Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...

We study learning curves for Gaussian process regression which characterise performance in terms of the Bayes error averaged over datasets of a given size. Whilst learning curves are in general very difficult to calculate we show that for discrete input domains, where similarity between input points is characterised in terms of a graph, accurate predictions can be obtained. These should in fact...

Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum–Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its ...

In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.

In this work we analyze fundamental properties of Random Apollonian Networks [37,38], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.

Abstract: In this article a continuous distribution, the so-called transmuted additive Weibull distribution, that extends the additive Weibull distribution and some other distributions is proposed and studied. Wewill use the quadratic rank transmutation map proposed by Shaw and Buckley (2009) in order to generate the transmuted additiveWeibull distribution. Various structural properties of the ...

Small area estimation using linear area level models typically assumes normality of the area level random effects (model errors) and of the survey errors of the direct survey estimates. Outlying observations can be a concern, and can arise from outliers in either the model errors or the survey errors, two possibilities with very different implications. We consider both possibilities here and in...

At the end of last lecture we introduced a very practical problem: how to generate a random graph with power law degree distribution. It turns out to be a nontrivial problem, so we will briefly look at several possible models here. In a random graph with a power law degree distribution, the expected number of degree k vertices is c n kα , where α is a parameter of the distribution (typically α ...

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we prove optimality condi...

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilib...