Related papers: Cumulative Information Generating Function and Gen…
In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$.…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modelling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing…
The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely…
We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can…
The categorical Gini correlation proposed by Dang et al. is a dependence measure to characterize independence between categorical and numerical variables. The asymptotic distributions of the sample correlation under dependence and…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
In this paper, we develop a relative cumulative residual information measure (RCRI) that aims to quantify the divergence between two survival functions. The dynamic relative cumulative residual information (DRCRI) measure is also…
In this study, the cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. To quantify this observation, a corresponding…
The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets.…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
In this work, we study the properties of cumulative residual entropy generating function. We then introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely.…
The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as…
The categorical Gini correlation is an alternative measure of dependence between a categorical and numerical variables, which characterizes the independence of the variables. A nonparametric test for the equality of K distributions has been…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function…