A parametric test for trend based on moving order statistics

In this paper, we propose a test statistic based on moving order statistics and establish an exact procedure to test for the presence of monotone trends. We show that the test statistic, under the null hypothesis of no trend, follows the closed skew normal distribution. An efficient algorithm is then developed to generate realizations from this null distribution. A simulation study is carried out for evaluating the proposed test under the alternative hypotheses with linear, logarithmic and quadratic trend functions. Finally, a real-life example is provided to illustrate the proposed test procedure.