Explore stan and R support for overlapping swindow and D

[seabbs]

An example that demonstrates functionality that I think should work is:

test_that(
  "rprimarycensoreddist is consistent with dprimarycensoreddist and
   pprimarycensoreddist when D is not cleanly divided by swindow",
  {
    n <- 10000
    pwindow <- 2
    swindow <- 3
    D <- 13
    rate <- 0.5

    samples <- rpcens(
      n, rexp, pwindow, swindow,
      D = D,
      rate = rate
    )

    # Check empirical mean and pmf
    empirical_pmf <- as.vector(table(samples) / n)
    empirical_mean <- mean(samples)
    empirical_sd <- sd(samples)

    # Theoretical calculations
    x_values <- seq(0, D, by = swindow)
    pmf <- dpcens(
      x_values, pexp, pwindow, swindow,
      D = D,
      rate = rate
    )
    theoretical_mean <- sum(x_values * pmf)
    theoretical_sd <- sqrt(sum((x_values - theoretical_mean)^2 * pmf))

    # Compare means and standard deviations
    expect_equal(empirical_mean, theoretical_mean, tolerance = 0.1)
    expect_equal(empirical_sd, theoretical_sd, tolerance = 0.1)

    # Compare empirical and theoretical PMFs
    expect_equal(empirical_pmf, pmf, tolerance = 0.1)

    # Check empirical CDF against theoretical CDF
    empirical_cdf <- ecdf(samples)(x_values)
    theoretical_cdf <- ppcens(
      x_values + swindow, pexp, pwindow, D,
      rate = rate
    )
    expect_equal(empirical_cdf, theoretical_cdf, tolerance = 0.02)

    # Ensure the last CDF value is close to 1
    expect_equal(theoretical_cdf[length(theoretical_cdf)], 1, tolerance = 1e-3)

    # Check that PMF sums to approximately 1
    expect_equal(sum(pmf), 1, tolerance = 1e-3)
  }
)

This issue is an extension of #23

On top of the above test passing we would also need an equivalent stan test to pass

[seabbs]

My current solution to this is to warn the user and force them to resize the offending windows. We should likely improve the warnings for this and possibly offer some functionality to do it automatically.