The Poisson distribution, in general remains sensitive to small departure of frequencies especially at the right tail of the distribution. In many situations it may happen that the Generalized Poisson Distribution (GPD) or a compound distribution provides a closer fit to a frequency distribution...

Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes...

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,...

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 practice, multivariate dependencies of extreme risks are often only assessed in a pairwise way. We propose a novel test to detect when bivariate simplifications produce misleading results. This occurs when a significant portion of the multivariate dependence structure in the tails is of...

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...

This paper provides a new approach to recover relative entropy measures of contemporaneous dependence from limited information by constructing the most entropic copula (MEC) and its canonical form, namely the most entropic canonical copula (MECC). The MECC can effectively be obtained by...

The contribution of this paper is to derive a bivariate distribution for inflation and output uncertainty with a well-defined role for subjective judgements. The marginal distributions for inflation and output growth are derived from uncertainty in the macro variables that are deemed to be...