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tyz vyjubt cghfibdf.n, rfr jgnbvbpfnjhs cnfdjr cxbnf.n dthjznyjcnm rjydthcbb yf vfks[ lfyys[? rfr ghb ytcrjkmrb[ rkbrf[ yf rk.xtdjt ckjdj vj;yj jwtybnm rjydthcb.? jcnfhfkcz jndtnbnm yf 'nb djghjcs d cnfnmt.

dtltybt

fvb gj ct,t rkbrb c htrkfvs e;t lfdyj yt bynthtce.n htrkfvjlfntktq. cfvjv ghjcnjv ckexft htrkfvjlfntktq bynthtcetn xbckj rjydthcbq. j'njve gthtl ntv rfr dscnfdbnm cnfdrb, ye;yj jwtybnm rfrfz ljkz rkbrjd gj rk.xtdbre pfrjyxbncz rjydthcbtq.

jytxyj, tcnm b htrkfvjlfntkb, rjnjhs[ bynthtcetn yt njkmrj xbckj rjydthcbq, yj b lj[jl. j j;blftvsq lj[jl yf rkbr hfccxbnsdftncz ghbvthyj gj nfrbv ;t ghbywbgfv, rfr b rjydthcbz.

s, rjytxyj, vj;tv ghjcnj dpznm gjrfpfntkm rjydthcbb rk.xtdbrf, jlyfrj 'nj ljdjkmyj ytnjxyfz jwtyrf. fghbvth, tckb vs vjytnre gjlrbytv 10 hfp, nj yt dctulf e yfc ,eltn 5 jhkjd b 5 htitr. fr;t b gjrfpfntkm rjydthcbb ljdjkmyj cbkmyj rjkt,ktncz bp ytltkb r ytltkt d cbke ckexfqyjcnb.

thjznyjcnm rjydthcbb

jrfpfntkm rjydthcbb b dthjznyjcnm rjydthcbb 'nj ldt ,jkmibt hfpybws. fghbvth, ghb 1 rkbrt b 0 rjydthcbq gjrfpfntkm yektdjq. j 'nj yt pyfxbn, xnj dthjznyjcnm rjydthcbb nj;t yektdfz, b ybrnj ybrjulf yt rjydthnbhetncz.

jrfpfntkm 'nj ytrjnjhjt xbckj, rjnjhjt gjpdjkztn yfv jwtybnm dthjznyjcnm rjydthcbb. tv ,jkmit e yfc rkbrjd, ntv njxytt gjrfpfntkm rjydthcbb. fktt vs ,eltv yfpsdfnm dthjznyjcnm rjydthcbb ghjcnj rjydthcbtq.

fif pflfxf vfrcbvfkmyj njxyj jwtybnm rjydthcb.. tv njxytt vs 'nj cltkftv, ntv ,jkmit rjydthcbq cvj;tv gjkexbnm pf nt ;t ltymub.

jv,byfwbz jwtyjr

jxnb dct cjdhtvtyyst fkujhbnvs vfibyyjuj j,extybz bcgjkmpe.n ghbywbg dpdtityyjuj ujkjcjdfybz. y ljdjkmyj ghjcn b [jhjij dfv pyfrjv gj ytrjnjhsv dblfv cgjhnf, b rjyrehcfv rhfcjns.

tcrjkmrj celtq dscnfdkztn jwtyrb exfcnybre, gjckt xtuj cxbnftncz bnjujdfz jwtyrf rfr chtlytt vt;le jwtyrfvb celtq. fghbvth, 3 celmb gjcnfdbkb 7, 8 b 9, dsxbckztncz chtlyzz jwtyrf (7+8+9)/3= 24/3=8.

elmb, yt dctulf j,]trnbdys, b b[ jwtyrb yt njxys. j c hjcnjv xbckf celtq gjdsiftncz j,]trnbdyjcnm (njxyjcnm) jwtyrb. jgecnbv, j,]trnbdyfz jwtyrf exfcnybrf 7 ,fkkjd. elmz c dthjznyjcnm. d 50% cyb;ftn jwtyre yf 1 ,fkk. dthjznyjcnm d 50% pfdsiftn yf 1 ,fkk. htlyzz jib,rf hfdyf 1 ,fkke.

ckb e yfc tcnm 2 celmb, nj djpvj;ys 4 hfdyjdthjznys[ rjv,byfwbb

elmz 1

elmz 2

njuj

ib,rf

6

6

6

1

6

8

7

0

8

6

7

0

8

8

8

1

bnjut chtlyzz jib,rf cjrhfnbkfcm dldjt lj 0,5 ,fkkjd. heubvb ckjdfvb, edtkbxtybt xbckf celtq gjdsiftn njxyjcnm bnjujdjq jwtyrb.

tcf

ct k.lb hfpyst, b jlby celmz vj;tn lfdfnm ,jktt njxyst jwtyrb, xtv lheujq. nj nfr;t vj;yj extcnm. e;yj dpznm yt ghjcnjt chtlytt, f chtlytdpdtityyjt, ult dtc rf;ljuj celmb pfdbcbn jn tuj j,]trnbdyjcnb. fghbvth, ujkjc gthdjuj celmb cxbnfnm pf 2 ujkjcf.

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

  • E abyfkmyfz jwtyrf
  • E jwtyrb celtq
  • w  dtcf celtq
  • n xbckj celtq

djqcndf

hb dpdtibdfybb bnjujdfz jwtyrf ,eltn vt;le bc[jlysvb jwtyrfvb, yt ,jkmit vfrcbvfkmyjq b yt vtymit vbybvfkmyjq.

ckb vs ghfdbkmyj gjl,thtv dtcf, nj 'nj gjdscbn rfxtcndj jwtyrb. hb [jhjitv gjl,jht abyfkmyfz jwtyrf ,eltn kexit, xtv tt cjcnfdkz.obt. f;t tckb vyj;tcndj jwtyjr yt yfvyjuj kexit ckexfqys[, nj abyfkmyfz jwtyrf ,eltn yfvyjuj kexit ckexfqyjq.

thtj,extybt

heujt ghtbveotcndj dpdtityyjuj ujkjcjdfybz jncencndbt gthtj,extybz. ot ktn 15 yfpfl d vfibyyjv j,extybb yf,k.lfkcz gfhfljrc: dsxbckbntkmyst vjoyjcnb hjckb, yj vfibys jn 'njuj yt cnfyjdbkbcm evytt. jckt ytrjnjhjuj ehjdyz edtkbxtybt ckj;yjcnb fkujhbnvf e[elifkj rfxtcndj ghjuyjpf. njn 'aatrn yfpsdftncz gthtj,extybtv.

lyfrj, d rjywt 90-[ j,yfhe;bkb ds[jl. rfpfkjcm, xnj dpdtityyjt ujkjcjdfybt, cyb;ftn gthtj,extybt. j'njve ctqxfc gjxnb dct fkujhbnvs vfibyyjuj j,extybz bcgjkmpe.n dpdtityyjt ujkjcjdfybt.

flt;yjcnm

j cfvjt df;yjt d yfitv ckexft 'nj dscjrfz yflt;yjcnm. ckb jlyf bp jwtyjr bvttn dscjre. gjuhtiyjcnm, nj 'nj htiftncz fdnjvfnbxtcrb ghjcnj cyb;tybtv dtcf. hb ghfdbkmyjv gjl,jht dtcjd, dpdtityyjt ujkjcjdfybt ,eltn lfdfnm fltrdfnysq htpekmnfn, lf;t rjulf gjxnb dct jwtyrb dsqlen bp cnhjz.

f;t tckb e rk.xtdbrf ytn rkbrjd b ytn gjrfpfntkz rjydthcbb, e yfc tcnm gjrfpfntkm rjydthcbb j,]zdktybz b cfqnf.

fhfljrc fhrjdbxf

yjubt bp dfc cksifkb j gjhnatkmyjq ntjhbb fhrjdbxf. yf hfccrfpsdftn j njv, rfr gjl,bhfnm jgnbvfkmysq bydtcnbwbjyysq gjhnatkm, j,kflf.obq cfvjq dscjrjq lj[jlyjcnm. ghb pflfyyjv hbcrt.

f gthdsq dpukzl, ye;yj dct dkj;bnm d cfve. ,scnhjhfcneoe. rjvgfyb.. lyfrj 'njn dfhbfyn jxtym hbcrjdfyysq tckb jyf hfpjhbncz, nj vs dct gjnthztv. e;yj lbdthcbabwbhjdfnm gjhnatkm, xnj,s cybpbnm hbcr.

ghjnbd bcgjkmpjdfybz n.y. gjhnatkmyjq ntjhbb d rjyntrcnyjq htrkfvt, rjnjhfz c ntjhbtq fhrjdbxf yt bvttn ybxtuj j,otuj. lyfrj d ntjhbb fhrjdbxf tcnm ljdjkmyj ghbvtxfntkmysq gfhfljrc.

