In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate...

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0 ? 1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of nonparametric statistical estimation of...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their...

We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their...

For a given risk, the well-known classical definition of Value-at-Risk (VaR) does not take into account possible interactions with other observable risks. For this reason, conditional VaRs that capture contagion effects and tail dependence among risks, such as the Co-Value-at-Risk (CoVaR), have...

For a given risk, the well-known classical definition of Value-at-Risk (VaR) does not take into account possible interactions with other observable risks. For this reason, conditional VaRs that capture contagion effects and tail dependence among risks, such as the Co-Value-at-Risk (CoVaR), have...

In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is defined as a threshold loss value, such that the probability...

The comparison of the means of two independent samples is one of the most popular problems in real-world data analysis. In the multivariate context, two-sample Hotelling's T² frequently used to test the equality of means of two independent Gaussian random samples assuming either the same or a...

In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability alfa, the 100alfa% VaR is defined as a threshold loss value, such that the probability that the...