Based on progressively type-II censored data, the maximum-likelihood estimators (MLEs) for the Lomax parameters are derived using the expectation–maximization (EM) algorithm. Moreover, the expected Fisher information matrix based on the missing value principle is computed. Using extensive simulation and three criteria, namely, bias, root mean squared error and Pitman closeness measures, we compare the performance of the MLEs via the EM algorithm and the Newton–Raphson (NR) method. It is concluded that the EM algorithm outperforms the NR method in all the cases. Two real data examples are used to illustrate our proposed estimators.

Estimation of the parameters of Weibull distribution is considered using different methods of estimation based on different sampling schemes namely, Simple Random Sample (SRS), Ranked Set Sample (RSS), and Modified Ranked Set Sample (MRSS). Methods of estimation used are Maximum Likelihood (ML), Method of moments (Mom), and Bayes. Comparison between estimators is made through simulation via their Biases, Relative Efficiency (RE), and Pitman Nearness Probability (PN). Estimators based on RSS and MRSS have many advantages over those that are based on SRS.

Survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Accelerated failure time (AFT) models provide a linear relationship between the log of the failure time and covariates that affect the expected time to failure by contracting or expanding the time scale. The AFT model has intensive application in the field of social, medical, behavioral, and public health sciences. In this article we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) or an Extreme Ranked Set Sampling (ERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This article demonstrates that these approaches provide a more powerful testing procedure, as well as a more efficient estimate of hazard ratio, than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural Health Study data are used to illustrate the methods developed in this article.

In this paper, we introduce a new nonparametric test of symmetry based on the empirical overlap coefficient using kernel density estimation. Our investigation reveals that the new test is more powerful than the runs test of symmetry proposed by McWilliams [31]. Intensive simulation is conducted to examine the power of the proposed test. Data from a level I Trauma center are used to illustrate the procedures developed in this paper.