test_that("Univariate ITL functions work accurately", {
  xi <- 1.5
  x <- c(0.1, 0.5, 1.0, 2.0)

  # PDF
  dens <- ditl(x, xi = xi)
  expect_true(all(dens > 0))
  expect_equal(length(dens), length(x))

  # Log PDF
  log_dens <- ditl(x, xi = xi, log = TRUE)
  expect_equal(log_dens, log(dens), tolerance = 1e-10)

  # CDF and Survival
  p_val <- pitl(x, xi = xi)
  s_val <- pitl(x, xi = xi, lower.tail = FALSE)
  expect_true(all(p_val >= 0 & p_val <= 1))
  expect_equal(p_val + s_val, rep(1, length(x)), tolerance = 1e-10)

  # Quantile exact roundtrip
  u_probs <- c(0.01, 0.1, 0.25, 0.5, 0.75, 0.9, 0.99)
  q_vals <- qitl(u_probs, xi = xi)
  expect_equal(pitl(q_vals, xi = xi), u_probs, tolerance = 1e-9)

  # Random generation
  set.seed(42)
  r_samp <- ritl(100, xi = xi)
  expect_equal(length(r_samp), 100)
  expect_true(all(r_samp > 0))

  # Hazard & Reversed Hazard
  h_val <- hitl(x, xi = xi)
  rh_val <- rhitl(x, xi = xi)
  expect_true(all(h_val > 0))
  expect_true(all(rh_val > 0))

  # Error handling
  expect_error(ditl(x, xi = -1))
  expect_error(pitl(x, xi = 0))
  expect_error(qitl(c(-0.1, 0.5), xi = 1))
})