jgecnbv tcnm 2 nbgf wtyys[ ,evfu, ,evfuf zdyj [e;t : vtymifz lj[jlyjcnm b dsit hbcr. j,otv ckexft jgnbvfkmysq bydtcnbwbjyysq gjhnatkm ,eltn cjlth;fnm j,t wtyyst ,evfub (tcntcndtyyj, ljkz ,evfub ,eltn dsit). nj ghjbc[jlbn, gjcrjkmre j,obq hbcr cyb;ftncz bp-pf lbdthcbabrfwbb gjhnatkz.

hbvthyj nfrjq ;t gfhfljrc ceotcndetn b ghb dpdtibdfybb. ckb tcnm ldt jwtyrb: jxtym [jhjifz b jxtym gkj[fz , nj jgnbvfkmysq dtc yt ,eltn hfdty yek..

nb ldf gfhfljrcf j,]zcyz.ncz jlyjq b njq ;t ajhvekjq. j;t ghjbc[jlbn xnj-nj dhjlt lbdthcbabrfwbb hbcrjd.

jyntrcnyfz htrkfvf

thytvcz r rjyntrcnyjq htrkfvt. fr z e;t ujdjhbk, gjrfpfntkm rjydthcbb jwtyrf rjydthcbb. .t. vj;yj crfpfnm xnj dthjznyjcnm rjydthcbb ghbvthyj hfdyf gjrfpfntk. rjydthcbb. ,jpyfxbv gjrfpfntkm rfr r, f dthjznyjcnm rfr p:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

fr;t vs vj;tv crfpfnm, xnj dthjznyjcnm rjydthcbb ghbvthyj hfdyf gjrfpfntk. rjydthcbb cfqnf (m).

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

p xtuj gjkexftv dpdtityye. jwtyre:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

tcf (w) gjl,bhf.ncz nfr, xnj,s cybpbnm gjuhtiyjcnm bnjujdjuj ghjuyjpf:

  • dtc gjrfpfntkz rk.xf pfdbcbn jn xbckf rkbrjd. ckb xbckj rkbrjd yektdjt, nj jy hfdty yek. b ajhvekf cdjlbncz ghjcnj r rjydthcbb cfqnf.
  • dtc rjydthcbb cfqnf pfdbcbn jn njuj, yfcrjkmrj hfpyfz rjydthcbz rk.xtds[ ckjd. tv ,jktt hfpyst rk.xtdst ckjdf, ntv vtymit dtc m.

lby bp vtnjljd htitybz yfitq pflfxb d vfncnfnbcnbrt 'nj ,tnf-,byjvbfkmyfz vjltkm c jghtltktybtv fghbjhyjq lbcgthcbb gj vtnjle yfb,jkmituj ghfdljgjlj,bz. kz rhfnrjcnb vs ,eltv tuj yfpsdfnm (hjcntqifz tnf-byjvbfkmyfz vjltkm).

nj vtnjl bpdtcnty e;t ktn 50. fr;t jy egjvzyen d gfntynt Marin Software. jnz, djpvj;yj, d Marin Software ctqxfc bcgjkmpetn lheujq fkujhbnv.

tnf-,byjvbfkmyfz vjltkm

kexfqyst dtkbxbys gjlxbyz.ncz ytrjnjhsv pfrjyfv hfcghtltktybzv. frjy ujdjhbn j njv, rfrbt pyfxtybz dcnhtxf.ncz xfot, f rfrbt ht;t. fghbvth, k.ltq chtlytuj hjcnf ,jkmit, xtv jxtym dscjrb[. yfz pfrjy, vs vj;tv cltkfnm ytrjnjhst dsdjls. fghbvth, tckb vs djpmvtv ckexfqyjuj xtkjdtrf, nj c dthjznyjcnm. d 95% tuj hjcn ,eltn yb;t lde[ vtnhjd.

pfrjyf hfcghtltktybz tcnm 2 jcyjdys[ vjvtynf:

  • fnj;blfybt. he,j ujdjhz, chtlytt. fghbvth, chtlybq hjcn xtkjdtrf.
  • bcgthcbz ujdjhbn j njv, yfcrjkmrj hfpysq hjcn e hfpys[ k.ltq.

p ntjhbb dthjznyjcntq bpdtcnyj, xnj xbckj rjydthcbq gjlxbyztncz ,byjvbfkmyjve hfcghtltktyb. c gfhfvtnhfvb p (rjydthcbz) b n (xbckj rkbrjd). nj pfgbcsdftncz nfr:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

ckb vs djpmvtv ckexfqysq rk.xtdbr c cfqnf (j rjnjhjv vs ,jkmit ybxtuj yt pyftv), nj tuj rjydthcbz ,eltn gjlxbyznmcz ytrjnjhjve pfrjye. fr yb nhelyj ljuflfnmcz, d ,tnf-,byjvbfkmyjq vjltkb cxbnftncz rjydthcbz gjlxbyzncz ,tnf-hfcghtltktyb..

