Related papers: Gini means and its applications in polymer chemist…
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
In this paper we will show that the Gini coefficient and the introduced measure of angular inequality are special cases of a wider indexed family of measurements. We will discuss the properties of the defined class based, inter alia, on a…
In 1938, Gini 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…
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. It contains as particular cases the famous means such as harmonic, geometric, arithmetic, etc. Also it contains, the power mean of…
In this paper, we draw attention to a promising yet slightly underestimated measure of variability - the Gini coefficient. We describe two new ways of defining and interpreting this parameter. Using our new representations, we compute the…
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
We obtain simple proofs of certain inequalites for bivariate means.
The distribution of errors is a central object in the assesment and benchmarking of computational chemistry methods. The popular and often blind use of the mean unsigned error as a benchmarking statistic leads to ignore distributions…
Measuring the degree of inequality expressed by a multivariate statistical distribution is a challenging problem, which appears in many fields of science and engineering. In this paper, we propose to extend the well known univariate Gini…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
In the present paper we are going to prove some necessary condition for a mean to be Hardy. This condition is then applied to completely characterize the Hardy property among the Gini means.
The melanins are a ubiquitous class of pigments found throughout nature from lower organisms to humans. It is one of the few biopolymers with fascinating functions in biology, medicine, chemistry, physics and engineering due to its relation…
Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement…
The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the…
The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a…
We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.