arXiv subjects

Chuancun Yin

Publications and source records attributed to Chuancun Yin.

At least 19 recordsLinked to original sources

arXiv2026

A Modified Dependence Measure Related to Chatterjee's Rank Correlation: Theoretical Properties and Asymptotic Analysis

In his recent breakthrough work [JASA, 2021], Chatterjee proposed a rank-based correlation coefficient $\xi(X,Y)$ to measure the dependence of a random variable $Y$ on $X$. Unlike classical measures such as Pearson, Spearman, or Kendall, $\xi$ satisfies $\xi=0$ if and only if $X$ and $Y$ are independent, and $\xi=1$ if and only if $Y$ is a measurable function of $X$, without requiring monotonicity or linearity. This paper proposes a refined measure of $\xi(X,Y)$ and investigates its theoretical properties. We derive several equivalent representations, construct an estimator, and establish its strong consistency as well as its asymptotic distribution. A natural extension of the proposed framework is also presented. The Monte Carlo simulations show that the proposed estimator outperforms Chatterjee's rank correlation in terms of finite-sample performance, particularly in controlling Type I error under the null.

math.ST↗

arXiv2026

Stochastic comparisons of sample mean differences for multivariate random variables

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the monotonicity of the Gini index in the usual stochastic order proposed by Samanthi, Wei and Brazauskas (2016) and Kim and Kim (2019) are also suitable for multivariate elliptical risks. We also study the tail probability of Gini index for multivariate elliptical risks and revised a large deviation result for the Gini indexes of multivariate normal risks in Kim and Kim (2019).

q-fin.RM↗

arXiv2025

Analyzing distortion riskmetrics and weighted entropy for unimodal and symmetric distributions under partial information constraints

In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp upper bounds of distortion riskmetrics and weighted entropy for symmetric distribution under known mean and variance. These results are applied to (weighted) entropies, shortfalls and other risk measures. Specifically, entropies include cumulative Tsallis past entropy, cumulative residual Tsallis entropy of order α, extended Gini coefficient, fractional generalized cumulative residual entropy, and fractional generalized cumulative entropy. Shortfalls include extended Gini shortfall, Gini shortfall, shortfall of cumulative residual entropy, and shortfall of cumulative residual Tsallis entropy. Other risk measures include nth-order expected shortfall, dual power principle and proportional hazard principle.

q-fin.RM↗

arXiv2024

Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the corresponding distortion functions. As examples, extremal cases of VaR, TVaR and RVaR are derived.

q-fin.RM↗

arXiv2024

Worst-cases of distortion riskmetrics and weighted entropy with partial information

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 measures. Furthermore, we also consider worst-case of weighted entropy for general distributions when only partial information is available. Specifically, we provide some applications for entropies, weighted entropies and risk measures. The commonly used entropies include Gini functional, cumulative residual entropy, tail-Gini functional, cumulative Tsallis past entropy, extended Gini coefficient and so on. The risk measures contain some premium principles and shortfalls based on entropy. The shortfalls include the Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy and shortfall of cumulative residual Tsallis entropy with order $α$.

q-fin.RM↗

arXiv2024

Extremal cases of distortion risk measures with partial information

This paper investigates the impact of distributional uncertainty on key risk measures under the partial knowledge of underlying distributions characterized by their first two moments and shape information (specifically symmetry and/or unimodality). We first employ probability inequalities to establish the theoretical best- and worst-case bounds on Value-at-Risk, reflecting the most extreme tail risk achievable within the moment and shape constraints, and then we extend this worst-case/best-case analysis to a broad class of distortion risk measures by the modified Schwarz inequality, deriving their corresponding robust bounds under the same partial information setting concerning moments and distribution shapes of the underlying distributions. In addition, we give a clear characterization of the distributions that attain the best- and worst-case scenarios. The proposed approach provides a unified framework for extremal problems of distortion risk measures.

q-fin.RM↗

arXiv2023

An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions

This paper examines eight measures of skewness and Mardia measure of kurtosis for skew-elliptical distributions. Multivariate measures of skewness considered include Mardia, Malkovich-Afifi, Isogai, Song, Balakrishnan-Brito-Quiroz, M$\acute{o}$ri, Rohatgi and Sz$\acute{e}$kely, Kollo and Srivastava measures. We first study the canonical form of skew-elliptical distributions, and then derive exact expressions of all measures of skewness and kurtosis for the family of skew-elliptical distributions, except for Song's measure. Specifically, the formulas of these measures for skew normal, skew $t$, skew logistic, skew Laplace, skew Pearson type II and skew Pearson type VII distributions are obtained. Next, as in Malkovich and Afifi (1973), test statistics based on a random sample are constructed for illustrating the usefulness of the established results. In a Monte Carlo simulation study, different measures of skewness and kurtosis for $2$-dimensional skewed distributions are calculated and compared. Finally, real data is analyzed to demonstrate all the results.

math.ST↗

arXiv2023

The Bessel function expression of characteristic function

The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some asymmetric distributions such as skew-elliptical distributions and their location-scale mixtures. In particular, we get simple closed form of characteristic functions for important cases such as the multivariate Student-$t$, Cauchy, logistic, Laplace, symmetric stable. The expressions of characteristic functions involve Bessel type functions or generalized hypergeometric series.

math.ST↗

arXiv2023

Stochastic representations and probabilistic characteristics of multivariate skew-elliptical distributions

The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established and then their probabilistic properties, such as characteristic function, moments, quadratic forms as well as transformation properties, are investigated.

math.ST↗

arXiv2023

Finite-time ruin probabilities of bidimensional risk models with correlated Brownian motions

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and $\{B_2(t), t\ge 0\}$ are correlated, we establish new results for the finite-time ruin probabilities. \textcolor{blue} {Our research has enriched the development of the ruin theory with heavy tails in unidimensional risk models and the dependence theory of stochastic processes.

math.PR↗

arXiv2023

Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions

In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such range-based risk measures are appropriate for risk management of regulation and investment purposes. The multivariate range correlation matrix (MRCorr) is introduced accordingly. To facilitate analytical analyses, we derive explicit expressions of the MRVaR and the MRCov in the context of the multivariate (log-)elliptical distribution family. Frequently-used cases in industry, such as normal, student-$t$, logistic, Laplace, and Pearson type VII distributions, are presented with numerical examples. As an application, we propose a range-based mean-variance framework of optimal portfolio selection. We calculate the range-based efficient frontiers of the optimal portfolios based on real data of stocks' returns. Both the numerical examples and the efficient frontiers demonstrate consistences with the desirable properties of the range-based risk measures.

math.ST↗

arXiv2023

Joint mixability of elliptical distributions and related families

In this paper, three different proofs to a result of Wang, Peng and Yang (2013) which related to the joint mixability of elliptical distributions with the same characteristic generator are present. Moreover, we generalize this result to any distributions with finite second moments. An open problem proposed by Wang (2015) is solved by constructing a bimodal-symmetric distribution. The joint mixability of slash-elliptical distributions and skew-elliptical distributions is studied and the extension to multivariate distributions is also investigated.

math.ST↗

arXiv2023

The mixability of elliptical distributions and log-elliptical distributions

The concept of $ϕ$-complete mixability and $ϕ$-joint mixability was first introduced in Bignozzi and Puccetti (2015), which is an extension of complete and joint mixability. Following Bignozzi and Puccetti (2015), we consider two more general cases of $ϕ$ and investigate the $ϕ$-joint mixability for elliptical distributions and logarithmic elliptical distributions. Some sufficient conditions for the $ϕ$-joint mixability of some distributions are investigated. In addition, a conjecture on the uniqueness of the center of $ϕ$-joint mixability and the forms of the densities for some elliptical distributions are given.

math.ST↗

arXiv2023

Hessian and increasing-Hessian orderings of multivariate skew-elliptical random vectors

In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special cases. Necessary and/or sufficient conditions of the orderings are provided simply based on a comparison of the underlying model parameters.

math.ST↗

arXiv2023

Generalized Location-Scale Mixtures of Elliptical Distributions: Definitions and Stochastic Comparisons

This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector $\boldsymbol{Z}$, independent of $\boldsymbol{X}$ and $\boldsymbol{Y}$, the scale parameter of this class of distributions is mixed with a function $α(\boldsymbol{Z})$ and its skew parameter is mixed with another function $β(\boldsymbol{Z})$. Sufficient (and necessary) conditions are established for stochastically comparing different random vectors stemming from this class of distributions by means of several stochastic orders including the usual stochastic order, convex order, increasing convex order, supermodular order, and some related linear orders. Two insightful assumptions for the density generators of elliptical distributions, aiming to control the generators' tail, are provided to make stochastic comparisons among mixed-elliptical vectors. Some applications in applied probability and actuarial science are also provided as illustrations on the main findings.

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arXiv2022

A Novel Exploration of Diffusion Process based on Multi-types Galton-Watson Forests

Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or any other resource constraints. In this paper, we use the degenerated multi-types Galton-Watson forest (MGWF) to interpret the diffusion process and establish an equivalent relationship between them. With the two-phase setting of the MGWF, one can interpret the diffusion process and the Google PageRank system explicitly. It also improves the convergence behaviour of the iterative diffusion process and Google PageRank system. We validate the proposal by experiment while providing new research directions.

cs.SI↗

arXiv2022

Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures

In this paper, we focus on multivariate doubly truncated first two moments of generalized skew-elliptical (GSE) distributions and derive explicit expressions for them. It includes many useful distributions, for examples, generalized skew-normal (GSN), generalized skew-Laplace (GSLa), generalized skew-logistic (GSLo) and generalized skew student-$t$ (GSSt) distributions, all as special cases. We also give formulas of multivariate doubly truncated expectation and covariance for GSE distributions. As applications, we show the results of multivariate tail conditional expectation (MTCE) and multivariate tail covariance (MTCov) for GSE distributions.

math.ST↗

arXiv2022

Doubly truncated moment risk measures for elliptical distributions

In this paper, we define doubly truncated moment (DTM), doubly truncated skewness (DTS) and kurtosis (DTK). We derive DTM formulae for elliptical family, with emphasis on normal, student-$t$, logistic, Laplace and Pearson type VII distributions. We also present explicit formulas of the DTE (doubly truncated expectation), DTV (doubly truncated variance), DTS and DTK for those distributions. As illustrative example, DTEs, DTVs, DTSs and DTKs of three industry segments' (Banks, Insurance, Financial and Credit Service) stock return in London stock exchange are discussed.

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