Page 127 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—8% fo"kerk ,oa i`Fkq'kh"kZRo % dkyZ fi;lZu] ckmys] oSQyh dh fof/;k¡

μ 3 μ − 2 uksV
γ = β – 3 = 4 2
2 2 2
μ 2
;fn γ ;k β – 3 = 0 rks oØ eè;e 'kh"kZ okyk (Meso-kurtic) gSA
2
2
;fn γ /ukRed gS rks oØ uqdhys 'kh"kZ okyk (Lepto-kurtic) gSA β > 3
2 2
;fn γ ½.kkRed gS rks oØ piVs 'kh"kZ okyk (Platy-kurtic) gSA β < 3
2
fo"kerk dh Hkkafr i`Fkq'kh"kZRo dk eki Hkh thou foKku rFkk HkkSfrd foKkuksa esa vf/d mi;ksxh gksrk gSA vkfFkZd]
lkekftd ,oa O;kikfjd ?kVukvksa esa bldk vf/d iz;ksx ugha gksrk D;ksafd bu {ks=kksa esa izlkekU; caVu cgqr de
ik;s tkrs gSaA

Illustration : fdlh vko`fÙk Js.kh esa lekUrj ekè; ls f}rh;] r`rh; o prqFkZ ifj?kkr 3, 0 o 26 gSaA ifj?kkrksa dh
lgk;rk ls fo"kerk rFkk 'kh"kZRo Kkr dhft,A
Solution :
Kkr gS] μ = 3, μ = 0 rFkk μ = 26.
3
4
2
μ 0 0
fo"kerk eki β = 1 3 = = = 0 fo"kerk ugha gSA
μ 3 2 3 3 27
μ 26 26
i`Fkq'kh"kZRo dk eki β = μ 4 2 2 = 3 () 2 = 9 = 2.889
2
∴ β = 2.889 < 3 oØ piVs 'kh"kZ okyk gSA
2
mnkgj.k (Illustration) 5: ,d leferh; caVu esa izeki fopyu 5 gSA prqFkZ osQUnzh; ifj?kkr dk ewY; D;k gks
rkfd caVu (a) uqdhys 'kh"kZ okyk gks] (b) eè;e 'kh"kZ okyk gks] (c) piVs 'kh"kZ okyk gks \
gy (Solution):
2
σ = 5 ∴μ = 5 = 25
2
(i) uqdhys 'kh"kZ okys esa μ > 3μ 2 2 vr% μ > 3 × (25) > 1875
2
4
4
(ii) Meso-kurtic Js.kh esa μ = 3μ 2 vr% μ > 3μ = 3 × 25 = 1875
2
2
4 2 4 2
(iii) Platy-kurtic Js.kh esa μ < 3μ 2 2 vr% μ < 3 × 25 ;k < 1875
2
4
4
8-5 vifdj.k] fo"kerk ,oa i`Fkq'kh"kZRo esa Hksn (Distinction Between Dispersion,
Skewness and Kurtosis)
bu rhuksa ekiksa dk ,d lkekU; mís'; vko`fÙk caVu dh cukoV dh tkudkjh nsuk gS ysfdu rhuksa ekiksa esa vUrj
ik;k tkrk gSμ
(1) vifdj.k osQUnzh; ewY; (ekè;) osQ pkjksa vksj ewY;ksa osQ fc[kjko ;k iSQyko (scatter of items) dk
vè;;u djrk gS ftlls ;g irk pyrk gS fd osQUnzh; ewY; iwjs caVu dk fdruk izfrfuf/Ro djrk
gSA vr% vifdj.k fopj.k dh ek=kk dh eki gSA
(2) tcfd fopj.k dh fn'kk vFkkZr~ ewY;ksa dk iSQyko ekè; ls Åij vf/d gS ;k uhps ;g tkudkjh
fo"kerk osQ eki miyC/ djkrs gSa vr% fo"kerk fopj.k dh fn'kk dk ekiu djrk gSA vr% ,d
izlkekU; caVu (Normal distribution) esa ekè; ls Åij o uhps fopyu ,d leku gksrs gSa tcfd
vlefer caVu (Asymmetrical Distribution) esa fopyu leku ugha gksrsA
(3) i`Fkq'kh"kZRo Js.kh osQ eè;orhZ Hkkx esa ewY;ksa ;k vko`fÙk;ksa osQ teko dk vè;;u djrk gSA vFkkZr~ ;g
caVu osQ Lo:i dks n'kkZrk gSA

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