Estimating Demand
set.seed(123456789)
N <- 1000
u <- sort(rnorm(N, mean = 1, sd = 3))
p <- 2
mean(u - p > 0)
## [1] 0.386
1 - pnorm(p, mean = 1, sd = 3)
## [1] 0.3694413
p <- runif(9, min = -10, max = 10)
s <- matrix(NA, length(p), 1)
for (i in 1:length(p)) {
s[i, 1] <- mean(u - p[i] > 0)
}
s
## [,1]
## [1,] 0.968
## [2,] 0.999
## [3,] 0.875
## [4,] 0.092
## [5,] 0.996
## [6,] 0.809
## [7,] 0.936
## [8,] 0.503
## [9,] 0.086
plot(1 - ecdf(u)(u), u, type = "l", lwd = 3, lty = 1, col = 1,
xlab = "s", ylab = "p", xlim = c(0, 1))
lines(sort(s), p[order(s)], type = "l", lwd = 3, lty = 2)
abline(h = 0, lty = 2)
legend("bottomleft", c("True", "Est."), lwd = 3, lty = c(1:2))
