#beta unknown and alpha known DST
rm(list = ls())
ltmode1=c(300,400,500)
utmode1=c(400,500,650)
pb=array(3)
bb=array(3)
lR=array(3)
uR=array(3)
mf=array(3)
mw=array(3)
mwf=array(3)
ubetaaggY=c()
lbetaaggY=c()
uTmin=c()
lTmin=c()
lt=c()
ut=c()
lmineta=c()
umineta=c()
aa=655
c=0.05
#T=285
T=c(50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,281,282,283,284,285,286,287,288,289,290,
300,350,400,410,420,430,440,450,460,470,480,490,500,510,520,530,540,550,560,570,580,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,610,620,630,640,650,660,670,680,690,700,710.720,730,740,750,760,770,780,790,800,850,900,1000,1100,1200,1400,1500,1600,2000)
for(jj in 1:length(T)){

for(j in 1:3){
f=function(b) {((b-1)/b)^(1/b)*aa-ltmode1[j]}
pb[j]=uniroot(f,c(1,1000))$root

f1=function(b) {((b-1)/b)^(1/b)*aa-utmode1[j]}
bb[j]=uniroot(f1,c(1,1000))$root[1]

lR[j]=exp(-(T[jj]/aa)^pb[j])
uR[j]=exp(-(T[jj]/aa)^bb[j])

mw[j]=lR[j]
mf[j]=1-uR[j]
mwf[j]=1-mw[j]-mf[j]

}

myw=prod(mw)+(mw[1]*mwf[2]*mw[3])+(mw[2]*mwf[1]*mw[3])+(mw[1]*mwf[3]*mw[2])+(mw[1]*mwf[2]*mwf[3])+(mwf[1]*mw[2]*mwf[3])+(mwf[1]*mwf[2]*mw[3])
myf=prod(mf)+(mf[1]*mwf[2]*mf[3])+(mf[2]*mwf[1]*mf[3])+(mf[1]*mwf[3]*mf[2])+(mf[1]*mwf[2]*mwf[3])+(mwf[1]*mf[2]*mwf[3])+(mwf[1]*mwf[2]*mf[3])
k=((mf[1]*mf[2]*mw[3])+(mf[1]*mw[2]*mf[3])+(mw[1]*mf[2]*mf[3])+(mw[1]*mw[2]*mf[3])+(mw[1]*mf[2]*mw[3])+(mf[1]*mw[2]*mw[3])+(mf[1]*mwf[2]*mw[3])
+(mf[1]*mw[2]*mwf[3])+(mw[1]*mwf[2]*mf[3])+(mw[1]*mf[2]*mwf[3])+(mwf[1]*mw[2]*mf[3])+(mwf[1]*mf[2]*mw[3]))
mywf=(mwf[1]*mwf[2]*mwf[3])+k

mdw=myw/(1-k)
mdw
mdf=myf/(1-k)
mdf
mdwf=(mwf[1]*mwf[2]*mwf[3])/(1-k)
mdwf
mdw+mdf+mdwf
lARY=mdw
lARY
uARY=1-mdf
uARY


ff=function(b) {exp(-(T[jj]/aa)^b)-lARY}
lbetaaggY[jj]=uniroot(ff,c(1,1000))$root

ff1=function(b) {exp(-(T[jj]/aa)^b)-uARY}
ubetaaggY[jj]=uniroot(ff1,c(1,1000))$root


a=seq(0,100,0.5)
Tmin=function(a){
   aa*(c/(a-1))^(1/a)
}

ubetaagg=optimize(Tmin, int=c(0,1000), lower = min(c(0,1000)), upper = max(c(0,1000)),
         maximum = FALSE)$minimum

if (lbetaaggY[jj] > ubetaagg){
lTmin[jj]=aa*(c/(lbetaaggY[jj]-1))^(1/lbetaaggY[jj])
uTmin[jj]=aa*(c/(ubetaaggY[jj]-1))^(1/ubetaaggY[jj])}
else {
lt[jj]=aa*(c/(ubetaaggY[jj]-1))^(1/ubetaaggY[jj])
ut[jj]=aa*(c/(lbetaaggY[jj]-1))^(1/lbetaaggY[jj])
lTmin[jj]=min(lt[jj],ut[jj])
uTmin[jj]=max(lt[jj],ut[jj])
}

lmineta[jj]=10^5*( lTmin[jj]^(ubetaaggY[jj]-1)/(aa)^(ubetaaggY[jj])+c/lTmin[jj])
umineta[jj]=10^5*( uTmin[jj]^(lbetaaggY[jj]-1)/(aa)^(lbetaaggY[jj])+c/uTmin[jj])
}

lTmin
uTmin
uTmin-lTmin
lmineta
umineta
umineta-lmineta
sort(uTmin-lTmin)[1]
orgeta=which.min(uTmin-lTmin)
lmineta[orgeta]
umineta[orgeta]
lTmin[orgeta]
uTmin[orgeta]

<pre>An Error occurred while handling another error:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/ErrorHandler.php(136): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/ErrorHandler.php(135): yii\web\ErrorHandler-&gt;renderException()
#3 [internal function]: yii\base\ErrorHandler-&gt;handleException()
#4 {main}
Previous exception:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(656): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/models/Files.php(696): yii\base\Application-&gt;end()
#3 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/controllers/FilesController.php(484): faravaghi\filemanager\models\Files-&gt;getFile()
#4 [internal function]: faravaghi\filemanager\controllers\FilesController-&gt;actionGetFile()
#5 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/InlineAction.php(57): call_user_func_array()
#6 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Controller.php(180): yii\base\InlineAction-&gt;runWithParams()
#7 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Module.php(528): yii\base\Controller-&gt;runAction()
#8 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Application.php(103): yii\base\Module-&gt;runAction()
#9 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(386): yii\web\Application-&gt;handleRequest()
#10 /var/www/html/prof-homepages/frontend/web/index.php(18): yii\base\Application-&gt;run()
#11 {main}</pre>