In this paper, we study the well-known Haezendonck–Goovaerts risk measures on their natural domain, that is on Orlicz spaces and, in particular, on Orlicz hearts. We provide a dual representation as well as the optimal scenario in such a representation and investigate the properties of the...

We study the Haezendonck risk measure (introduced by [Haezendonck, J., Goovaerts, M., 1982. A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1, 41-53] and by [Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2003. A unified approach to generate risk...

Scaled and Studentized statistics are encountered frequently, and they often play a decisive role in statistical inference and testing. For instance, taking the sample mean vector X̄=∑j=1NXj/N and the sample covariance matrix S=∑j=1N(Xj−X̄)(Xj−X̄)′/(N−1) for an iid sample...

We suggest several goodness-of-fit (GOF) methods which are appropriate with Type-II right censored data. Our strategy is to transform the original observations from a censored sample into an approximately i.i.d. sample of normal variates and then perform a standard GOF test for normality on the...

This paper gives a unified treatment of the limit laws of different measures of multivariate skewness and kurtosis which are related to components of Neyman's smooth test of fit for multivariate normality. The results are also applied to other multivariate statistics which are built up in a...