We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based ...We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based on the well-known Kiefer–Wolfowitz algorithm so that it is applicable to more general and practical settings where customer’s behavior is unknown to service providers in prior.We first establish a convergence result for KWiQ-H when the service times have a finite fifth moment.Then,we show that under a stronger condition with a finite seventh moment,KWiQ-H could achieve sample complexity with the same asymptotic order as in the case when service times are light-tailed in Chen et al.(Oper Res,2023).Complementing the theoretic results,we carry out comprehensive numerical experiments to test the efficiency and robustness of KWiQ-H in a variety of model settings.展开更多
This study introduces the type-I heavy-tailed Burr XII(TIHTBXII)distribution,a highly flexible and robust statistical model designed to address the limitations of conventional distributions in analyzing data character...This study introduces the type-I heavy-tailed Burr XII(TIHTBXII)distribution,a highly flexible and robust statistical model designed to address the limitations of conventional distributions in analyzing data characterized by skewness,heavy tails,and diverse hazard behaviors.We meticulously develop the TIHTBXII’s mathematical foundations,including its probability density function(PDF),cumulative distribution function(CDF),and essential statistical properties,crucial for theoretical understanding and practical application.A comprehensive Monte Carlo simulation evaluates four parameter estimation methods:maximum likelihood(MLE),maximum product spacing(MPS),least squares(LS),and weighted least squares(WLS).The simulation results consistently show that as sample sizes increase,the Bias and RMSE of all estimators decrease,with WLS and LS often demonstrating superior and more stable performance.Beyond theoretical development,we present a practical application of the TIHTBXII distribution in constructing a group acceptance sampling plan(GASP)for truncated life tests.This application highlights how the TIHTBXII model can optimize quality control decisions by minimizing the average sample number(ASN)while effectively managing consumer and producer risks.Empirical validation using real-world datasets,including“Active Repair Duration,”“Groundwater Contaminant Measurements,”and“Dominica COVID-19 Mortality,”further demonstrates the TIHTBXII’s superior fit compared to existing models.Our findings confirm the TIHTBXII distribution as a powerful and reliable alternative for accurately modeling complex data in fields such as reliability engineering and quality assessment,leading to more informed and robust decision-making.展开更多
This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly...This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly correlated with returns.To this end,we propose a robust test which can capture empirical phenomena such as heavy tails,stationary,and local to unity.Moreover,we develop related asymptotic results without the second-moment assumption between the predictive variable and returns.To make the proposed test reasonable,we propose a generalized correlation and provide theoretical support.To illustrate the applicability of the test,we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon.Finally,we provide an empirical study for further illustration,to which the proposed test is applied to a U.S.equity data set.展开更多
Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussia...Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussian distribution.In some cases,this assumption no longer holds and the performance of the traditional SLAM algorithms declines.In this paper,we present a robust SLAM algorithm based on variational Bayes method by modelling the observation noise as inverse-Wishart distribution with "harmonic mean".Besides,cubature integration is utilized to solve the problem of nonlinear system.The proposed algorithm can effectively solve the problem of filtering divergence for traditional filtering algorithm when suffering the time-variant observation noise,especially for heavy-tai led noise.To validate the algorithm,we compare it with other t raditional filtering algorithms.The results show the effectiveness of the algorithm.展开更多
This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and F...This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.展开更多
In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating acco...In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.展开更多
The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues.In this article,we introduce a new class of heavy-tailed distributions useful for modeling data in ...The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues.In this article,we introduce a new class of heavy-tailed distributions useful for modeling data in financial sciences.A specific sub-model form of our suggested family,named as a new extended heavy-tailed Weibull distribution is examined in detail.Some basic characterizations,including quantile function and raw moments have been derived.The estimates of the unknown parameters of the new model are obtained via the maximum likelihood estimation method.To judge the performance of the maximum likelihood estimators,a simulation analysis is performed in detail.Furthermore,some important actuarial measures such as value at risk and tail value at risk are also computed.A simulation study based on these actuarial measures is conducted to exhibit empirically that the proposed model is heavy-tailed.The usefulness of the proposed family is illustrated by means of an application to a heavy-tailed insurance loss data set.The practical application shows that the proposed model is more flexible and efficient than the other six competing models including(i)the two-parameter models Weibull,Lomax and Burr-XII distributions(ii)the three-parameter distributions Marshall-Olkin Weibull and exponentiated Weibull distributions,and(iii)a well-known four-parameter Kumaraswamy Weibull distribution.展开更多
