Related papers: Stochastic comparisons of sample mean differences …
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
In several recent works on infinite-dimensional systems of ODEs \cite{cao_derivation_2021,cao_explicit_2021,cao_iterative_2024,cao_sticky_2024}, which arise from the mean-field limit of agent-based models in economics and social sciences…
The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
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 note, we introduce a general version of the well-known elliptical potential lemma that is a widely used technique in the analysis of algorithms in sequential learning and decision-making problems. We consider a stochastic linear…
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…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
This paper derives the elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation is proposed, instead of the independent element by element…
Via an axiomatic approach, we characterize the family of n-th order Gini deviation, defined as the expected range over n independent draws from a distribution, to quantify joint dispersion across multiple observations. This family extends…
We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
Wide class of elliptically contoured distributions is a popular model of stock returns distribution. However the important question of adequacy of the model is open. There are some results which reject and approve such model. Such results…
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have…
The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional Gini index, which measures the inequality of a distribution…
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…
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…
The key indicators of model stability are the population stability index (PSI), which uses the difference in population distribution, and the Kolmogorov-Smirnov statistic (KS) between two distributions. When deriving a binary choice model,…
Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size…
We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…