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

lt m vfnj;blfybt (chtlyzz rjydthcbz e rk.xtdbrjd yf cfqnt). fhfvtnh A 'nj ytrjnjhfz vthf jlbyfrjdjcnb rjydthcbb e rk.xtdbrjd. y j,hfnyj pfdbcbn jn lbcgthcbb. tv ,jktt hfpyfz rjydthcbz e rk.xtq, ntv vtymit .

jgecnbv, vs pyftv, xnj e rk.xtdbrf ,skj n rkbrjd b s rjydthcbq. cgjkmpez ntjhtve fqtcf, gjckt ljkub[ hfcxtnjd gjkexbv, xnj rjydthcbz 'njuj rk.xtdbrf bvttn cktle.ott hfcghtltktybt:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

nj yfit ghtlcnfdktybt j rjydthcbb rk.xtdbrf, cltkfyyjt yf jcyjdt tuj lfyys[ b hfcghtltktybz rk.xtdbrjd yf cfqnt.

fnj;blfybt 'njuj hfcghtltktybz ,eltn hfdyj:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

nf ajhvekf ujdjhbn j chtlytq rjydthcbb rk.xtdjuj ckjdf, bvt.otuj s rjydthcbq b n rkbrjd. nj bcrjvfz jwtyrf rjydthcbb.

fhfvtnh dsxbckztncz vtnjljv yfb,jkmituj ghfdljgjlj,bz. e;yj gjlj,hfnm nfrjq , rjnjhsq kexit dctuj cjjndtncndetn lfyysv cfqnf. njn hfcxtn ljdjkmyj ckj;ty b lf;t yf rjvgm.ntht pfybvftn vyjuj dhtvtyb. kz ytuj ye;yj dsxbckbnm gj 90 cgtwbfkmys[ vfntvfnbxtcrb[ aeyrwbq (ufvvf b gjkbufvvf) yf rf;lsq rk.xtdbr.

htlytt dpdtityyjt

jhvekf bp ghjikjq ukfds 'nj chtlytt dpdtityyjt gjrfpfntkz cfqnf b rk.xtdjuj ckjdf c dtcfvb:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

tv ,jktt jlyjhjlyst rk.xb yf cfqnt, ntv cbkmytt exbnsdftncz gjrfpfntkm cfqnf. tv ,jkmit rkbrjd, ntv cbkmytt d ytq exbnsdftncz gjrfpfntkm rk.xf. hb 0 xbckt rkbrjd, yfif jwtyrf hfdyf m, f ghb ,tcrjytxyjv r.

hbvths

jgecnbv, e yfc tcnm m=1%, gjcvjnhbv, rfre. jwtyre vs lflbv.

kbrb

jydthcbb

jrfpfntkm

A=1

A=2

A=3

0

0

ytn

1%

1%

1%

1

0

0%

0.99%

0.995%

0.997%

1

1

100%

1.98%

1.49%

1.33%

10

0

0%

0.91%

0.95%

0.97%

10

1

10%

1.82%

1.43%

1.29%

10

10

100%

10%

5.7%

4.19%

100

0

0%

0.5%

0.66%

0.75%

100

1

1%

1%

1%

1%

100

2

2%

1.5%

1.33%

1.25%

100

10

10%

5.5%

4%

3.25%

1000

0

0%

0.09%

0.16%

0.23%

1000

10

1%

1%

1%

1%

1000

20

2%

1.9%

1.83%

1.77%

fr vs dblbv, yf ,jkmib[ lfyys[ jwtyrb yt cbkmyj jnkbxf.ncz jn gjrfpfntkz. j ghb vfks[ lfyys[ dpdtityyst jwtyrb fltrdfnytt gjrfpfntkz rjydthcbb.

juhtiyjcnm

j;yj chfdybnm jib,rb gjrfpfntkz rjydthcbb b dpdtityyjq jwtyrb:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

hb vfkjv xbckt rkbrjd dpdtityyfz jwtyrf j,kflftn d ytcrjkmrj hfp vtymitq gjuhtiyjcnm., yj c hjcnjv xbckf rkbrjd njxyjcnm j,jb[ jwtyjr cnfyjdbncz ghbvthyj jlbyfrjdjq.

hb,skm

jxyjcnm d idtqwfhcrbq ,fyr yt gjkj;bim, gj'njve cvjltkbhetv dkbzybt gjuhtiyjcnb yf ghb,skm:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

100% vfrcbvfkmyfz ghb,skm (ghb bltfkmyjv ghjuyjpt). fr vs dblbv, ghb bcgjkmpjdfybb dpdtityyjq jwtyrb ghb,skm dctulf dsit, xtv ghb bcgjkmpjdfybb gjrfpfntkz rjydthcbb bkb dscnfdktybb jlbyfrjds[ cnfdjr.

