Howor#3 urvval Aalyss Na: Huag Xw 黃昕蔚 Quso: uppos ha daa ( follow h odl ( ( > ad < <. L b h ubr of dahs. ( Wr dow h log-llhood fuco ( log L(.. ( Drv h scor fucos ( ad ( (3 Drv h fd-po rao algorh ad apply o h daa of Eapl. (4 Drv h Hssa ar of (. (5 Drv h Nwo-Raphso algorh ad apply o h daa of Eapl. p whr ad (6 Drv h Nwo-Raphso algorh udr h rasford parar log( apply o h daa of Eapl. (7 Copar h ubrs of raos all h hr algorhs. oluo: ( ; Daa: ( Modl: ( ( Obsrvd survval : T cagory ; cagory csord ; obsrvd p whr > ad < < Th cuulav dsy fuco s F( ( p( dsy fuco s f ( h ( f ( ( F ( h probably ( p h hazard fuco s ( ( h ( whr ( p p h s h basl hazard fuco ad h cuulav hazard fuco s
du h du u h H. For a co odl h llhood fuco of dah could b dfd as { [ ] T T H h L p { [ ] p. Th h log-llhood fuco s { [ ] log log I log log whr ad I. ( Th scor fucos ar ad whr ad. (3 To solv h scor fucos sg h fucos qual o zro
h soluo s ˆ.89857 ad ˆ log -.45465. By h Fd-po rao hod w ca drv h rlaoshp fro h scor fucos Fd-po rao algorh:. log p : h al po ( ; p : ( ( ( ( ; log p 3: If ( ( 5 < ad ( 5 < h sop. ˆ ( ad ˆ ; Els go p. (4 Th scod dffra of h log-llhood fuco ar ( (
( whr ad. Thus h hssa ar s H. (5 Nwo-Raphso algorh : p : h al po ( ad ( ; p : ( ( ( ( ( ( ( ( ( ; ( p 3: If ( ( 5 < ad ( 5 < h sop. ˆ ( ad ˆ ; Els go p. (6 ubsu log by ( log.
Th scor fucos ar ad. Th scod dffra of h log-llhood fuco ar. Thus h hssa ar s H. Nwo-Raphso algorh : p : h al po ad ; p : p 3: If 5 < ad 5 < h sop. ˆ ad ˆ ; Els go p.
(7 Irao Fd-po rao Nwo-Raphso Nwo-Raphso -. log(..7486 -.836.4847 4.467665 -.8769 -.9769.79365 -.8768.4 3.55593 -.7855 -.937345 3.84336 -.344845.34.875-3.69835 -.83643 4.8658 -.3746934.4934.698948-4.46347 -.5986 5.879 -.389969.9975.88-5.8398 -.9943 6.885936 -.397683.8.7339-6.473 -.3973 7.889383 -.45665.3974.4383-6.65549 -.777 8.897 -.43539.494583.9397844-6.9675 -.4648436 9.89986 -.44489.6975 -.739-7.9355 -.47936.894 -.449769.84434 -.3696-7.8 -.454666.89639 -.45.889 -.4656-7.84 -.45465.89748 -.45343.89836 -.454494 - - 3.8983 -.4544.89857 -.45465 - - 4.8983 -.454346.89857 -.45465 - - 5.89844 -.454498 - - - - 6.8985 -.454575 - - - - For fd po algorh oo 5 raos o covrg o h ac valu calculad by MLEs. For Nwo-Raphso algorhs f w subsu log by h ubr of raos could rduc fro 3 o ss o b or ffccy. Abou choosg al valu s hard o dcd whch sar po o us sc h daa s qu sall ay chag o al valu wll a dffr rsuls. I hs wo Nwo-Raphso algorhs I choos. ad log log. ad o b h al pos. Th rsul ss good ( ad (4 ca rasfor o ach ohr.
covrg plo
covrg plo
Appd R cod daa as.daa.fra( cbd(dah. c(65 3 7 45 5 38 8 54 dla c( c( daa daa[ordr(daa$dah.dcrasgf] for ( c(:row(daa{ daa$[] su(-daa$[:row(daa] daa$[] su(daa$[:row(daa] su(daa$dla su(daa$dla[daa$ ] su(daa$dah.[daa$ ] su(daa$dah.[daa$ ] ############Algorh#################### ###Fd po fd.po fuco(fuc al crr{ dffrc rp( lgh(al j pu.valu al whl (ay(dffrc > crr{ ca("irao"j": " j j oupu.valu fuc(pu.valu ca(oupu.valu "\" dffrc abs(oupu.valu - pu.valu pu.valu oupu.valu
###Nwo Raphso Nwo.Raphso fuco(.fuco H.Fuco al crr{ dffrc rp( lgh(al pu.valu al j whl (ay(dffrc > crr{ ca("irao"j": " j j oupu.valu pu.valu - solv(h.fuco(pu.valu %*%.Fuco(pu.Valu ca(oupu.valu "\" dffrc abs(oupu.valu - pu.valu pu.valu oupu.valu ########################################### ###Fd po s rao.fuco4 fuco(ha{ labda ha[] ba ha[] labda.w / (p(ba * ba.w log( / (labda.w * rur(c(labda.w ba.w fd.po(rao.fuco4 c(. ^(-5 ###Nwo Rapso s Hssa fuco(ha{ labda ha[] ba ha[] h ar(c(- / labda^ -p(ba * -p(ba * -labda * p(ba * row
rur(h cor fuco(ha{ labda ha[] ba ha[] h ar(c( / labda - p(ba * - - labda * p(ba * row rur(h Nwo.Raphso(cor Hssa c(. ^(-5 Hssa fuco(ha{ labda ha[] ba ha[] h ar(c(- p(labda ba * - p(labda * - p(labda ba * - p(labda ba * - p(labda ba * row rur(h cor fuco(ha{ labda ha[] ba ha[] h ar(c( - p(labda ba * - p(labda * - p(labda ba * row rur(h Nwo.Raphso(cor Hssa c(log(. ^(-5