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M.A. epoa (Moca) PMEHEHE PACPEEEH BEA HEEHO P AHAE TEEH THOOTECOO OHTA1 B cae paccope ocoe coca pacpeee Beya-e eo. Oocoao peee

oo pacpeee cceoa ax o oeax acye co, xapaepyxc coa o apeoc, papaoaa cooecya oe oooc ec. C oo pax cacecx oeo poep cooecyx oe peoea eoa oca oe ce apaepo ocea oeo ce xapaepa poecca.

ee coa: aeaecoe oepoae, pacpeeee Be ya-eeo, y pca, aa cac a, ooec o, coaa ap eoc, poec.

Pacpeeee Beya-eeo paoo coyec oca pee opao, ocaex a c ae. Oo o aao ec ecoo cceoae Ba o Beya (Waloddi Weibull) [1, . 6], peeo eo oca pee oao paoo a, ecoo pyccoo aeaa .B. eeo. o pacpeeee cooaoc oca pee epox ycpoc, a, o Map Aeceea epoa acpaa aep cex eoo ayea BM M. E-mail: petrova-ma@rambler.ru.

aa paoa eec o ay pyooco a. .-a. ay B.A. e ocoo.

Cooo: 4M. 2003. 16.

pueeue pacnpeeeu Beya-eeo...

o ae eoopx acox aa, a ae o ca ee pax coax poecco, o ce eyapox oo [2, p. 2055;

3]. B acoc, eo, ocoa a caceco apoca pacpeeee Beya-eeo oceoaeoc peex epao ey oopo co, xapaepy o, poe eacy apoa cye aaa ypae oa caoc Poccco accoa eo p oepoa eyapox ooe oaa p eey ooc oca oecx poecco [3, c. 1].

y pacpeee Beya-eeo ocaec paee F(x) = 1 - exp{-xm}.

Ocoe apaep m oo pacpeee cace aac cooeceo apaepa op acaa.

Hapy c ye pacpeee ae paccapaec y pca, y ecoc, oopa ee h(t) = f(t)/(1-F(t)) = mtm1.

ec y ecoc h(t) epooc oo e co eee aoo epaa pee p yco, o aae epaa co e pooo, f(t) ooc, a F(t) y pacpeee. Pacpeeee Beya oo e o oepoa pae oae a pae op y ecoc. aaa pae apaep pacpe ee, oo oy paec e y pca. Ha pc. 1 pee y ecoc apaepo m = 0,5, m = 1, m = 2 m = 5. Hapaee poca y ecoc ac o ae apaepa op cxooo pacpeee.

Ec m = 1, o ecoc paccapaeoo poecca ocoa e ac o pee;

ec m < 1, o poecc oc ayxa xapaep, ecoc cceyeoo poecca yeaec co peee;

ec m > 1, o ecoc poec ca opacae co peee [3, c. 4].

M.A. empoa Puc. 1. yuu umecuocmu pacnpeeeu Beya-eeo paux aeu napaempo oocoa cooa pacpeee Beya eeo oca poecx ec peoax Ceep oo aaa a ocpoea oe ee ooecoo oa. B pecaeo oe peoaaec, o cac ecoe pacpeeee epoo pee ey poec ec (ca coao aoc) ec yxa paepec pacpeeee Beya-eeo. Toa oce axoe o ope apaepa op pacpeee Be ya-eeo oo ea o o xapaepe poecca e e ooecoo oa. ep cooa o oxo .. eepce, p o o peoaa, o eya pox eecx ooex cyecy eoope aece ao, oope ec o pee, o oope oo yo ya [2, p. 11-15].

Oo ax aa ao pao ec oc o e ce xapaepa pacpeee. o ooe ocea o ce xapaepa poea oa pecaa apaee oo ee.

pueeue pacnpeeeu Beya-eeo...

Paccapaec opa a (z1, z2, z3, , zn), aaea poumeco opo, e zi o eace, oaoo pacpeeee cyae e c ooc epooc (z). Muuaa cmamucmua opeeec a Zmin( n) = min (z1,z2,...,zn ).

Bopy, cocoy Zmin( n), aa oepe opo.

Ooa ee y pacpeee Zmin( n) a Fmin(n)(x).

Fmin(n) (x) = P(Zmin(n) < x) = 1- P(Zmin(n) > x) = = 1- P(zi > x, 1 i n) = 1- (1- (x))n, e x (x) = (z).

oceee paeco ceye opeee y pac peee eacoc z.

