In agricultural, animal, fisheries, and industrial experiments, block designs are frequently adopted to control variability; however, systematic trends within blocks may still influence the response variable. Although such trends are often considered negligible, they can exert a substantial effect and therefore should be incorporated into the experimental model to ensure valid inference. Trend-free block designs constitute an important class of designs in which treatment effects are orthogonal to trend effects, allowing the data to be analyzed using standard block design procedures. Existing research on trend-free incomplete block designs has largely focused on balanced and partially balanced incomplete block designs. This paper addresses the construction of Trend-free block designs based on partially balanced incomplete block designs (PBIBD) using two distinct approaches: one based on group divisible designs and the other on rectangular designs. Theoretical proofs supporting the proposed construction methods are also presented.
The joint adaptive progressive censoring scheme proposed by Sultana et al. (2021) reduces experimental time and cost in life-testing experiments. In this paper, we extend this scheme by developing statistical inference for two independent Chen populations under jointly adaptive progressive Type-II censoring. Unlike earlier works that mainly focused on exponential models, we consider the flexible Chen distribution, which can model both increasing and bathtub-shaped hazard rates. We obtain maximum likelihood estimates and construct asymptotic and bootstrap confidence intervals. We also apply Bayesian methods to derive credible intervals under squared error loss and LINEX loss functions. The methods are illustrated using real data. Likelihood ratio tests are used to examine whether the two populations have similar shape parameters under both single-sample and joint-sample approaches. An extensive simulation study is carried out to evaluate the performance of the methods and to suggest suitable censoring schemes. The results show that the joint censoring scheme performs better than the single-sample censoring scheme.
Francis Galton, in his seminal 1886 work titled “Regression Towards Mediocrity in Hereditary Stature", scrutinized the heights of 928 adult offspring along with 205 pairs of parents to elucidate the new concept of “regression toward the mean”. Despite the recurrent use of Galton’s data to exemplify this concept, several studies have contested its conformity to his chosen straight-line linear regression model, attributing a discrepancy to an apparent non-linearity in the data, now recognised as “Galton’s bend". In our paper, we provide a possible explanation for the presence of Galton’s bend by advancing the theory of errors-in-variables regression where we show that E[Y | x] is only linear for specific cases of errors-in-variables models.
In clinical trials, multiple correlated continuous and binary variables are often employed as primary endpoints, and evaluation using multiple endpoints establishes evidence for the efficacy of the test treatment. When dealing with multiple endpoints, the familywise error rate of statistical tests must be kept below the nominal significance level. In several studies, procedures have been developed that can be applied to multiple primary endpoints with only a superiority test. However, a procedure that simultaneously incorporates non-inferiority and superiority tests and includes multiple continuous as well as binary variables has not yet been discussed. In this study, we propose a testing procedure that recognizes the efficacy of test treatment only when the superiority of at least one endpoint and the non-inferiority of the remaining endpoints are achieved. The type I error rates and powers of the proposed testing procedure are evaluated through simulations and are compared with those of the closed testing procedure. Regardless of the correlation between endpoints, sample size, or the magnitude of the difference between endpoints in the two groups, the type I error rate was shown not to be inflated. The proposed testing procedure showed higher power than the closed testing procedure. When any of the endpoints are within the non-inferiority margin, the power is drastically reduced depending on the correlation coefficient, indicating the importance of obtaining reliable information a priori.
This article presents two novel goodness-of-fit tests for the Rayleigh distribution, specifically designed for analyzing Type-II censored data. The development of these tests is based on the Kullback–Leibler information criterion. Both tests exhibit consistency, and one of the test statistics possesses a nonnegative property akin to the Kullback–Leibler information. To assess the performance of the proposed tests, a comprehensive simulation study is conducted. The simulation results provide percentile points and power values, offering valuable insights into the effectiveness of the tests in detecting departures from the Rayleigh distribution. Furthermore, a real-life data analysis is included to demonstrate the practical application of the proposed tests. This application showcases how these tests can be utilized to assess the goodness-of-fit of the Rayleigh distribution when analyzing real-world data.
