Related papers: Cumulative Information Generating Function and Gen…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
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…
In this paper, we introduce the cumulative past information generating function (CPIG) and relative cumulative past information generating function (RCPIG). We study its properties. We establish its relation with generalized cumulative past…
We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…
Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed…
We consider a generalization of information density to a partitioning into $N \geq 2$ subvectors. We calculate its cumulant-generating function and its cumulants, showing that these quantities are only a function of all the regression…
The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have…
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…
This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…
In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative extropy are…
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…
In this work, we propose two information generating functions: general weighted information and relative information generating functions, and study their properties. { It is shown that the general weighted information generating function…
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 discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
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…
Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…
Different strategies of reliability theory for the analysis of coherent systems have been studied by various researchers. Here, the Gini-type index is utilized as an applicable tool for the study and comparison of the ageing properties of…