Estimation based on ranked set sampling for the two-parameter Birnbaum–Saunders distribution

Abstract

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and non-parametric inference. In this paper, we consider RSS-based estimation for the two-parameter Birnbaum–Saunders (BS) distribution, which is widely used in reliability analysis. The estimation methods considered for comparison purposes were: maximum likelihood (ML), modified method of moments (MMM), maximum product of spacings (MPS), and Anderson–Darling (AD). The performance of the RSS-based estimators was evaluated through Monte Carlo simulations under both perfect and imperfect ranking assumptions. The bias, mean squared error, and mean integrated squared error were used as the criteria for comparison. The results revealed that the RSS-based estimators perform better than their simple random sampling (SRS) counterparts. The ML estimator performed the best under the perfect ranking assumption, while the MMM provided better performance for higher levels of imperfect ranking. Additional simulations based on data from a forest inventory corroborated our findings.

Keywords:

• Monte Carlo simulation
• maximum likelihood estimation
• modified moments
• Anderson–Darling
• maximum product of spacings
• mean integrated squared error

2010 Mathematics Subject Classifications:

• 62D05
• 62F10

Disclosure statement

No potential conflict of interest was reported by the author(s).