Dependent and independent sampling techniques for modeling radiation and failure data

Abstract

Ordered set sampling techniques are among the most popular current techniques used in estimation, especially for small sample sizes, and their efficiency has been proven in many articles as the best estimators for unknown parameters for several distributions. Systematic ranked set sampling and centralized ranked set sampling are two recently developed techniques in ranked set sampling that fall under dependent sampling techniques. The probability density function for each using the inverse Lomax distribution is extracted. Furthermore, the maximum likelihood method is used to estimate the values of the Inverse Lomax distribution parameters using several ordered set sampling techniques. Several of these techniques are new and have not been used in various distributions. There are two types of ranked set sampling techniques that were used: independent set sampling includes ranked set sampling (RSS), and dependent set sampling includes neoteric ranked set sampling (NRSS), extended neoteric ranked set sampling (ENRSS), systematic ranked set sampling (SRSS), and centralized ranked set sampling (CRSS) In the Monto Carlo simulation with varying sample sizes, the NRSS, ENRSS, SRSS, and CRSS estimators outperformed the RSS estimator. Additionally, the ENRSS method is more effective than competing RSS-based techniques. It has also been demonstrated that CRSS is not as effective as other techniques, particularly for large mean square errors. Finally, two real datasets related to radiation and failure rate show how the distribution can change depending on the sampling techniques.