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An increase in location is often accompanied by an increase in variability. Moreover, in randomized studies, the presence of heteroscedasticity can indicate a treatment effect. In these cases a location-scale test is appropriate. A common approach of a location-scale test is to use the sum of a location and a scale test statistic. In this study, we focus on one-sided location-scale tests. We introduce a one-sided Lepage-type test statistic. Since right-skewed data are common in many real-world applications, we design test statistics that are powerful also for right-skewed data. Moreover, this paper introduces both a maximum test and an adaptive test utilizing the one-sided Lepage-type test statistics. The limiting distributions of the maximum test statistics are also derived. We assess the performance of the different test statistics in various scenarios for continuous distributions through Monte Carlo simulations. Our simulation results demonstrate that the proposed new test statistics can significantly increase and stabilize statistical power, making it strong competitors to existing location-scale tests. We present practical illustrations based on example data and conclude with some final remarks. [ABSTRACT FROM AUTHOR]

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 examines interpoint distance-based tests for random elements from probability distributions in infinite-dimensional space. Some asymptotic properties such as the limiting distributions and the asymptotic power of the Biswas–Ghosh type test (Biswas and Ghosh in J Multivar Anal 123: 160–171, 2014) are presented using the theory of U-statistic. In addition, the p-value approximation based on the jackknife variance estimators and the Welch–Satterthwaite equation is proposed. Simulation studies are conducted to evaluate the performance of the proposed test statistics in functional data analysis. The proposed tests are shown to have better power than the existing method for functional data in some situations. [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]

In several fields of applications, the underlying theoretical distribution is unknown and cannot be assumed to have a specific parametric distribution such as a normal distribution. Nonparametric statistical methods are preferable in these cases. Nonparametric testing hypotheses have been one of the primarily used statistical procedures for nearly a century, and the power of the test is an important property in nonparametric testing procedures. This review discusses the unbiasedness of nonparametric tests. In nonparametric hypothesis, the best‐known Wilcoxon–Mann–Whitney (WMW) test has both robustness and power performance. Therefore, the WMW test is widely used to determine the location parameter. In this review, the unbiasedness and biasedness of the WMW test for the location parameter family of the distribution is mainly investigated. An overview of historical developments, detailed discussions, and works on the unbiasedness/biasedness of several nonparametric tests are presented with references to numerous studies. Finally, we conclude this review with a discussion on the unbiasedness/biasedness of nonparametric test procedures. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Nonparametric Methods [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]

Phase-I analysis of historical data from a statistical process is a strategic problem in Statistical Process Monitoring and control. Before the establishment of process stability, it is challenging to model historical data. Consequently, a distribution-free approach is a natural choice in Phase-I monitoring. Existing distribution-free Phase-I control charts are suitable for detecting instability in location and scale parameters only and are often insensitive in complex processes involving skewness or shape parameters. A new Phase-I control chart is proposed to identify more general shifts, including location, scale and skewness. The proposed Phase-I scheme is efficient in such a situation. The proposed Phase-I scheme uses subsamples, and the plotting statistic is based on the omnibus multi-sample linear rank statistic corresponding to the location, scale and skewness shifts. The new scheme can identify subsamples that are not in control, and it can also indicate one or more process parameters where a deviation has occurred. The encouraging performance of the proposed scheme is established with a large-scale numerical study based on Monte-Carlo in detecting shifts of various nature in a comprehensive class of situations. An illustration based on monitoring the waiting time data from a customer service centre is given. Some concluding remarks and some future research problems are also offered. [ABSTRACT FROM AUTHOR]