Ec pao opecoc y y (x) yoeope ceyey yco: z+0 z (z) = c, c > 0, o oo oaa, lim o p peeoe pacpeeee ao cac n ye pacpeeee Beya-eeo [4, p.115-118], .e.

n x lim Fmin(n) (x) = lim1- 1- =1- exp(-x ). B yxapaep n n n eco pacpeee Beya-eeo apaep , ope ec oeee y ooc (z) opecoc y.

o ccy aa caca opaae oe enou:

eoe n ee, coe pocxo, oa pec caoe caoe eo.

M.A. empoa aoo a paccapaec 2 aopa onno uuo acmpo omoocm ecmu. Onnouuo acmpo xapaepye cocooc eoea coepa po ece ec pa oce ao-o e. eoe, e e onnouuooo acmpo ( aa oe), e y e coepa ax-o poecx ec o co cyae o ex op, oa ao acpo e oc. ye peoaa, o onnouuo acmpo - apa ea. oo o poec cococ, eoxo onpeee ypoe coua oo eoocma, pae c accox ec ae ce peeoo cpeca coax epee [5, c. 1]. o ypoe eooca - ooo acpo - cococye pocy epa1 aa poecx ec.

coyec peooee o o, o poece ec ae ceo coepac pye. e, y oopx ao acpo ec, oc oe py eoeo. yc eoopa pya e ecye, a eoe eoe. apaep omoocm ecmu oe pa pae oo ee ee ae oaae pepo ceyee: omo ocm ecmu oo onpeem a ouecmo e, omopoe ocmaoc o npomecmx ecmu npu euex eux ycoux, omoocm 1 ecmoam npo ce ac, omoocm 2 ecmoam ampa u m.n. oa y ooo ( ecox) eo py o apaep pae 1, eo acpo epeaec py, pya ooa ecoa coep ae eoopoe poecoe ece, pocxo eoopoe co mue. oce oo omoocm ecmu y cex eo py peo aae, y aoo a co ypoe. Co oe aa pecppoa.

epa - eocao ooecx ooax oop, oepx aece acx oco eoeecoo oa.

pueeue pacnpeeeu Beya-eeo...

B ao oe oooc ec cyaa e a, cooecya poeco ope (z1, z2, z3, , zn), oepe ope Zmin( n) oxo cyaa ea, oca a coe. oa y pae ee, pocxo co e, poeca opa coep pe, epe oopoe o ooc ye pao ee, aa caca pae aoe aoe pe. o ocpoe oe co, o ec poecc (cooyoc poecx ec, coepex ao pyo) ocaec pacpeeee Beya-eeo.

Ceoaeo, peeo epa ey co (poec ec, coepe oo pyo) ye oc ac pacpeeee Beya-eeo. .. eepcea oaao [2, p. 20], o ec py eac py o pya, o peypyee pacpeeee oe ye pacpeeee Be ya-eeo. Ec e ec pax py c aoac (o ee eco peao ), o yco , p oopx peypyee pacpeeee ec pac peeee Beya-eeo, o oa e e.

coyee ae - poey pee ey co , xapaepyc coao apeoc1. B aece tn epec poeyo pee ey coe c oepo n c oepo n - 1. o ec a oo ocpo y(t) - pecy y pacpeee op {tn}. Paccapae a cyaa ea - poeyo pee ey poec ec, (t1, , tn) - opa peaa cyao e c eeco ye pacpeee.

oye A.. Maco peyae aaa coo MB o aecay, 2001-2002 .

M.A. empoa peoaaec, o y pacpeee y Beya-eeo FW(t) = 1 - exp(-tm). Toa poep oe o e pacpeee eec op coyec pep coac ooopoa [6, c. 107]. oe apae po pacpeee peec eo acaoo pao oo. oce aca oapa y paooo axo, o cooecye oe, m o yoe op cey yco [2, p. 30]:

n = (1) n m t i i= nn n m f (m) = + ) - (2) ln(t n ln(t )ti.

i i n m m i=1 = t i i= Ta a oceee ypaee e oe peeo aa ec, coe oe apaepo oy oye c o o epaox cex eoo.

ocoy poecc oye oe op {tn} o oo pacy o pee (eec op oye eee 400-500 e, ooe oop, pax ycox), eecoopao cxo, o ( cy ex p y pex coc oepyeoo oea) apaep pacpeee oy op o ec. Ec eoopx oax o ec, o oo peoo, o poecc ee ooecoo oa ee co xapaep. a pepe, xapaepy peya oo, ec a eco apoca peco y eopeeco (p ep ooopoa).

pueeue pacnpeeeu Beya-eeo...

