gompertz karya

gompertz vakr kinwa gompertz karya heey velechya malikesathi ganiteey pratiman aahe, jyala benjamin gompertz (1779-1865) chey naav denyat aale aahe. heey eka sigmoid karya aahe jeey dilelya kalavadhichya suruvatila aanee shevati vadhiche varnan sarvat mand asalyache karate. karyachya ujavya bajuchya kinwa bhavishyatil moolya asymptotkade davya bajuchya kinwa qamee mulyachya asymptotpeksha vakradvare adhik haloohaloo sampark sadhala jaato. heey sadhya logistic karyachya viruddha aahe jyamadhye donhi asymptotes vakradvare samamitiyapane gathale jaatat. heey samanyikrut logistic karyache eka vishesh udaharan aahe. heey karya moolatah manvi mrutyuche varnan karnyasathi tayar kele gele hote, parantu tevhapasoon tapshilvar loksankhyechya sandarbhat jivashastrat lagoo karnyasathi tyat badal karnyat aale aahet.
itihas.
benjamin gompertz (1779-1865) heey londonmadhil ekchyuri hote jeey khajgi shikshan ghet hote. 1819 madhye teey shahee samajache sadasya mhanoon nivadle gele. heey karya pahilyanda 16 juuna 1825 roji tyanchya peparmadhye prushth 518 chya talashi sadar karnyat aale. gompertz karyane jeevan saranitil mahiticha lakshaniy sangrah ekach karyat qamee keela. heey ekhadya vyaktichya vayanusar mrutyuche praman zapatyane vadhate yaa gruhitkavar aadharit aahe. parinami honare gompertz karya heey vayache karya mhanoon dilelya vayat vayat vyaktinchya sankhyesathi asate.
mrutyunchya karyatmak pratimanchya bandhkamavar purviche kaam french ganitshastradnya abraham dii moivar (1667-1754) yanni 1750 chya dashakat kele hote. tathapi, mrutyudar sthir asalyache dii moivrey yanni gruheet dharale. 1860 madhye ingraji actuary aanee ganitshastradnya william mathyu makeham (1826-1891) yanni gompertzchya kamacha vistar prastavit keela hota, jyanni gompertzchya zapatyane zapatyane mrutyudarat satat parshvabhoomi darr jodala.
sootra.
sootra _ 1
kuthe?
malmatta.
tii sathee sootra _ 3 sodavun ardha bindu shodhala jaato.
sootra _ 4
vadhichya kamal daracha bindu (sootra _ 5) t sathee sootra _ 6 sodavun aadhalato.
sootra _ 7
sootra _ 8 varr vaadh aahe
sootra _ 9
vyutpatti.
karya vakrata hii mrutyuchya gompertz niyamavarun ghetali jaau shakate, jyamadhye asey mhatale aahe qee sampoorn mrutyudar (kshay) haah darr sadhyachya aakaranusar vegane qamee hoto. ganitiyadrushtya,
sootra _ 10
kuthe?
udaharanadakhal vapar.
gompertz vakransathichya vaparachya udaharananmadhye khaleel goshtincha samavesh hotoh
anuprayog.
gompertz vakr.
loksankhyeche jivashastra visheshtah gompertz karyashi sambandhit aahe. heey karya visheshtah jivanchya vishisht loksankhyechya jalad vadhiche varnan karnyasathi upayukt aahe, tarr ekada vahoon nenyachi kshamata nishchit jhaali qee (pathar peshi/loksankhya sankhya), shevati aadvya asymptotsathi dekhil jababdar aahe.
