Page 398 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV fcUnq vkdyu (Point Estimation)
tc U;kn'kZ ds izfrn'kZt ls lexz ds izkpy dk ,d vuqeku@vkdyd Kkr fd;k tkr gS rks bl vkdyd dks
fcUnq vkdyd dgk tkrk gS rFkk bl izfØ;k dks fcUnq vkdyu dgk tkrk gSA mnkgj.kkFkZ]
2
(i) ekuk ekè; μ rFkk izlj.k σ (;k izeki fopyu] σ) ds lexz esa x , x , ... x ,d ;kn`fPNd izfrn'kZ gSA
1 2 n
1 n
x = ∑ x
x
;gn izfrn'kZ@U;kn'kZ ds ekè; n i = 1 i dks lexz ekè; ds LFkku ij iz;ksx fd;k tkrk gS rks dks
lexz ds vKkr (Unknown) ekè; μ dk vkdyd dgrs gSaA

lexz ds ekè; dk fcUnq vkdyd (Point Estimate of Population mean) = izfrn'kZ dk ekè;
(Sample Mean) gksrk gSA

(ii) ekuk fdlh xq.k ds vk/kj ij lef"V esa ml xq.k dks j[kus okys vo;oksa dk vuqikr P gSA blesa ls n
vo;oksa dk ,d U;kn'kZ fy;k tkrk gS ftlesa ml xq.k dks j[kus okys vo;oksa dk vuqikr P ;fn P vKkr
gks rks bldks P ls vuqekfur fd;k tkrk gSA vFkkZr~ lexz ds vuqikr dk fcUnq vkdyd (Point
Estimate of Population Proportion) = izfrn'kZ dk vuqikr (Sample Proportion)A

2
(iii) mi;qZDr mnkgj.k (i) esa ;fn lexz ds izlj.k σ dks izfrn'kZ ds izlj.k s 2 = 1 ∑(– )x x ls vuqekfur
2
n
2
fd;k rks S , lexz ds izlj.k dk fcUnq vkdyd (Point Estimate) gSA
fdlh Hkh mfpr izfrn'kZt (Statistics) dks lexz ds izkpy dk fcUnq vkdyd fy;k tk ldrk gSA ,d vPNs
fcUnq vkdyd esa pkj fo'ks"krk,a gksuh pkfg,%
(a) vufHkurrk (Unbiasedness)
(b) n{krk (Efficiency)

(c) laxfr (Consistency)
(d) i;kZIrrk (Sufficiency)

vUrjky izkDdyu (Interval Estimation)

lexz ds izkpyksa dk ,slk vuqeku tks nks lhekvksa ds eè; gks vUrjky vuqeku dgykrk gSA tc fcUnq vkdyd
ds vk/kj ij lexz izkpy ds fy, ,d vUrjky (c ≤ μ ≤ d) fu/kZfjr fd;k tkrk gS rFkk ;g ekuk tkrk gS fd
,d fuf'pr izkf;drk@fo'oluh;rk ds lkFk izkpy μ dk eku iM+sA lhekvksa c vkSj d dks vUrjky lhek,a]
vUrjky (c ≤ μ ≤ d) dks fo'okL;rk vUrjky (confidence interval) dgk tkrk gSA lhekvksa c vkSj d dks
fo'okL;rk lhek,a (confidence limits) dgrs gSaA fo'okL;rk Lrj dks 1 esa ls ?kVkus ds ckn izkIr jkf'k dks
fo'okL;rk xq.kkad (confidence coefficient) dgk tkrk gSA lw=k :i esa]

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