test_that("baseline_hazard works correctly", {
  t <- seq(0.1, 2, by = 0.1)
  par <- c(1.5, 0.8)
  bh <- baseline_hazard(t, par)
  
  expect_length(bh$H0, length(t))
  expect_length(bh$h0, length(t))
  expect_true(all(bh$H0 >= 0))
  expect_true(all(bh$h0 >= 0))
})

test_that("alpha_power_functions works correctly", {
  t <- 1:5
  eta <- 0
  theta <- 0.5
  par <- c(1.5, 0.8)
  
  gf <- alpha_power_functions(t, eta, theta_frailty = theta, par = par)
  
  expect_length(gf$S, length(t))
  expect_length(gf$f, length(t))
  expect_length(gf$h, length(t))
  expect_length(gf$H, length(t))
  expect_true(all(gf$S >= 0 & gf$S <= 1))
  expect_true(all(gf$f >= 0))
  expect_true(all(gf$h >= 0))
  expect_true(all(gf$H >= 0))
})

test_that("r_alpha_power generates valid samples", {
  set.seed(123)
  n <- 50
  par <- c(1.5, 0.8)
  
  samples <- r_alpha_power(n, alpha = par[1], beta = par[2])
  
  expect_length(samples, n)
  expect_true(all(samples > 0))
  expect_true(all(is.finite(samples)))
})

test_that("fit_alpha_power works with simple data", {
  set.seed(123)
  dat <- r_alpha_power_reg(50, par = c(1.5, 0.8), theta = 0.3,
                          cen_type = "right", cen_rate = 0.2)
  
  fit <- fit_alpha_power(dat$time, dat$status, frailty = TRUE)
  
  expect_s3_class(fit, "alpha_power_fit")
  expect_true(fit$logLik < 0)
  expect_true(fit$AIC > 0)
  expect_true(fit$BIC > 0)
})

test_that("predict_alpha_power and residuals_alpha_power work", {
  set.seed(123)
  dat <- r_alpha_power_reg(50, par = c(1.5, 0.8), theta = 0.3,
                          cen_type = "right", cen_rate = 0.2)
  fit <- fit_alpha_power(dat$time, dat$status)
  
  pred <- predict_alpha_power(fit, type = "survival")
  expect_true(is.matrix(pred$survival))
  expect_true(all(pred$survival >= 0 & pred$survival <= 1))
  
  res <- residuals_alpha_power(fit)
  expect_true(is.list(res))
  expect_true("cox_snell" %in% names(res))
  expect_true("martingale" %in% names(res))
  expect_true("deviance" %in% names(res))
  expect_length(res$cox_snell, length(dat$time))
})