Package 'neutroPPS'

Neutrosophic PPSWOR Sampling and Estimation

Description

neutro_pps performs probability proportional to size sampling without replacement (PPSWOR) using Lahiri's method for interval-valued (neutrosophic) data. It computes neutrosophic first- and second-order inclusion probabilities and estimates population totals and means using the neutrosophic Horvitz–Thompson (NHT) and neutrosophic generalized regression (NGREG) estimators. The function also provides variance estimation, coefficients of variation, and relative efficiency measures.

Usage

neutro_pps(data_neutro, n, seed = NULL, verbose = FALSE)

Arguments

data_neutro	A data frame containing the following columns: Auxili_min, Auxili_max, Study_min, and Study_max.
n	Desired sample size. Must be an integer satisfying $2 \le n \le N$, where $N$ is the population size.
seed	Optional random seed for reproducible sample selection. If NULL, sampling is performed without setting a seed.
verbose	Logical value indicating whether progress messages, intermediate tables, and estimation results should be printed. Defaults to FALSE.

Value

An invisible list with the following components:

sample_indices	Integer vector containing the indices of the selected sample units.
inclusion_probs	A list containing the lower and upper first-order neutrosophic inclusion probabilities (pi_l and pi_u) for all population units.
joint_inclusion	A data frame containing lower and upper joint inclusion probabilities for all sampled pairs.
ht	A list containing the neutrosophic Horvitz–Thompson estimates, including estimated totals, means, auxiliary totals, variance estimates, and coefficients of variation.
greg	A list containing the neutrosophic generalized regression estimates, including estimated totals, coefficients of variation, and relative efficiency measures.

Author(s)

Neha Purwar, Kaustav Aditya, and Achal Lama.

References

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons.

Lahiri, D. B. (1951). “A Method of Sample Selection Providing Unbiased Ratio Estimates.” Bulletin of the International Statistical Institute, 33, 133–140. Available at: https://cir.nii.ac.jp/crid/1370588381061610886/

Särndal, C. E., Swensson, B., and Wretman, J. (1992). Model Assisted Survey Sampling. Springer.

Smarandache, F. (2014). Introduction to Neutrosophic Statistics. Available at: https://digitalrepository.unm.edu/math_fsp/40/

Examples

data_neutro <- data.frame(
  Auxili_min = c(10, 15, 20, 25, 30),
  Auxili_max = c(12, 18, 25, 32, 40),
  Study_min  = c(50, 60, 75, 90, 110),
  Study_max  = c(55, 70, 85, 105, 130)
)
# Returns an invisible list - assign it to explore results
res <- neutro_pps(
  data_neutro,
  n = 2,
  seed = 12,
  verbose = FALSE
)

res$ht      # Neutrosophic Horvitz-Thompson results
res$greg    # Neutrosophic GREG results

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