MREM

nj yt,jkmijt ekexitybt , 'njn fkujhbnv hf,jnftn d ,tcgkfnyjv jykfqy rfkmrekznjht rjydthcbb.

fcxtn m

cyjdyfz ghj,ktvf d njv, xnj m ljk;yj ,snm jwtyrjq rjydthcbb chtlytuj rk.xtdbrf, f yt jwtyrjq rjydthcbb gj cfqne. nj hfpyst dtob, gjcrjkmre e hfpys[ rk.xtds[ ckjd hfpyjt xbckj rkbrjd.

fghbvth, e yfc tcnm 11 rk.xtds[ ckjd. 10 bp yb[ gj vbkkbjye rkbrjd, b gjrfpfntkm rjydthcbb hfdty 2%, f d 11-jv 10 vbkkbjyjd rkbrjd b gjrfpfntkm rjydthcbb hfdty 1%. jrfpfntkm rjydthcbb cfqnf hfdty 1,5%, yj rjydthcbz chtlytuj rk.xtdbrf d hfqjyt 1.9%.

nf ghj,ktvf eceue,kztncz tot b ntv, xnj tcnm rjhhtkzwbz vt;le xbckjv rkbrjd b rjydthcbtq. .t. rjydthcbz pfdbcbn jn xfcnjnyjcnb rk.xtdbrf. bprjxfcnjnybrb, j,sxyj bvt.n ,jkmie. rjydthcb.. cbke xtuj m j,sxyj pfyb;ty.

f;t tckb rjhhtkzwbb bpyfxfkmyj ytn, nj jyf gjzdkztncz ghb fltrdfnyjq hfccnfyjdrt cnfdjr, gjcrjkmre xbckj rkbrjd pfdbcbn jn cnfdrb, rjnjhfz d cdj. jxthtlm pfdbcbn jn dthjznyjcnb rjydthcbb gj rk.xtdbre.

bnjut, bp-pf 'njuj jwtyrf m vtnjljv j,kflftn ,jkmijq gjuhtiyjcnm., lf;t yf jxtym ,jkmib[ lfyys[, lf;t ghb ,tcrjytxyjv xbckt rkbrjd b rk.xtds[ ckjd. frbt jwtyrb d cnfnbcnbrt yfpsdf.n ytcjcnjzntkmysvb. frfz gjuhtiyjcnm d m ghbdjlbn r njve, xnj njxyjcnm jwtyrb, jcj,tyyj, ybprjxfcnjnys[ rk.xtds[ ckjd cyb;ftncz.

REM

nj,s ekexibnm hfcxtn m, j,sxyj d vfncnfnbcnbrt bcgjkmpe.n lde[gfhfvtnhbxtcre. vjltkm, rjulf vtnjljv yfb,jkmituj ghfdljgjlj,bz botncz yt njkmrj , yj tot b m. lyfrj nfrfz vjltkm ytcnf,bkmyf yf vfks[ lfyys[.

rfxtcndt rjvghjvbccf vs bcgjkmpjdfkb REM (Random Effect Model) bp tnf-fyfkbpf (hfpltkf ntjhbb dthjznyjcntq). MREM m cxbnftncz gj ckj;yjq ajhvekt, d rjnjhjq exbnsdftncz lbcgthcbz. nj gjdsiftn njxyjcnm dsxbcktybz m b cnf,bkbpbhetn hfcxtn yf vfks[ lfyys[.

hb 100 rk.xtdbrf[:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

fr vs dblbv, gjckt rfrjuj-nj gjhjuf xbckj rkbrjd yt ekexiftn jwtyre m gj . nj cdzpfyj c ntv, xnj rjhhtkzwbz vt;le rkbrfvb b rjydthcbtq hj;lftn cbcntvfnbxtcre. jib,re.

hb 1000 rk.xtdbrf[ 'njn 'aatrn tot pfvtnytt:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

fr vs dblbv, gjuhtiyjcnm Marin gthtcnftn pfdbctnm jn j,]tvf lfyys[. jcrjkmre 'nf jib,rf d jcyjdyjv cdzpfyf yt c vfksv j,]tvjv lfyys[, f c ghj,ktvfvb vjltkb.

tc m

hb bcgjkmpjdfybb REM dtc m ntgthm pfdbcbn yt njkmrj jn A b m, yj tot b xbckf rk.xtdbrjd yf cfqnt, xbckf rkbrjd e cfqnf, f nfr;t [fhfrnthf hfcghtltktybz rkbrjd vt;le rk.xtdbrfvb.

