An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.

Ranked set sampling is a very useful method to collect data when the actual measurement of the units in a population is difficult or expensive. Recently, the generalized quasi-Lindley distribution is suggested as a new continuous lifetime distribution. In this article, the ranked set sampling method is considered to estimate the parameters of the generalized quasi-Lindley distribution. Several estimation methods are used, including the maximum likelihood, the maximum product of spacings, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling methods. The performance of the proposed ranked set sampling based estimators is achieved through a simulation study in terms of bias and mean squared errors compared to the simple random sample. Additional results are obtained based on real data for the survival times of 72 guinea pigs and 23 ball bearings. The simulation study results and the real data applications showed the superiority of the proposed ranked set sampling estimators compared to the simple random sample competitors based on the same number of measuring units.

This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback–Leibler, Kolomogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs’ power increases.