Caaa opeec oac, oopx oy coepac o ce apaepo. C o e ec o pe o ce ecoc poecca (o pay ecoc).

peaec oo ooea opa. oce oo a ao oopeo epae pooc ce ya poeypa, ocaa T. oy [4, p. 117]. ypae FW(t) = 1 - exp(-tm) o oappoae oyaec paee ln(ln{1/[1 - FW(t)]}) = mlnt + ln.

aaa paccapac pa ln(ln{1/[1-y(t)]}), e o oc accc ooeo lnt. B cyae cooec pec oo pacpeee (a epae) pacpeee Beya-e eo o pa oe po, pe oe a oa o po cooecye apaepy op m, a acc ca oe 0 (intercept) - apaepy acaa. Haee c oo eoa aex apao pee ae apaepo m coyc aece aaoo p e pee ypae (2) eoo poco epa p ce oeo acaoo paooo.

Puc. 2. pau nomopoo oapua nupueco yuu pacnpeeeu u ueoe npuueue no emoy aueux apamo M.A. empoa peca y pacpeee Apoca Beya-eeo Puc. 3. pau nupueco yuu pacnpeeeu u meopemueco yuu Beya-eeo c napaempau, oeeu c noo yuu acuaoo npaonoou Cey a: c oo pep ooopoa opee ec cooece eopeeco y pacpeee peco a ao epae. Tae o pep Cpoa poepec oea oopooc cex cocex ace aeoo pae op. B cyae, ec oea oopo oc oepaec, aea oa e cooecye cee apaepo, oeco eeo pae copaaec.

Puc. 4. cmpau npoepu unome oopoocmu pueeue pacnpeeeu Beya-eeo...

Ha pc. 4 oaa 2 pae pece y pac peee, cooecye pa ac op, x a poca pacpeeee Beya-eeo. B paccapa eo pepe oea oopooc e oepaec.

Ta opao, c oo eocao poeyp o o ocea o ce apaepo, opa eopeec y y pacpeee. o, co oepe, ooe, o epx, poopoa eee ooecoo oa p eex ex ycox, o-opx, aapoa o ce xapaepa poecca o ooe a opee , o eo oeo a coo caa, , cooece o, ayxae poecca.

B aee yoca poee aaa ax c o o pacpeee Beya-eeo a coaa popa a, peaaea aaa ax pao ppo, pe ooeo ex pacpeeee Beya-eeo. Cpea papao Borland C++Builder 5. paeco peaa cooaac oea VCL. eae oaoc c po pao oy opaac eocpec-eo aopy.

Ocaa cooyoc eo (pepecco aa, aa apaepo pacpeee Beya-eeo) ooe cceoa poopoa eee ooecoo o a. ocpoea oe peec peax paceo.

TEPATPA 1. epo ye o cace. M.: StatSoft. http://www.statsoft.ru/ home/textbook/default.htm.

2. Petersen I.D. The Dynamic Laws of International Political Systems 1823 1973. Institute of Political Studies, University of Copenhagen, Copenhagen Political Studies, 1980.

3. pemo B.C., Baco .E., poo .B. Heoope ace coa eeyax opaox cce ooo // HT. 1994. 11.

4. Indow T. Weibull Form in Memory, Reaction Time, and Social Behavior:

Asymptotic Distribution of Minima from Heterogeneous Population // Institute for Mathematical Behavioral Sciences, Technical Report Series, MBS 95-04, 1995.

M.A. empoa 5. Bauupo A.A. oecoe oeee eo op. http://kosilka.h1.ru.

6. eo.., Meee .. Maeaeca caca. M.: Bca oa, 1984.

7. eocu B.A. aeca oe ooecoo oa:

ocpoee, oooc peya pee // Maeaecoe oe poae coax poecco. M.: -o M, 2000. B. 2.

8. Indow T. Analyses of Events Counted on Time-Dimension: a Soft Model of Extreme Statistics // Behaviometrika. 1993. Vol. 20. 2.




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