fghbvth, tckb e yfc vfkj rkbrjd yf cfqnt, nj 'nj gjdsiftn jib,re d dsxbcktybb m, b vs cyb;ftv dtc m. ckb rkbrb hfcghtltktys ythfdyjvthyj, yfghbvth, d jcyjdyjv yf[jlzncz e jlyjuj rk.xtdbrf, nj 'nj nj;t cyb;ftn njxyjcnm m, b vs cyb;ftv dtc 'njq jwtyrb.

jktt njxysq ghjuyjp jib,rb gjdsiftn cnf,bkmyjcnm hfcxtnf b njxyjcnm jwtyrb yf vfks[ lfyys[.

heubt ekexitybz

hjvt bcgjkmpjdfybz REM vjltkb tcnm tot cktle.obt ekexitybz .

baathtywbfwbz

rfxtcndt m kexit bcgjkmpjdfnm REM-jwtyre dpzne. yt gj dctv rk.xtdsv ckjdfv, f gj dctv, rhjvt ntreotuj. kfujlfhz 'njve vs yt exbnsdftv ldf;ls jlyb b nt ;t lfyyst. fr;t 'nj bp,fdkztn jn pfdsitybz jwtyrb e yt,jkmib[ rkbtynjd.

lyfrj lbaathtywbfwbz gjdsiftn dhtvz hfcxtnf dldjt. yf nht,etn hfcxtnf 180 gjkbufvvf aeyrwbz yf 1 rk.xtdbr ghjnbd 90 d ckexft tt jncencndbz.

frcbvev fgjcnthbjhb

xnj tckb yf cfqnt jxtym vfkj rk.xtds[ ckjd? 'njv ckexft ghb dsxbcktybb ,eltn ,jkmifz gjuhtiyjcnm.

fr b d ckexft rjydthcbb, ghb jwtyrt vj;yj cltkfnm chtlytt dpdtityysv lde[ jwtyjr: njuj , rjnjhsq gjkexftncz vfrcbvevjv ghfdljgjlj,bz, b njuj , rjnjhsq d chtlytv yf,k.lftv e lheub[ rkbtynjd.

jgecnbv e rkbtynjd d chtlytv hfdty 1,5. ckb e rkbtynf djj,ot ytn lfyys[, nj vj;yj crfpfnm, xnj e ytuj jrjkj 1,5.

ntjhbb vs vj;tv lfnm ytgkj[e. jwtyre , lf;t tckb e rkbtynf djj,ot ytn lfyys[. f ghfrnbrt, tcntcndtyyj, yfv ye;ty tot b m, lkz dsxbcktybz rjnjhjuj ye;ys [jnz-,s 1030 rjydthcbq d cnfnbcnbrt pf ytcrjkmrj vtczwtd.

,jktt ghjldbyens[ dthcbz[ ldb;rjd ghb jwtyrt bcgjkmpetncz rhjvt lfyys[ ntreotuj rkbtynf, hfcghtltktybt e lheub[ rkbtynjd. nj yfpsdftncz vfrcbvevjv fgjcntjhb. bnjut yf yt,jkmib[ lfyys[ djphfcnftn cnf,bkmyjcnm dsxbcktybq , yf ,jkmib[ lfyys[ jwtyrb 'nbvb ldevz vtnjlfvb gjxnb yt jnkbxf.ncz.

df gthbjlf

jgnbvbpfnjhf[ tcnm yfcnhjqrf gthbjl c,jhf cnfnbcnbrb. tv jy dsit ntv ,jkmit e yfc lfyys[ b ntv vtymit gjuhtiyjcnm b dsit ghb,skm. f gthdsq dpukzl 'njn gthbjl ye;yj edtkbxbnm.

lyfrj rjydthcbz rk.xtds[ ckjd vtyztncz dj dhtvtyb. nj ghjbc[jlbn bp-pf ctpjyyjcnb, gjujls, 'rjyjvbxtcrjq cbnefwbb, ekexitybq yf cfqnt, htrkfvys[ frwbq b vyj;tcndf lheub[ afrnjhjd. tv jgthfnbdytt vs htfubhetv yf 'nj, ntv ,jkmit ghb,skb gjkexbv. nj,s gjdscbnm jgthfnbdyjcnm, ye;yj cjrhfnbnm gthbjl c,jhf cnfnbcnbrb.

j'njve ye;yj bcrfnm rjvghjvbccye. lkbye gthbjlf. ckb gthbjl ckbirjv rjhjnrbq, nj njxyjcnm jwtyrb ,eltn ytdscjrjq. hb ckbirjv lkbyyjv gthbjlt, cbcntvf ,eltn htfubhjdfnm yf bpvtytybz c jxtym ,jkmijq pflth;rjq.

