ratio CI

R/analysis/ratio.CI.R

@@ -29,20 +29,30 @@ mvrnorm <-
 
 ## define param
 mean.v <- c(0.15, 0.25)
-Sigma <- matrix(c(0.02,0.01,0.01,0.05),2,2)
+Sigma <- matrix(c(0.002,0.001,0.001,0.005),2,2)
 # MC
 res.mc <- mvrnorm(n = 10000, mean.v, Sigma)
 ratio.mc <- res.mc[,1]/res.mc[,2]
-hist(ratio.mc, breaks = 100)
-lines(v = quantile(ratio.mc, probs = c(0.025, 0.975)))
+par(mfrow = c(2,2))
+hist(res.mc[,1], breaks = 100)
+abline(v = quantile(res.mc[, 1], probs = c(0.025, 0.975)))
+hist(res.mc[,2], breaks = 100)
+abline(v = quantile(res.mc[, 2], probs = c(0.025, 0.975)))
+hist(ratio.mc, breaks = 1000, xlim = c(0, 1.4))
+abline(v = quantile(ratio.mc, probs = c(0.025, 0.975)))
+abline(v = mean(res.mc[, 1])/mean(res.mc[, 2]), col = 'red')
 
 ## Fieller's theorem
 
 
 ##because lot of data approximate teh student by a normal
 ta <-  qnorm(0.025)
-g <- mean.v[1]*mean.v[2] - ta*Sigma[1,2]
-d <- mean.v[2]^2 - ta*Sigma[2,2]
-b <- mean.v[1]^2 - ta*Sigma[1,1]
+g <- mean.v[1]*mean.v[2] - ta^2*Sigma[1,2]
+d <- mean.v[2]^2 - (ta*Sigma[2,2])^2
+b <- mean.v[1]^2 - (ta*Sigma[1,1])^2
 
 ci.b <- sqrt(g^2-d*b)
+
+q.l <- (g-ci.b)/d
+q.h <- (g+ci.b)/d
+abline(v = c(q.l, q.h), col = 'green')