlj.k xq.kèkeZ dgykrk gSA
(ii) ewy U;kn'kZ X = (X , X , ... X ) lnk ,d ;Fks"V vpy gksrk gSA
1
2
n
(iii) vpy t = (x , x , ... x ) izkpy θ dk ;Fks"B vkx.kd gksrk gS ;fn vkSj osQoy ;fn laHkkfork iQyu
n
2
1
1
fuEu izdkj ls gSμ
n
L = ∏ fx(, ) fx , )
θ
θ
(
1
i
i = 1
= g (t θ). k(x , x ...... x )
1 1
2
n
1
tcfd g (t , θ) vpy t dk izkf;drk ?kuRo iQyu gS vkSj k(x , x , ...... x ) osQoy U;kn'kZ leqfDr;ksa dk iQyu
1 1 1 1 2 n
gS] tks θ ij fuHkZj ugha gSA
izkpyu ofjek fdls dgrs gS\
oszQej&jko fo"kerk

oszQej&jko fo"kerk izkpy γ(θ) lacaèkh vkx.kd osQ izlj.k gsrq ,d fuEurj ifjcaèk iznku djrh gSA
;fn t izkpy θ osQ iQyu γ(θ) dk ,d vufHker vkx.kd gks
∂ L O 2
M ∂θ N L(, θ) P Q 2
x
γθ)]
Var (t) ≥ ∂ L O = [( ′
θ
E M ∂θ N log L P Q I()
U
2
I(θ) = E S M L ∂ R θ , )V P O
L
vkSj ∂θ T M log (x
N W P Q
γθ
′
[( )] 2
;gk¡ ij fuEurj ifjcaèk gSA
I ()
θ
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