We continue the research of Latała on improving estimates of the pth moments of sums of independent random variables with logarithmically concave tails. We generalize some of his results in the case of 2 ≤ p ≤ 4 and present a combinatorial approach for even moments.
By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes...
We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions...