The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

The paper introduces a new journal impact measure called The Reference Return Ratio (3R). Unlike the traditional Journal Impact Factor (JIF), which is based on calculations of publications and citations, the new measure is based on calculations of bibliographic investments (references) and returns (citations). A comparative study of the two measures shows a strong relationship between the 3R an...

Natural selection acts strongly on the proportional numbers of male and female offspring among the progeny of adults. The equilibrium is often one at which males and females are produced in roughly equal numbers, but under certain ecological and genetic circumstances there may be dramatic population-wide biases, and even in populations with balanced sex ratios, parents are often selected to pro...

Let P be a class of graphs. A P-set in a graph G is a vertex subset X such that G(X) ∈ P . We define the P-stability number of a graph G, αP(G), as the maximum cardinality of a P-set in G. AP-dominating set in a graph is a dominatingP-set. Accordingly, the P-domination number of a graph G, γP(G), is the minimum cardinality of a P-dominating set in G. For each r ≥ 1, we define a graph G to be an...

HSMR is calculated as a ratio of the actual number of deaths to the expected number of deaths among patients in acute care hospitals. An HSMR of 100 indicates there is no difference between the hospital’s mortality rate and the overall average rate. Therefore a rate greater than 100 means the hospital’s mortality rate is higher than the overall average and a rate lower than 100 means the hospit...

What are they? In human health it is generally the case that the more people studied, and the longer the surveillance of them, the greater the number of new occurrences of any specified condition there are likely to be. This is because of the increase in total time ‘at risk’ of having an event, that is, the increased persons-and-time of observation. A rate is an arithmetic way of quantifying th...

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

Local ratio is a well-known paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a local-ratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this process, a solution S is constructed such that S is α-approximate with respect to each model used in...

A family of arc-transitive graphs is studied. The vertices of these graphs are ordered pairs of distinct points from a finite projective line, and adjacency is defined in terms of the cross ratio. A uniform description of the graphs is given, their automorphism groups are determined, the problem of isomorphism between graphs in the family is solved, some combinatorial properties are explored, a...