### ratio CI

parent 8593643c
 ... ... @@ -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*mean.v - ta*Sigma[1,2] d <- mean.v^2 - ta*Sigma[2,2] b <- mean.v^2 - ta*Sigma[1,1] g <- mean.v*mean.v - ta^2*Sigma[1,2] d <- mean.v^2 - (ta*Sigma[2,2])^2 b <- mean.v^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')
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