Differences of means

Certain Bounds for the Differences of Means

Let Pn,r(x) be the generalized weighted power means. We consider bounds for the differences of means in the following form: max { Cu,v,β x 1 , Cu,v,β x n } σn,w′,β ≥ P n,u − P n,v α ≥ min { Cu,v,β x 1 , Cu,v,β x n } σn,w,β . Here β 6= 0, σn,t,β( x) = ∑n i=1 ωi[x β i −P β n,t(x)] andCu,v,β = u−v 2β2 . Some similar inequalities are also considered. The results are applied to inequalities of Ky Fa...

Inequalities among Differences of Gini Means and Divergence Measures

In 1938, Gini [3] studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities arising due to particular values of each parameter of Gini’s mean. This sequence generates many nonnegative differences. Not all of them are convex. We have ...

Estimating Measurement Precision by Means of Measurement Differences

When it is necessary to determine the precision of a certain instrument B, devoted to point position measurement for instance, but not necessarily, one way is to measure a certain number of points with B as well as with another instrument A, whose precision is known. Forming the differences between the B and A measurements, it is possible to calculate B precision by means of the dispersion of t...

Statistical Phylogenetic Tree Analysis Using Differences of Means

We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by two input alignments, instead of comparing point estimations of trees. This statistical approach can be applied to gene tree analysis for example, detecting unusual events in genome evolution such as ...

Research Article On Logarithmic Convexity for Differences of Power Means