Probability inequalities for certain dependence structures

In this paper we introduce a sequence of inequalities for a joint probability of equicoordinate, one-sided rectangles of higher dimension based on joint probabilities of lower dimension, and show that the resulting lower and upper bounds hold for certain cases of equicorrelated multivariate normal and improve as the dimension increases. The sequence of lower bounds is shown to be superior to existing bounds, and the sequence of upper bounds represents new inequalities for a joint probability. We further provide numerical evidence that the sequence of bounds holds for stationary random sequences with either MTP2 or S-MRR2 property.