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Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
Determining an upper bound, particularly the optimal upper bound of the Gini coefficient when dealing with grouped data without specified income brackets, remains an important and open question. In this paper, we introduce an efficient…
In the field of genetics, the concept of heritability refers to the proportion of variations of a biological trait or disease that can be explained by genetic factors. Quantifying the heritability of a disease is a fundamental challenge in…
This paper pays tribute to Professor Giovanni Andrea Cornia's lifelong contributions to the measurement of global inequality. We review twelve world and regional databases of the Gini coefficient, illustrate their coverage, overlapping, and…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
This paper proposes a new Bayesian approach to estimate the Gini coefficient from the Lorenz curve based on grouped data. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on…
We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
Weighting estimators based on propensity scores are widely used for causal estimation in a variety of contexts, such as observational studies, marginal structural models and interference. They enjoy appealing theoretical properties such as…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome…
The aim of this note is to prove the inversion formula, which can be used to compute the Levi measure of an infinitely divisible distribution from its characteristic function. Obtained formula is similar to the well-known inversion formula…
We consider the problem of inferring the values of an arbitrary set of variables (e.g., risk of diseases) given other observed variables (e.g., symptoms and diagnosed diseases) and high-dimensional signals (e.g., MRI images or EEG). This is…
For frequentist settings in which parameter randomness represents variability rather than uncertainty, the ideal measure of the support for one hypothesis over another is the difference in the posterior and prior log odds. For situations in…
The problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…