tyache khalilpramane pratirupan kele aaheh
sootra _ 12
kutheh
pathar peshi kramankacha haah vichar vastavik jivanatil loksankhyechya gatishilatechi achook nakkal karnyasathi upayukt tharato. heey karya sigmoid karyache dekhil palan karate, jeey samanyatah loksankhyechya vadhiche tapshilvar varnan karnyache sarvat vyapakpane sweekarle jaanare sampraday aahe. yavyatirikt, heey karya prarambhik vadhichya daracha vapar karate, jeey samanyatah jivanu aanee karkarogachya peshinchya loksankhyet disun yete, jeey logg tappyatoon jaatat aanee sankhyet vegane vadhatat. tyachi lokpriyata asoonahi, rugnasobat asalele vegvegale sookshmakrumi kinwa loksankhya jivashastrachya babatit vegvegale paryavaraniy ghatak lakshat gheta, arbud vadhicha prarambhik darr purvanirdharit karane katheen aahe. karkarogachya rugnanmadhye, vay, aahar, vanshikta, anuvanshik purv-vikar, chayapachay, jivanshaili aanee metastasische mool yasarkhe ghatak arbudachya vadhicha darr nirdharit karnyat bhoomika bajavtat. yaa ghatakanchya aadhare vahoon nenyachi kshamata dekhil badalane apekshit aahe aanee tyamule asha ghatananche varnan karane katheen aahe.
chayapachay vakr.
chayapachay karya visheshtah jivanmadhil chayapachay darachya hishobane sambandhit aahe. heey karya arbud peshinvar dekhrekh thevanyasathi lagoo kele jaau shakate; chayapachay darr gatishil aahe aanee khoop lavchik aahe, jyamule karkarogachya vadhicha tapasheel denyat teey adhik achook aahe. chayapachay vakr shareer uutinchi dekhbhal aanee nirmiti karnyasathi pradan karate tee urja vicharat ghete. hii urja chayapachay manali jaau shakate aanee peshi vibhajanatil vishisht namunyache anusaran karate. urja sanvardhanacha vapar asha vadhiche pratirup banavanyasathi keela jaau shakato, mug too vividh vastuman aanee vikasacha kaal asso. serve varg samaan vadhicha namuna samayik karatat aanee parinami, heey model, peshi vibhajan, tumourchya vikasacha paya manato.
sootra _ 17
vishrantichya velee vaparali jaanari urja aanee chayapachay daratil farak heey modella vadhicha darr adhik achookpane nirdharit karnyas anumati dete. vishrantichi urja uutinchya dekhbhalisathi vaparlya jaanarya urjepeksha qamee asate aanee ektritpane vidyaman uutinchya dekhbhalisathi aavashyak urjeche pratinidhitva karate. yaa done ghatakancha vapar, naveen ootee tayar karnyasathi aavashyak asalelya urjesah, vadhichya daracha sarvasamaveshak nakasha tayar karane aanee shivay, vilamb tappyache achook pratinidhitva karane.
arbudanchi vaadh.
1960 chya dashakat aaa.keey. lerdney prathamach gathichya vadhichi mahitee basavanyasathi gompertz vakr yashasviritya vaparali. kharey tarr, tumour mhanje maryadit jaaget vadhanari pesheey loksankhya jithe poshak tatvanchi upalabdhata maryadit asate. gathicha aakar x (t) mhanoon darshavitana gompertz vakr khalilpramane lihine upayukt aaheh
kutheh
x (0)> 0 varr swatantrapane. upchar ityadinchya anupasthitit heey lakshat ghya.. samanyatah teey x (0) <k asate, tarr upcharanchya upasthitit teey x (0)> k asoo shakate;
heey darshavile jaau shakate qee x (t) chee gatishilata gompertz vibhedak samikaranadvare niyantrit kelee jaateh
sootra _ 29
aay.eae. too tutalyavar too asha swarupacha asatoh
sootra _ 30
"eff (ex)" haah peshijanya loksankhyecha tatkal prasar darr aahe, jyache ghatate swaroop heey peshijanya loksankhyechya vadhimule poshak tattvansathichya spardhemule aahe, tasech logistic vadhichya daramule aahe. tathapi, eka moolbhut farak aaheh logistic prakaranat lahan pesheey loksankhyesathi prasar darr maryadit aaheh
sootra _ 31
tarr gompertzchya babatit prasar darr amaryad aaheh
sootra _ 32
polad aanee whildonchya lakshat alyanusar, peshijanya loksankhyecha prasar darr shevati peshi vibhajanachya velene maryadit asato. asha prakare, heey eka purava asoo shakate qee gompertz samikaran lahan gathee vadhavanyasathi changle nahee. shivay, agadi alikade asey lakshat aale aahe qee, rogpratikarak pranalishi parasparsanvad, gompertz aanee amaryadit eff (0) dware darshavilele itar niyam rogpratikarak dekharekhichi shakyata rokhatil.
