Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m−variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matr...

A k-hypertournament is a complete k-hypergraph with each k-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a k-hypertournament, the score si (losing score ri) of a vertex vi is the number of arcs containing vi in which vi is not the last element (in which vi is the last element). The total score of vi is defined as ti = si − ri. In this ...

Introduction: Although income is among the major social determinants of mental health of middle-aged and older individuals, socially marginalized groups gain less health from their income and other socioeconomic status (SES) resources compared to socially privileged groups. This pattern is called marginalization-related diminished returns (MDRs). Most of the existing knowledge ...

SEMI-MARKOV DECISION INCLUDING AN UNKNOWN Masami Kurano Chiba University PROCESSES PARAMETER (Received February 27, 1984: Revised May 8,1985) We consider the problem of minimizing the long-run average (expected) cost per unit time in a semiMarkov decision process including an unknown parameter. In the case of general state and action spaces and compact parameter space we construct the adaptive ...

— The Economics of Happiness is one of the research areas of greatest growth in recent years. Throughout this work, a venture based model in which satisfaction of Spanish entrepreneurs with their professional life is performed. We analyze the responses of 9,989 entrepreneurs using data from the Global Entrepreneurship Monitor (GEM), and six hypothesis are discussed. The results show that, for t...