This paper is a further investigation of large deviations for sums of random variables Sn=i=1∑n Xi and S（t）=i=1∑N（t）Xi,（t≥0）, where {X_n,n≥1） are independent identically distribution and non-negative random...This paper is a further investigation of large deviations for sums of random variables Sn=i=1∑n Xi and S（t）=i=1∑N（t）Xi,（t≥0）, where {X_n,n≥1） are independent identically distribution and non-negative random variables, and {N（t）,t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.展开更多
This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random...This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.展开更多
A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Ran...A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.展开更多
In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator ...In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.展开更多
The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-...The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.展开更多
Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline ...Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.展开更多
Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ：...Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ： k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P（X〉x）/P（τ〉x）→0 as x →∞.展开更多
Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {X...Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {Xk, k 〉 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = fi Xk and S（n） =∑ k=1 n 〉 1, and their randomized versions ST and S（τ） are studied. Some risk theory are presented. max Sk for 1〈k〈n applications to the展开更多
We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail...We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.展开更多
Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail o...Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.展开更多
The error patterns of a wireless channel can be represented by a binary sequence of ones(burst) and zeros(run),which is referred to as a trace.Recent surveys have shown that the run length distribution of a wireless c...The error patterns of a wireless channel can be represented by a binary sequence of ones(burst) and zeros(run),which is referred to as a trace.Recent surveys have shown that the run length distribution of a wireless channel is an intrinsically heavy-tailed distribution.Analytical models to characterize such features have to deal with the trade-off between complexity and accuracy.In this paper,we use an independent but not identically distributed(inid) stochastic process to characterize such channel behavior and show how to parameterize the inid bit error model on the basis of a trace.The proposed model has merely two parameters both having intuitive meanings and can be easily figured out from a trace.Compared with chaotic maps,the inid bit error model is simple for practical use but can still be deprived from heavy-tailed distribution in theory.Simulation results demonstrate that the inid model can match the trace,but with fewer parameters.We then propose an improvement on the inid model to capture the 'bursty' nature of channel errors,described by burst length distribution.Our theoretical analysis is supported by an experimental evaluation.展开更多
This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptoti...This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.展开更多
Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subcla...Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subclass DKc and subclass DK 1 are obtained.展开更多
基金funded by Science,Technology and Innovation Commission of Shenzhen Munici pality(No.RCYX20210609103124047)the National Natural Science Foundation of China(Nos.72171205 and 72394361)Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence(No.2023B1212010001).
文摘We develop a gradient-based simulation optimization algorithm,dabbed KWiQ-H,for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions.Our algorithm is designed based on the well-known Kiefer–Wolfowitz algorithm so that it is applicable to more general and practical settings where customer’s behavior is unknown to service providers in prior.We first establish a convergence result for KWiQ-H when the service times have a finite fifth moment.Then,we show that under a stronger condition with a finite seventh moment,KWiQ-H could achieve sample complexity with the same asymptotic order as in the case when service times are light-tailed in Chen et al.(Oper Res,2023).Complementing the theoretic results,we carry out comprehensive numerical experiments to test the efficiency and robustness of KWiQ-H in a variety of model settings.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(Grant Number IMSIU-DDRSP2501).