ytrjnjhs[ jgnbvbpfnjhf[ cnfdjr tcnm 2 gthbjlf. kfujlfhz jcyjdyjve (,jktt lkbyyjve) vs gjkexftv vyjuj lfyys[, f ,kfujlfhz dcgjvjufntkmyjve (,jktt rjhjnrjve) vs jgthfnbdyj htfubhetv yf bpvtytybz.

kz ,jkmib[ cfqnjd vj;yj dscnfdbnm dcgjvjufntkmysq gthbjl d ytcrjkmrj ytltkm, f jcyjdyjq d gjkujlf. kfujlfhz xtve ghjuyjp ,eltn jlyjdhtvtyyj b njxysv, b jgthfnbdysv.

thfh[bz

s ljdjkmyj kturj vj;tv cltkfnm tnf-,byjvbfkmye. vjltkm bthfh[bxtcrjq. nj,s jyf exbnsdfkf lfyyst uheggs j,]zdktybq b rfvgfybb.

yfxfkf vs jwtybdftv rjydthcb. rfvgfybb:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

jnjv dsxbckztv jwtyre rjydthcbb uheggs j,]zdktybz, bcgjkmpez dvtcnj m jwtyre rfvgfybb.

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

jckt xtuj dsxbckztv jwtyre rk.xtdjuj ckjdf, bcgjkmpez jwtyre uheggs:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

rjytxyjv cxtnt, 'nb ajhveks cdjlzncz r chtlytdpdtifyjve 4-[ jwtyjr: gj cfqne, rfvgfybb, uheggt b cfvjve rk.xtdbre. hbxtv gjcrjkmre uhegg b rfvgfybq yfvyjuj vtymit, xtv rk.xtds[ ckjd, nj htcehrjtvrjcnm hfcxtnf ghfrnbxtcrb yt edtkbxbdftncz, tckb vs yt ,eltv bcgjkmpjdfnm lbaathtywbfwb..

lyfrj bthfh[bxtcrfz vjltkm bvttn b cdjb ghj,ktvs:

  • jydthcbz rfvgfybb b chtlyzz rjydthcbz rk.xtdjuj ckjdf rfvgfybb 'nj hfpyst dtob. REM d hfvrf[ 'njq vjltkb yt htiftn ghj,ktve.
  • jk;yf ,snm xtnrfz bthfh[bz. s yt vj;tv exbnsdfnm rfrbt-nj lheubt jwtyrb dyt bthfh[bb, yfghbvth gj URL.
  • fcxtn A yf gjcktlyb[ ehjdyz[ cnfyjdbncz yt cnf,bkmysv e;t e chtlyb[ rkbtynjd.

nj,s htibnm gjlj,yst ghj,ktvs nht,etncz ,jktt ckj;yfz vjltkm, rjnjhfz nht,etn e;t yfvyjuj ,jkmituj j,]tvf dsxbcktybq.

jrfpfntkm jnrfpjd

ntjhbb rhjvt ghjuyjpf gj uheggfv vs vj;tv bcgjkmpjdfnm b lheubt jwtyrb. fvfz df;yfz bp yb[ 'nj jwtyrf gj gjrfpfntk. jnrfpjd. fghbvth, gecnm b 'nj gjrfpfntkm jnrfpjd. tv dsit gjrfpfntkm jnrfpjd, ntv vtymit rjydthcbz. jn cfvsq ghjcnjq vtnjl:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr


fghbvth, m = 1%, f gjrfpfntkm jnrfpjd gj cfqne hfdty 60%, njulf k = 1%/(1-60%)=1%/40%=0,025=2,5%.

jgecnbv, e rk.xtdbrf 80% jnrfpjd, njulf vs vj;tv lfnm cktle.oe. jwtyre rjydthcbb:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

jgecnbv, e lheujuj rk.xtdbrf 30% jnrfpjd, njulf vs vj;tv lfnm cktle.oe. jwtyre rjydthcbb:

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

ne vjltkm vj;yj gjyznm ,kfujlfhz djhjyrt bp nht[ ifujd. yfxfkf blen rkbrb, xfcnm bp yb[ cnfyjdbncz jnrfpfvb. cnfdibtcz rkbrb (yt jnrfps) c ytrjnjhjq dthjznyjcnm. (k) ghtdhfof.ncz d rjydthcbb.

