如何在R中自动化数据帧中的mle2()？

install.packages("bbmle")
library(bbmle)

df <- data.frame(x = c(1, 2, 3), y = c(2, 4, 6))

# 定义正态分布函数
normal_distribution <- function(x, mean, sd) {
  dnorm(x, mean = mean, sd = sd)
}

# 定义似然函数
likelihood_function <- function(parameters) {
  mean <- parameters[1]
  sd <- parameters[2]
  x <- df$x
  y <- df$y
  log_likelihood <- sum(log(normal_distribution(y, mean = mean, sd = sd)))
  return(-log_likelihood)  # 注意使用负号，因为mle2()函数最小化目标函数
}

# 拟合模型
fit <- mle2(likelihood_function, start = list(mean = 0, sd = 1))