set.seed(112)
population_size <- 600
# the number of samples to be ranked in each set
H <- 3

with_replacement <- FALSE
sigma <- 4
mu <- 10
n_rankers <- 3
# sample size
n <- 30

rhos <- rep(0.75, n_rankers)
taus <- sigma * sqrt(1 / rhos^2 - 1)
population <- qnorm((1:population_size) / (population_size + 1), mu, sigma)

data <- InPlotSampling::jps_sample(
  population,
  n,
  H,
  taus,
  n_rankers,
  with_replacement
)
data <- data[order(data[, 2]), ]

InPlotSampling::rss_jps_estimate(
  data,
  set_size = H,
  method = "JPS",
  confidence = 0.80,
  replace = with_replacement,
  model_based = FALSE,
  pop_size = population_size
)
#>          Estimator Estimate Standard Error 80% Confidence intervals
#> 1       UnWeighted    9.570          0.526               8.88,10.26
#> 2      Sd.Weighted    9.595          0.569             8.849,10.341
#> 3 Aggregate Weight    9.542          0.500             8.887,10.198
#> 4     JPS Estimate    9.502          0.650             8.651,10.354
#> 5     SRS estimate    9.793          0.783             8.766,10.821
#> 6          Minimum    9.542          0.500             8.887,10.198

set.seed(112)

# SBS sample size, PPS sample size
sample_sizes <- c(5, 5)

n_population <- 233
k <- 0:(n_population - 1)
x1 <- sample(1:13, n_population, replace = TRUE) / 13
x2 <- sample(1:8, n_population, replace = TRUE) / 8
y <- (x1 + x2) * runif(n = n_population, min = 1, max = 2) + 1
measured_sizes <- y * runif(n = n_population, min = 0, max = 4)

population <- matrix(cbind(k, x1, x2, measured_sizes), ncol = 4)
sample_result <- sbs_pps_sample(population, sample_sizes)

# estimate the population mean and construct a confidence interval
df_sample <- sample_result$sample
sample_id <- df_sample[, 1]
y_sample <- y[sample_id]

sbs_pps_estimates <- sbs_pps_estimate(
  population,
  sample_sizes,
  y_sample,
  df_sample,
  n_bootstrap = 100,
  alpha = 0.05
)
print(sbs_pps_estimates)
#>   n1 n2 Estimate  St.error 95% Confidence intervals
#> 1  5  5    2.849 0.1760682              2.451,3.247