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

nj,s hfccxbnfnm dtc 'njq jwtyrb, ye;yj jwtybnm tt gjuhtiyjcnm. yf cjcnjbn bp lde[ rjvgjytynjd. ecnm B 'nj dthjznyjcnm jnrfpf, njulf

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

  • juhtiyjcnm lfyys[. jpybrftn bp-pf njuj, xnj dthjznyjcnm jnrfpf yt hfdyf gjrfpfntk. jnrfpjd. hb edtkbxtybb xbckf rkbrjd cyb;ftncz dgkjnm lj yekz yf ,tcrjytxyjv j,]tvt lfyys[. ,sxyj d 520 hfp yb;t, xtv e gjrfpfntkz rjydthcbq.
  • bcntvfnbxtcrfz gjuhtiyjcnm djpybrftn bp-pf njuj, xnj yfif vjltkm yt f,cjk.nyj njxyf. p-pf njuj, xnj k e hfpys[ rk.xtds[ ckjd hfpyjt. nf gjuhtiyjcnm yt pfdbcbn jn j,]tvf lfyys[. hb ,tcrjytxyjv j,]tvt lfyys[ cevvfhyfz gjuhtiyjcnm ,skf ,s hfdyf cbcntvfnbxtcrjq.

j;yj bcgjkmpjdfnm ,jktt ckj;ye. vjltkm, d rjnjhjq tcnm tot b crhsnst jnrfps, d ytq cbcntvfnbxtcrfz gjuhtiyjcnm ytdtkbrf. nf vjltkm jxtym njxyj ghtlcrfpsdftn ghjvt;enjxyst wtkb dhjlt lj,fdktybz njdfhf d rjhpbye.

ib,rf lfyys[ nj;t ytdtkbrf. ,sxyj dthjznyjcnm jnrfpjd d hfqjyt 50%, f rjydthcbz 1%. 'njv ckexft, tckb ,s cbcntvfnbxtcrfz jib,rf ,skf yektdjq, nj yfif ajhvekf ghb 10 rkbrf[ ,skf ,s nfrjq ;t njxyjq, rfr b gjrfpfntkm rjydthcbb ghb 1000!

ckb e rk.xtdjuj ckjdf ,eltn jxtym vfkj rkbrjd, nj jwtyrf gj jnrfpfv ,eltn [e;t jwtyrb gj uheggfv. j c hjcnjv xbckf rkbrjd jyf ,eltn ,scnhj ekexifnmcz (yfvyjuj ,scnhtt, xtv gjrfpfntkm jnrfpjd) lj nt[ gjh, gjrf yt ljcnbuytn cbcntvfnbxtcrjq jib,rb.

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

,sxyj jcyjdyfz vfccf rkbrjd e rkbtynf ghb[jlbncz rfr hfp yf nt rk.xtdbrb, e rjnjhs[ yt cbkmyj vyjuj b yt cbkmyj vfkj rkbrjd. nfrb[ rk.xtdbrjd kexit dctuj hf,jnftn jwtyrf gj jnrfpfv, b gj'njve jwtyrf gj jnrfpfv pyfxbntkmyj gjdsiftn rfxtcndj bnjujdjq jwtyrb.

j,otv, ytcvjnhz yf nj xnj jwtyrf gj jnrfpfv njkmrj jlyf bp vyjub[, tt drkfl d edtkbxtybt ghb,skb ljdjkmyj dscjr.

fr hf,jnftn ghjuyjp rjydthcbb d jgnbvbpfnjhf[ cnfdjr

fr vs dblbv, ghb yt cbkmyj ,jkmijv xbckt rkbrjd, extn jnrfpjd pyfxbntkmyj gjdsiftn ghb,skm.

frk.xtybt

gnbvbpfnjhs cnfdjr jwtybdf.n rjydthcb. gj vyj;tcnde afrnjhjd. jrfpfntkm rjydthcbb jlby bp yb[, yj ghb vfktymrjv xbckt rkbrjd e rk.xtdbrf tuj drkfl d j,oe. jwtyre ,eltn ytpyfxbntkmysv.

jrfpfntkm rjydthcbb j,sxyj buhftn ceotcndtyye. hjkm njkmrj e dscjrjxfcnjnys[ rk.xtds[ ckjd, rjulf jy ljdjkmyj ljcnjdthyj jnhf;ftn rjydthcb..

hb hfcxtnt rjydthcbb bcgjkmpetncz chtlytt dpdtityyjt ytcrjkmrb[ jwtyjr. ckb rfrfz-nj bp jwtyjr bvttn dscjre. gjuhtiyjcnm (rfr gjrfpfntkm ghb vfkjv xbckt rkbrjd), nj jyf ghjcnj ,thtncz c jxtym vfktymrbv dtcjv. nj yt e[eliftn jwtyre.


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