In this paper, a characterization of the joint distribution function for the maximum and minimum of a vector is presented in terms of the joint distribution function for the vector. If the joint distribution function is given explicitly, for instance by a copula and marginals, this leads to an...

In terms of regulatory and economic capital, credit risk is the most significant risk faced by banks. We implement a credit risk model - based on publicly available information - with the aim of developing a tool to monitor credit risk in a sample of large and complex banking groups (LCBGs) in...

We give an example of an asymmetric distribution with zero skewness.Zero skewness is often taken to mean that the distribution is asymmetric. However, this is not correct. There exist asymmetric distributions that have zero third central moment. Here we give an example. First, we give the...

Sample covariance is known to be a poor estimate when the data are scarce compared with the dimension. To reduce the estimation error, various structures are usually imposed on the covariance such as low-rank plus diagonal (factor models), banded models and sparse inverse covariances. We...

In this note we derive closed formulas for the quantiles of a class of cumulative distribution functions (CDF) that can be expressed as mixtures. Generally quantiles of mixtures are only computable numerically. In this case, we assume that the support of the component densities are disjoint,...

In this paper we consider the interval availability distribution of a two state single unit. WE fit the interval availability distribution directly to a Beta distribution, such that the probability of nil and a hundred percent availability is correct as well as the espectation and the variance

In terms of regulatory and economic capital, credit risk is the most significant risk faced by banks. We implement a credit risk model - based on publicly available information . with the aim of developing a tool to monitor credit risk in a sample of large and complex banking groups (LCBGs) in...