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An extension of the omnibus test statistic of Ebner et al. [A new omnibus test of fit based on a characterization of the uniform distribution. Statistics. 2022;56:1364–1384. doi: 10.1080/02331888.2022.2133121] is considered for the general two-sample alternative. In addition, using the extension this paper introduces a maximum test statistic and an adaptive test statistic for testing the equality of two distributions. The power performance in various situations is investigated for continuous and discrete distributions. Simulation studies based on Monte-Carlo show that the proposed test statistics are good competitors of the existing nonparametric test statistics. The proposed test statistic displays outstanding performance in certain situations, and is illustrated using real data. Finally, we offer some concluding remarks. [ABSTRACT FROM AUTHOR]

This study proposes two modified Anderson-Darling test statistics that emphasize the upper or lower tails of distribution. Under the finite sample sizes, various models are used to estimate the upper tail percentage points of the proposed test statistic. The limiting distribution of the proposed test statistics is derived with a sum of infinite series. The polynomial approximation, the method of Durbin and Knott and the normal and non normal saddlepoint approximations are used to approximate the limiting distribution of the suggested test statistics. Simulations are used to investigate the accuracy of various approximations. The asymptotic power of the proposed statistics is obtained to compare with various statistics. The proposed test statistics are illustrated by the analysis of real data. [ABSTRACT FROM AUTHOR]

The original or generalized Lindley distribution has been proposed in order to fit a stochastic model to real data, that is, it establishes the distribution of the sum of independent variables. The distribution of the sum of independent and non identically generalized Lindley random variables is obtained by using inverse transformation of the moment generating function. A saddlepoint and a normal approximations are used to approximate the derived distribution. The accuracy of the approximations is shown by numerical simulations. [ABSTRACT FROM AUTHOR]

One-sample testing problem is one of the most important topics in statistics. The sign and Wilcoxon tests are commonly used for testing the location parameter. An extension of the sign and Wilcoxon signed-rank tests has been proposed. However, when the sample size increases, the exact critical value of the statistic becomes difficult to determine. Therefore, in this study, we used a saddlepoint approximation with continuity correction to approximate the distribution of the statistic. Our numerical results illustrate that the saddlepoint approximation to the statistic is more suitable than the normal approximation. We also derived the asymptotic power under the alternative hypothesis and investigated the unbiasedness and biasedness of the test conducted in this study. [ABSTRACT FROM AUTHOR]

In two-sample testing problems, Student's t-test and the Wilcoxon rank-sum test are often used to test the location parameter, and have been discussed by many authors over the years. The Wilcoxon rank-sum test is more powerful than the t-test for non-normal data. Previous studies consider combining these two tests within a maximum test and show that it controls the type I error and has good statistical power for various distributions. The power of the maximum test is similar to the more powerful of the two tests. However, the limiting distribution of the test has not been derived. This study derives the limiting distribution of the maximum test under the null hypothesis and uses simulations to investigate the convergence of the maximum test to the limiting distribution in various cases. [ABSTRACT FROM AUTHOR]