cascuness

sambhaavyata siddhaantam mariyu ganankalalo, cascuness anedi moodu yaadruchchika chararaasulu kalisi entha marutayo koliche kolata. coascuness anedi moodava praamaanika cross central moment, idhi vakrataku sambandhinchinadi, endukante covarians anedi vyatyaasaaniki sambandhinchinadi. sambandhinchinadi, cross mariyu litzenberger stock market pettubadulalo pramaadaanni pariseelinchadaaniki dheenini upayoginchaaru. upayoginchaaru harway mariyu siddiq dwara pramaadaaniki darakhaastu vistarinchabadindi.
moodu yaadruchchika chararaasulu saanukuula cascunessnu pradarsiste avi oke samayamlo teevramaina vichalanaalaku lonavutaayi, veetilo besi sankhya saanukuula disalo untundi (kabatti moodu yaadruchchika chararaasulu teevramaina saanukuula vichalanaalaku lonavutaayi, ledhaa okati teevramaina saanukuula vichalananiki lonavutaayi, migilina rendu teevramaina pratikuula vichalanaalaku lonavutaayi). adevidhamgaa, moodu yaadruchchika chararaasulu pratikuula cascunessnu pradarsiste avi oke samayamlo teevramaina vichalanaalaku lonavutaayi, veetilo sarri sankhya saanukuula disalo untundi (kabatti moodu yaadruchchika chararaasulu teevramaina pratikuula vichalanaalaku lonavutaayi, ledhaa okati teevramaina pratikuula vichalananiki lonavutaayi, migilina rendu teevramaina saanukuula vichalanaalaku lonavutaayi).
rakalu.
detaalo cascuness yokka sthaayiki rendu ververu kolatalu unnaayi.
cascaveness.
moodu yaadruchchika chararaasulu "x", "y" mariyu "z" kosam, chinnapati cascuness ganaamkam ilaa nirvachinchabadindih
ikkada e ["x"] anedi "x" yokka anchanaa viluva, dheenini "x" yokka sagatu anie kooda pilustaaru, mariyu suutram _ 2 anedi "x" yokka praamaanika vichalanam.
praamaanika rank cascuness.
bernard, chenn, ruchendorff mariyu wandfell moodu yaadruchchika chararaasulu "x", "y" mariyu "z" yokka praamaanika rank cascunessnu ilaa nirvachinchaaruh
ikkada "f" x "(" x ")," f "y" ("y") mariyu "f" z "(" z ") anevi varusaga" x "," y "mariyu" z "yokka sanchita pampinhee vidhulu.
aastulu.
moodu yaadruchchika chararaasulu okela unnappudu vakrata anedi cascuness yokka pratyeka sandarbhamh
rendu yaadruchchika chararaasulaku, "x" mariyu "y", mottam yokka vakrata, "x" + "y",
ikkada "s" "x" anedi "x" yokka vakrata mariyu suutram _ 2 anedi "x" yokka praamaanika vichalanam. rendu yaadruchchika chararaasulu verucheyabadinappudu sunna vakratanu kaligi unnappatikee ("s" x "= 0 mariyu" s "y" = 0) rendu yaadruchchika chararaasula mottaanni vakramgaa ("s" x "+" y "incul 0) cheyavachu.
x" mariyu "y" chararaasula madhya coascuness anedi chararaasulu vyakteekarinchabade sthaayi meeda aadharapadi undadu. manam "x" mariyu "y" madhya sambandhaanni vislaeshistunnatlayitee, "x" mariyu "y" madhya cascuness anedi "a" + "bx" mariyu "c" + "dy" madhya cascuness vale untundi, ikkada "a", "b", "c" mariyu "d" sthiraamkaalu.
praamaanika rank cascuness "rs" ("x", "y", "z") eee krindi lakshanaalanu santruptiparustundihi
(1) −1 ≤ "rs" ("x", "y", "z") ≤1.
(2) 1 yokka eguva sarihaddu bernard, chenn, ruchendorff mariyu wandfell (2023) loe (3.3) loe ivvabadina kopula dwara pondabadutundi. −1 yokka diguva sarihaddu adhe kaagitamlooni kopula (3.5) dwara pondabadutundi.
(3) idhi khachitamgaa perugutunna parivartanala krinda asthiramgaa untundi, i.ii., phai, i = 1,2,3, ekapakshamgaa khachitamgaa perugutunna functionlu ayinappudu, "rs" ("x", "y", "z") = "rs" ("f" 1 ("x"), "f" 2 ("y"), "f" 3 ("z")).
(4) "x", "y" mariyu "z" swatantramgaa unte "rs" ("x", "y", "z") = 0.
udaaharana.
x" anedi saadhaaranamgaa pampinhee cheyabadina pramaanikamainadigaa undanivvandi mariyu "x" <0 ayinappudalla "x" = "y" nii amarchadam dwara mariyu "x"> 0 ayinappudalla praamaanika sagam-saadhaarana pampinhee nundi swatantramgaa "y" geeyadam dwara pondina pampinhee "y". maroe maatalo cheppalante, "x" mariyu "y" rendoo saadhaaranamgaa pratikuula viluvalaku puurtigaa paraspara sambandham kaligi untaayi mariyu saanukuula viluvalaku sanketam kakunda sambandham laeni lakshanamtho pampinhee cheyabadataayi. ummadi sambhaavyata saandrata function
ikkada "h" ("x") anedi havicide step function mariyu δ ("x") anedi diarock delta function. eee saandrataku sambandhinchi ekikrutam cheyadam dwara moodava kshanaalanu sulabhamgaa lekkinchavachhuh
x" mariyu "y" saadhaaranamgaa vyaktigatamgaa pramaanikamgaa pampinhee cheyabadinappatiki, "x" + "y" mottam yokka pampinhee gananeeyamgaa vakramgaa undani gamaninchandi. saandrataku sambandhinchi ekikarana nundi, "x" mariyu "y" yokka sahasambandham anie manam kanugonnamu
dheeni nundi vaati mottam yokka praamaanika vichalanam ilaa untundi
paie vakrata mottam suutraanni upayoginchi, manaku undhi
dheenini mottam yokka sambhaavyata saandrata function nundi neerugaa lekkinchavachhuh
bernard, chenn, ruchendorff mariyu wandfell (2023) eee krindi pattikalo chuupina vidhamgaa konni prasiddha upanta pampineelaku cascunespy pramaada parimitulanu kanugonnayi.
ikkada suutram _ 13 anedi gaama function.

