test_that("MLE fitting and methods work accurately", {
  set.seed(42)
  sim <- rbitl(60, xi1 = 1.5, xi2 = 1.2, delta = 0.4)
  fit <- mle_bitl(sim[, "x"], sim[, "y"])

  expect_s3_class(fit, "mle_bitl")
  expect_equal(length(fit$par), 3)
  expect_true(all(fit$par[1:2] > 0))
  expect_true(fit$par[3] >= -1 && fit$par[3] <= 1)
  expect_true(is.finite(fit$loglik))
  expect_true(is.finite(fit$aic))
  expect_true(is.finite(fit$bic))
  expect_true(is.finite(fit$aicc))
  expect_true(is.finite(fit$hqic))

  expect_equal(length(coef(fit)), 3)
  expect_s3_class(logLik(fit), "logLik")
  expect_equal(dim(vcov(fit)), c(3, 3))
  expect_equal(AIC(fit), fit$aic)
  expect_equal(BIC(fit), fit$bic)
})