fornalsky aanee itaranni kelela saiddhantik abhyas. parabolic karya adhik yogya asalelya agadi suruvatichya tappyashivay karkarogachya vadhisathi gompertz vakratecha jaivbhautik aadhar darshavila. tyanna asehi aadhalale qee gompertz vakr karkarogachya gatishilatechya karyanchya vyapak kutumbatil sarvat vaishishtyapurn prakaranache varnan karate.
gompertz vaadh aanee logistic vaadh.
gompertz vibhedak samikaran
sootra _ 29
heey samanyikrut logistic vibhedak samikaranache maryadit prakaran aahe
sootra _ 34
(jethe sootra _ 35 hii eka sakaratmak vastavik sankhya aahe)
sootra _ 36.
yavyatirikt, samanyikrut logistic karyachya aalekhamadhye eka paravartan bindu asato jevha
sootra _ 37
aanee gompertz karyachya aalekhatil eka jevha
sootra _ 38.
gomp-ex vadhicha niyam.
vareel vicharanchya aadhare, wheeldonne gathichya vadhiche ganiteey model prastavit kele, jyala gomp-ex model mhanatat, jeey gompertz niyamat kinchit badal karate. gomp-ex modelmadhye asey manale jaate qee suruvatila sansadhanansathi konatihi spardha nahee, jenekarun ghatankiy niyamache palan karoon cellular loksankhya vistarel. tathapi, eka gambhir aakar threshold sootra aahe _ 39 asey qee sootra _ 40 sathee. sansadhanansathi spardha nahee heey gruheet bahutek paristhitinmadhye kharey tharate. tathapi, maryadit ghatakanmule tyacha parinam houu shakato, jyasathi up-ghatak chull tayar karane aavashyak aahe.
vaadh hii gompertz niyamache anusaran karateh
sootra _ 41
jenekarunah
sootra _ 42
yethe sootra _ 39 sathee kahee sankhyatmak andaj aaheth
inverse gompertz function.
gompertz karya heey eka-teey-eka patravyavahar aahe (jyala bijective karya dekhil mhanatat) aanee mhanoon tyache inverse karya paramparik karyatmak sanketankamadhye ekach nirantar karya mhanoon spashtapane vyakt kele jaau shakate. formche gompertz function dile aaheh
sootra _ 46
kuthe?
sambandhit ulat karya asey vyakt kele jaau shakateh
sootra _ 49
inverse function tyachya done asymptotschya darmyan vastavik sankhyanchya sanchamadhye keval sankhyatmak moolye tayar karate, jeey aata forward gompertz functionpramane aadvyaivaji anulamb aahet. ubhya asymptotsdware paribhashit kelelya shrenichya baher, inverse functionsathi nakaratmak sankhyanchya laghuganakachi ganana karane aavashyak aahe. yaa aanee itar karananmule, inverse gompertz function thet detamadhye basavanyacha prayatna karane anekada avyavharik asate, visheshtah jarr ekhadyakade tulanene qamee deta points upalabdh asateel jyatoon fitchi ganana karata yeil. tyaeivaji ekhadi vyakti detacha transposed sambandh forward gompertz functionmadhye basavoo shakate aanee nantar varr dilelya doghanmadhil sambandh vaparoon tyache samatulya inverse functionmadhye rupantar karoo shakate.
asha prakare inverse functionche anek upayog aahet. udaharanarth, kahee elissa parikshananmadhye eka manak vakr asate jyachi sandrata gompertz karyadvare tyanchya optical ghanateshi atyant changlya prakare julali jaau shakate. ekada manke asha prakare gompertz karyasathi yogya jhaali qee, pramanit vakr basavatana tayar jhalelya gompertz karyachya ulat vaparun tyanchya mojalelya optical ghanatetun parikshanatil namunyanchya adnyat sandratechi ganana kelee jaate.

