| The Code for the Examples |
| two_R.txt |
| rm(list = ls()) |
| #set.seed(99) |
| n = 200 |
| r = 195 |
| af = 1 |
| th = 2 |
| z1 = runif(n,0,1) |
| z2 = sort(((1-z1)^(-1/th)-1)^(1/af)) |
| x = z2[1:r] |
| xaf = log(1 + x^(af)) |
| t = sum(xaf) + (n-r)xaf[r] |
| b = 1 |
| u = 3 |
| v = 3 |
| a = 1 |
| yebs = 0 |
| yebl = 0 |
| p = 0 |
| yebs11 = 0 |
| yebl11 = 0 |
| while (p < 5000) { |
| k = runif(1,0,b) #EBS1 |
| # k1 = runif(1,0,1) #EBS23 |
| # k = b(1-sqrt(1-k1)) #EBS2 |
| # k = bsqrt(k1) #EBS3 |
| c = rbeta(1,u,v) |
| m = n-r |
| s = 1 |
| ybs11 = 0 |
| ybl11 = 0 |
| q = 5000 |
| y = rexp(q,a) |
| while (s < m + 1) { |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| ybs = t(((1 + log(1 + y^af)%o%sg/(k + t))^(-r-c))exp(ay))((ta/a)rosg) |
| ybs1 = apply(ybs,2,sum) |
| ybs11 = rbind(ybs11,ybs1) |
| ybl = t((1 + log(1 + y^af)%o%sg/(k + t))^(-r-c))(tarosg) |
| ybl1 = apply(ybl,2,sum) |
| ybl11 = rbind(ybl11,ybl1) |
| s = s + 1 |
| } |
| ybs111 = apply(ybs11,1,sum)/q |
| ybl111 = apply(ybl11,1,sum)/q |
| ybl111 = -log(1-ybl111)/a |
| yebs = yebs+ybs111 |
| yebs11 = cbind(yebs11,ybs111) |
| yebl = yebl+ybl111 |
| yebl11 = cbind(yebl11,ybl111) |
| two_R.txt |
| p = p + 1 |
| } |
| yebs1 = yebs/p |
| yebl1 = yebl/p |
| yebs11 = yebs11[,1:p + 1] |
| yebl11 = yebl11[,1:p + 1] |
| deta = 0.90 |
| low = ceiling((1-deta)p/2) |
| up = ceiling((1 + deta)p/2) |
| yebs1low = apply(yebs11,1,sort)[low,] |
| yebs1up = apply(yebs11,1,sort)[up,] |
| yebl1low = apply(yebl11,1,sort)[low,] |
| yebl1up = apply(yebl11,1,sort)[up,] |
| s = 1 |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| z3 = ybs111 [1] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1 + deta)/2)/f2 |
| } |
| ybslow1 = z3 |
| z3 = ybs111 [2] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1-deta)/2)/f2 |
| } |
| ybsup1 = z3 |
| s = 2 |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| z3 = ybs111 [2] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1 + deta)/2)/f2 |
| } |
| ybslow2 = z3 |
| z3 = ybs111 [3] |
| two_R.txt |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1-deta)/2)/f2 |
| } |
| ybsup2 = z3 |
| s = 3 |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| z3 = ybs111 [3] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1 + deta)/2)/f2 |
| } |
| ybslow3 = z3 |
| z3 = ybs111 [4] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1-deta)/2)/f2 |
| } |
| ybsup3 = z3 |
| s = 4 |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| z3 = ybs111 [4] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1 + deta)/2)/f2 |
| } |
| ybslow4 = z3 |
| z3 = ybs111 [5] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1-deta)/2)/f2 |
| } |
| ybsup4 = z3 |
| s = 5 |
| ta = 1/beta(s,m-s + 1) |
| rosg = ((-1)^c(0:(s-1)))/(beta(c(1:s),s + 1-c(1:s))s(m-s + c(1:s))) |
| sg = m-s + c(1:s) |
| z3 = ybs111 [3] |
| two_R.txt |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1 + deta)/2)/f2 |
| } |
| ybslow5 = z3 |
| z3 = ybs111 [6] |
| z4 = 1 |
| while ((1-z4/z3)^2 > 10^(-16)){ |
| f1 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c))tarosg) |
| f2 = sum(((1 + log(1 + z3^af)sg/(k + t))^(-r-c-1)(z3^(af-1)/(1 + z3^af)))tarosgsg(r + c)af/(k + t) |
| ) |
| z4 = z3 |
| z3 = z3 + (f1-(1-deta)/2)/f2 |
| } |
| ybsup5 = z3 |
| x |
| z2 |
| ybs111[1:m + 1] |
| ybslow1 |
| ybsup1 |
| ybslow2 |
| ybsup2 |
| ybslow3 |
| ybsup3 |
| ybslow4 |
| ybsup4 |
| ybslow5 |
| ybsup5 |
| ybl111[1:m + 1] |
| yebs1[1:m + 1] |
| yebs1low[1:m + 1] |
| yebs1up[1:m + 1] |
| yebl1[1:m + 1] |
| yebl1low[1:m + 1] |
| yebl1up[1:m + 1] |
