library(tidyverse)
cal_ll_o <- list()
cal_ll_o$a <- function(theta, y_i, sigma) {
ll <- prod(dnorm(y_i, mean = theta, sd = sigma))
return(ll)
}
cal_ll_o$b <- function(theta, y_bar, sigma) {
ll <- prod(dnorm(y_bar, mean = theta, sd = sigma))
return(ll)
}
cal_ll_o$c <- function(theta, y_i, sigma) {
pnorm(y_i, mean = theta, sd = sigma)^5 *
(1 - pnorm(y_i, mean = theta, sd = sigma))^5 *
dnorm(y_i, mean = theta, sd = sigma)
}
cal_ll_o$d <- function(theta, y_i, sigma) {
(pnorm(y_i[2], mean = theta, sd = sigma) -
pnorm(y_i[1], mean = theta, sd = sigma))^9 *
dnorm(y_i[2], mean = theta, sd = sigma) *
dnorm(y_i[1], mean = theta, sd = sigma)
}
cal_ll_o$e <- function(theta, y_i, sigma) {
(1 - pnorm(y_i[2], mean = theta, sd = sigma))^9 *
dnorm(y_i[1], mean = theta, sd = sigma) *
dnorm(y_i[2], mean = theta, sd = sigma)
}
y_i <-
tibble(y = c(73, 75, 84, 76, 93, 79, 85, 80, 76, 78, 80))
sigma <- sd(y_i$y)
theta_k <- seq(min(y_i) - 3, max(y_i) + 3, by = 0.01)
n <- length(y_i)
par(mfrow = c(1, 1))
ll_o <- list()
ll_o$a <-
tibble(theta = theta_k) %>%
add_column(ll = sapply(theta_k, cal_ll_o$a, y_i = y_i$y, sigma = sigma))
plot(theta_k, ll_o$a / max(ll_o$a), type = "l")
ll_o$b <- sapply(theta_k, cal_ll_o$b, y = mean(y_i), sigma = sigma / sqrt(n))
lines(theta_k, ll_o$b / max(ll_o$b), col = 2, type = "l")
ll_o$c <- sapply(theta_k, cal_ll_o$c, y = median(y_i), sigma = sigma)
lines(theta_k, llc / max(llc), col = 3)
ll_o$d <- sapply(theta_k, lld.f, y_i = c(min(y_i), max(y_i)), sigma = sigma)
lines(theta_k, lld / max(lld), col = 4)
ll_o$e <- sapply(theta_k, lle.f, y_i = sort(y_i)[1:2], sigma = sigma)
lines(theta_k, lle / max(lle), col = 5)
rug(y_i)
lines(mean(y_i) * c(1, 1), c(-1, 2), col = 2, lty = 2)
lines(median(y_i) * c(1, 1), c(-1, 2), col = 3, lty = 2)
lines((diff(range(y_i)) / 2 + min(y_i)) * c(1, 1), c(-1, 2), col = 4, lty = 2)
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