In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.

It is common for conclusions of empirical studies to depend on multiple significant outcomes. This practice may seem reasonable, but it has some unintended effects. In particular, the compound Type I error rate (the likelihood concluding that an effect exists when does not) can be much lower than individual studies. in itself not a problem since low desirable. However, there also accompanying d...

The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset.