Reliability Estimation of the Lomax Distribution under Ranked Set Sampling (RSS) With Application

Abstract

Sometimes the researcher faces a problem in obtaining data, or there may be difficulty in obtaining it due to cost, effort, or other reasons related to the time. In this case, sampling methods are used that ensure the researcher achieves his desired goal with a short time, effort, and cost, by using Ranked Set Sampling (RSS). In this paper, the reliability function of the Lomax Distribution was estimated under the (RSS) using four estimation methods, which are the Maximum Likelihood Estimators (MLE), the Maximum Product of Spacings (MPS), the Least Squares (LS) method, and Weighted Least Squares (WLS). The Monte Carlo simulation method was also used to determine the best method, and the best estimate was chosen using the Mean Square Error (MSE) criterion, and the results were applied in the theoretical aspect using the R-program, as the simulation results showed that the most efficient method among the methods used to estimate the reliability function of the Lomax distribution under (RSS) is the (MPS) method. The experimental aspect was applied to real data representing the times of the beginning of complete recovery (times of disease remission) in months for bladder cancer patients for a sample consisting of 96 patients drawn using the (RSS) method.

Keywords

• ranked set sampling
• lomax distribution
• maximum likelihood
• maximum product of spacing estimator
• least squares
• weighted least squares