Page 129 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

• fo"kerk osQ izFke eki (First Measures of Skewness) Hkh dgrs gSaA fujis{k eki bl ekU;rk ij uksV
vkèkkfjr gS fd ,d fo"ke caVu esa lekUrj ekè;] eè;dk rFkk cgqyd ewY; leku ugha gksrsA vr% buesa
ls fdUgha nks ewY;ksa (ekè;ksa) osQ chp dk vUrj] fo"kerk dh ek=kk gksrh gSA
• nks Jsf.k;ksa ;k caVuksa dh rqyuk djus osQ fy, fo"kerk osQ lkis{k eki Kkr fd, tkrs gSaA budks fo"kerk
xq.kkad (Coefficient of skewness) Hkh dgrs gSaA lkis{k eki ;k fo"kerk xq.kkad Kkr djus osQ fy,
fujis{k eki dks vifdj.k osQ fdlh Hkh eki ls foHkkftr dj fn;k tkrk gSA ijUrq è;ku jgs] O;ogkj
esa osQoy izeki fopyu dk gh iz;ksx fd;k tkrk gS] D;ksafd vifdj.k osQ vU; eki fdlh&u&fdlh
:i esa lhekxzflr gSa tcfd izeki fopyu ,d vkn'kZ eki gSA
• fi;lZu xq.kkad dh fo'ks"krk,¡μ(i) ;fn J dk eku 'kwU; gS rks caVu fo"kerk jfgr vFkkZr~ lefer gksrk
gSA (ii) ;fn J dk eku (+) esa gS rks /ukRed fo"kerk vkSj (–) gksus ij Í.kkRed fo"kerk gksrh gSA (iii)
fl¼kUr :i esa bl xq.kkad dh dksbZ lhek ugha gS (tksfd bldk izeq[k nks"k gS) ijUrq O;ogkj esa ;g
lkekU;r;k ± 1 osQ chp jgrk gSA oSdfYid lw=k dh fLFkfr esa xq.kkad dh lhek,¡ ± 3 gksrh gSaA
• oSQyh dk fo"kerk xq.kkad ckmys lw=k dk la'kksf/r :i gSA ckmys lw=k tksfd prqFkZdksa ij vk/kfjr gS]
osQ vUrxZr caVu osQ izFke 25% vkSj vafre 25% ewY; NksM+ fn, tkrs gSaA pw¡fsd ,d vPNk eki og gS
tks caVu osQ lHkh ewY;kas ij vk/kfjr gks vr% bl n`f"V ls oSQyh us prqFkZdksa osQ LFkku ij n'kedksa ;k
'kredksa osQ iz;ksx dk lq>ko fn;k gSA
• vifdj.k ls fdlh caVu dh cukoV dk Kku gksrk gSA ljy 'kCnksa esa] vifdj.k dh ekiksa ls bl ckr
dk irk pyrk gS fd Js.kh osQ fofHkUu in&ewY;ksa dk vkil esa ;k fdlh ekè; ls fdruk fopyu ;k
fc[kjko gSA blosQ foijhr fo"kerk osQ eki ;g crkrs gSa fd Js.kh osQ ekè; ls nksuksa vksj osQ Hkkxksa dk
fopj.k cjkcj gS vU;Fkk fdl Hkkx esa fopj.k vf/d gSA
• vifdj.k ls lewg dh cukoV (composition) dk Kku gksrk gS] tcfd fo"kerk ls lewg osQ Lo:i
(shape) dk irk pyrk gSA
• vifdj.k] leadksa eas fopyu'khyrk dh ek=kk dks Kkr djus esa mi;ksxh gS tcfd fo"kerk ;g crkrh
gS fd teko cM+s ewY;ksa esa vf/d gS ;k NksVs ewY;ksa esaA
• vifdj.k osQ eki f}?kkrh; ekè;ksa (Averages of the Second Order) ij vk/kfjr gSa tcfd fo"kerk
osQ eki eq[;r;k izFke ?kkrh; ekè;ksa (Averages of First Order) ij vk/kfjr gSaA

• mi;qZDr vUrj osQ ckotwn vifdj.k rFkk fo"kerk osQ eki ,d&nwljs osQ vuqiwjd gSaA lp rks ;g gS fd
vko`fÙk&caVu osQ fof/or~ fo'ys"k.k osQ fy, osQUnzh; izo`fÙk] vifdj.k rFkk fo"kerk rhuksa osQ ekiksa dk
Kku ijeko';d gSA tgk¡ osQUnzh; izo`fÙk osQ eki ls vko`fÙk&caVu dk lkjka'k Kkr gksrk gS] ogk¡ vifdj.k
ls leadksa osQ fc[kjko dk irk yxrk gS vkSj fo"kerk ls ;g tkudkjh gksrh gS fd ekè; ls fdl vksj
dk vifdj.k (fc[kjko) vf/d gSA

• xzhd Hkk"kk esa Kurtosis 'kCn dk vFkZ gS mHkjk gqvk mHkjkiu (bulge or bulginess)A blh rjg lkaf[;dh
eas Hkh i`Fkq'kh"kZRo izlkekU;rk osQ lUnHkZ esa vko`fÙk oØ dh f'k[kjh;rk dk |ksrd gSA vr% izlkekU; oØ
dh rqyuk esa fdlh vko`fÙk oØ osQ uqdhysiu ;k 'kh"kZRo (Peakedness) vFkok piVsiu (Flatness) osQ
eki dks i`Fkq'kh"kZRo dgrs gSaA

• i`Fkq'kh"kZRo dh eki prqFkZ ,oa f}rh; ifj?kkrksa osQ vk/kj ij ifj?kkr vuqikr (moment ratio) }kjk dh
tkrh gSA blosQ fy, dkyZ fi;lZu ls fuEu lw=k dk iz;ksx fd;k gSμ
μ prqFkZ ifj?kkr Fourth moment
i`Fkq'kh"kZRo dh eki (β ) = μ 4 2 2 = (f}rh; ifj?kkr) 2 = (Second moment) 2
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