workspace/logistic.r

In JonasMoss/univariateML: Maximum Likelihood Estimation for Univariate Densities

x <- rlogis(2000, 1, 2)

microbenchmark::microbenchmark(mllogis_(x), mllogis2_(x))

p <- c(1, 2)

sum_x <- sum(x)

f <- function(p) {
  n <- length(x)
  mu <- p[1]
  s <- p[2]
  -(sum_x - n * mu) / s - n * log(s) - 2 * sum(log(1 + exp(-(x - mu) / s)))
}

mllogis2_ <- function(x, ...) {
  m <- stats::median(x)
  mad <- stats::median(abs(x - m))
  n <- length(x)
  sum_x <- sum(x)
  f <- function(p) {
    mu <- p[1]
    s <- p[2]^2
    (sum_x - n * mu) / s + n * log(s) + 2 * sum(log1p(exp(-(x - mu) / s)))
  }
  values <- suppressWarnings(stats::nlm(f = f, p = c(m, mad^2)))
  list(
    estimates = c(values$estimate[1], exp(values$estimate[2])),
    logLik = -values$minimum,
    i = values$iterations
  )
}

microbenchmark::microbenchmark(mllogis_(x), mllogis2_(x))