Comparison of monotonic trend tests for some counting processes

One of the important problems in the analysis of series of events is to identify the stochastic model to be used for the systems since improving or optimizing the procedures applied for the systems and/or estimating the model parameters correctly usually depend on the stochastic model assumption. The accurate implementation of the procedures of determining the model is only possible by detecting the existence of the trend in the pattern of the data set. In real-world applications, it is observed that the data set which is known to have a trend usually contains a monotonic trend (decreasing or increasing). For this reason, in this study, the trend tests which investigate the presence of the monotone trend are compared by considering the commonly used counting processes and lifetime distributions in the literature. An extensive simulation study is performed to calculate the type 1 errors and powers of the tests.