Identities and bounds for the reliability of coherent systems are analysed and computed using the techniques of commutative algebra. The techniques are applied to the analysis of some of the most relevant k-out-of-n class systems. The efficiency of the algebraic approach in obtaining exact...

In this paper we consider the problem of optimal allocation of a redundant component for series, parallel and k-out-of-n systems of more than two components, when all the components are dependent. We show that for this problem is naturally to consider multivariate extensions of the joint...

A Bayesian hierarchical model for simultaneously estimating and partitioning probability density functions is presented. Individual density functions are flexibly modeled using Bernstein densities, which are mixtures of beta densities whose parameters depend only on the number of mixture...

The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of...

The objective of this article is to develop a computationally efficient estimator of the regression function subject to various shape constraints. In particular, nonparametric estimators of monotone and/or convex (concave) regression functions are obtained by using a nested sequence of Bernstein...