Crack growth in an anisotropically rolled thin plate, which contains many initial defects, is investigated by Monte Carlo simulation on a square lattice. Each initial defect is assumed to have two crack tips like the Griffith crack and the effect of anisotropy of a medium on crack growth...

Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (201x) have introduced the class of...

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each...

Denecke and Müller (CSDA 55:2724–2738, <CitationRef CitationID="CR2">2011</CitationRef>) presented an estimator for the correlation coefficient based on likelihood depth for Gaussian copula and Denecke and Müller (J Stat Planning Inference 142: 2501–2517, <CitationRef CitationID="CR3">2012</CitationRef>) proved a theorem about the consistency of general estimators based on...</citationref></citationref>

In this paper, a novel projection-based depth based on the Rayleigh quotient, Rayleigh projection depth (RPD), is proposed. Although, the traditional projection depth (PD) has many good properties, it is indeed not practical due to its difficult computation, especially for the high-dimensional...