make_3state_t_fit <- function(seed = 11) {
  set.seed(seed)
  ret <- rnorm(150)
  fit <- fit_hmm_em(ret, K = 3L, model = "student",
                    n_starts = 1L, max_iter = 20L, verbose = FALSE,
                    nu_grid = c(4, 8, 15))
  KRONX:::reorder_fit_by_scale(fit)
}

test_that("hazard_from_nu is monotone decreasing in nu", {
  nu  <- c(3, 5, 10, 20)
  eps <- KRONX:::hazard_from_nu(nu, epsilon_min = 0.01, c_hazard = 0.05)
  expect_true(all(diff(eps) < 0))
  expect_true(all(eps > 0))
})

test_that("build_Q row sums are <= 1 (sub-stochastic)", {
  fit <- make_3state_t_fit()
  eps <- KRONX:::hazard_from_nu(fit$params$nu)
  Q   <- KRONX:::build_Q(fit$A, eps)
  expect_true(all(rowSums(Q) <= 1 + 1e-12))
  expect_true(all(Q >= 0))
})

test_that("build_K diagonal is negative", {
  fit  <- make_3state_t_fit()
  eps  <- KRONX:::hazard_from_nu(fit$params$nu)
  Q    <- KRONX:::build_Q(fit$A, eps)
  Kmat <- KRONX:::build_K(Q)
  expect_true(all(diag(Kmat) < 0))
})

test_that("fundamental_matrix N has positive entries", {
  fit  <- make_3state_t_fit()
  eps  <- KRONX:::hazard_from_nu(fit$params$nu)
  Q    <- KRONX:::build_Q(fit$A, eps)
  Kmat <- KRONX:::build_K(Q)
  Nmat <- KRONX:::fundamental_matrix(Kmat)
  expect_true(all(Nmat > 0))
})

test_that("quasi_stationary_distribution sums to one", {
  fit  <- make_3state_t_fit()
  eps  <- KRONX:::hazard_from_nu(fit$params$nu)
  Q    <- KRONX:::build_Q(fit$A, eps)
  pi   <- KRONX:::quasi_stationary_distribution(Q)
  expect_equal(sum(pi), 1, tolerance = 1e-10)
  expect_true(all(pi > 0))
})

test_that("residence_weight_vector sums to one", {
  fit  <- make_3state_t_fit()
  eps  <- KRONX:::hazard_from_nu(fit$params$nu)
  Q    <- KRONX:::build_Q(fit$A, eps)
  Kmat <- KRONX:::build_K(Q)
  Nmat <- KRONX:::fundamental_matrix(Kmat)
  pi   <- KRONX:::quasi_stationary_distribution(Q)
  w    <- KRONX:::residence_weight_vector(Nmat, pi)
  expect_equal(sum(w), 1, tolerance = 1e-10)
})

test_that("left_tail_state_probs are in (0, 1)", {
  fit <- make_3state_t_fit()
  ret <- rnorm(150)
  thr <- as.numeric(stats::quantile(ret, 0.01))
  q   <- KRONX:::left_tail_state_probs(fit, thr)
  expect_length(q, 3L)
  expect_true(all(q > 0 & q < 1))
})

test_that("ruin_bound is in (0, 1)", {
  fit   <- make_3state_t_fit()
  eps   <- KRONX:::hazard_from_nu(fit$params$nu)
  Q     <- KRONX:::build_Q(fit$A, eps)
  Kmat  <- KRONX:::build_K(Q)
  Nmat  <- KRONX:::fundamental_matrix(Kmat)
  pi_qs <- KRONX:::quasi_stationary_distribution(Q)
  pi_r  <- KRONX:::residence_weight_vector(Nmat, pi_qs)
  ret   <- rnorm(150)
  thr   <- as.numeric(stats::quantile(ret, 0.01))
  q     <- KRONX:::left_tail_state_probs(fit, thr)
  bar_q <- sum(pi_r * q)
  bar_l <- sum(pi_r * eps)
  rb    <- 1 - exp(-bar_l * bar_q * 250)
  expect_true(rb > 0 && rb < 1)
})