This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probabi...

the microstructure of dual phase steels can be considered as a matrix of ferrite phase reinforced by martensite particles. recent measurements show that the mechanical properties of the ferrite phase are changed with the distance from the martensite grains. in this paper, a new method has been proposed to consider this phenomenon in finite element modeling of dual phase steels microstructure. i...

We calculate the complex refractive index of inhomogeneous thin films using the transfer matrix method and reflection/transmission measurements. To this end we have developed a model for both the 3D distribution of inhomogeneities inside thin films and for light propagation through the inhomogeneities. The model involves splitting the light into contributions from the homogeneous section of the...

In this paper we propose a novel inhomogeneous Gibbs model by the minimax entropy principle, and apply it to face modeling. The maximum entropy principle generalizes the statistical properties of the observed samples and results in the Gibbs distribution, while the minimum entropy principle makes the learnt distribution close to the observed one. To capture the fine details of a face, an inhomo...

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ Rd and a gauge body B ⊂ Rd such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z), uB(L,Z), pB(L,Z), lB(L,Z)) given that Z ∩L = ∅, where Z is a Boolean model, dB(L...