文摘This study introduces the type-I heavy-tailed Burr XII(TIHTBXII)distribution,a highly flexible and robust statistical model designed to address the limitations of conventional distributions in analyzing data characterized by skewness,heavy tails,and diverse hazard behaviors.We meticulously develop the TIHTBXII’s mathematical foundations,including its probability density function(PDF),cumulative distribution function(CDF),and essential statistical properties,crucial for theoretical understanding and practical application.A comprehensive Monte Carlo simulation evaluates four parameter estimation methods:maximum likelihood(MLE),maximum product spacing(MPS),least squares(LS),and weighted least squares(WLS).The simulation results consistently show that as sample sizes increase,the Bias and RMSE of all estimators decrease,with WLS and LS often demonstrating superior and more stable performance.Beyond theoretical development,we present a practical application of the TIHTBXII distribution in constructing a group acceptance sampling plan(GASP)for truncated life tests.This application highlights how the TIHTBXII model can optimize quality control decisions by minimizing the average sample number(ASN)while effectively managing consumer and producer risks.Empirical validation using real-world datasets,including“Active Repair Duration,”“Groundwater Contaminant Measurements,”and“Dominica COVID-19 Mortality,”further demonstrates the TIHTBXII’s superior fit compared to existing models.Our findings confirm the TIHTBXII distribution as a powerful and reliable alternative for accurately modeling complex data in fields such as reliability engineering and quality assessment,leading to more informed and robust decision-making.
基金The research of WONG Hsin-Chieh is partially supported by the NSTC(111-2118-M-305-004-MY2)the research of PANG Tian-xiao is partially supported by the National Social Science Foundation of China(21BTJ067)。
文摘This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly correlated with returns.To this end,we propose a robust test which can capture empirical phenomena such as heavy tails,stationary,and local to unity.Moreover,we develop related asymptotic results without the second-moment assumption between the predictive variable and returns.To make the proposed test reasonable,we propose a generalized correlation and provide theoretical support.To illustrate the applicability of the test,we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon.Finally,we provide an empirical study for further illustration,to which the proposed test is applied to a U.S.equity data set.
基金the National Natural Science Foundation of China(No.61803260)。
文摘Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussian distribution.In some cases,this assumption no longer holds and the performance of the traditional SLAM algorithms declines.In this paper,we present a robust SLAM algorithm based on variational Bayes method by modelling the observation noise as inverse-Wishart distribution with "harmonic mean".Besides,cubature integration is utilized to solve the problem of nonlinear system.The proposed algorithm can effectively solve the problem of filtering divergence for traditional filtering algorithm when suffering the time-variant observation noise,especially for heavy-tai led noise.To validate the algorithm,we compare it with other t raditional filtering algorithms.The results show the effectiveness of the algorithm.
基金Supported by the Natural Science Foundation of the Education Department of Anhui Province(0505101)
文摘This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.
基金supported by the National Natural Science Foundation of China(11101451)Ph.D.Programs Foundation of Ministry of Education of China(20110191110033)
文摘In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.
文摘The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues.In this article,we introduce a new class of heavy-tailed distributions useful for modeling data in financial sciences.A specific sub-model form of our suggested family,named as a new extended heavy-tailed Weibull distribution is examined in detail.Some basic characterizations,including quantile function and raw moments have been derived.The estimates of the unknown parameters of the new model are obtained via the maximum likelihood estimation method.To judge the performance of the maximum likelihood estimators,a simulation analysis is performed in detail.Furthermore,some important actuarial measures such as value at risk and tail value at risk are also computed.A simulation study based on these actuarial measures is conducted to exhibit empirically that the proposed model is heavy-tailed.The usefulness of the proposed family is illustrated by means of an application to a heavy-tailed insurance loss data set.The practical application shows that the proposed model is more flexible and efficient than the other six competing models including(i)the two-parameter models Weibull,Lomax and Burr-XII distributions(ii)the three-parameter distributions Marshall-Olkin Weibull and exponentiated Weibull distributions,and(iii)a well-known four-parameter Kumaraswamy Weibull distribution.
文摘This paper is a further investigation of large deviations for sums of random variables Sn=i=1∑n Xi and S（t）=i=1∑N（t）Xi,（t≥0）, where {X_n,n≥1） are independent identically distribution and non-negative random variables, and {N（t）,t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.
基金Supported by the National Social Science Fund of China (Grant No.22BTJ060)the Humanities and Social Sciences Foundation of the Ministry of Education of China (Grant No.20YJA910006)+3 种基金the Natural Science Foundation of Jiangsu Province (Grant No.BK20201396)the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.19KJA180003)the Grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No.HKU17306220)the 333 High Level Talent Training Project of Jiangsu Province。
文摘This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.
文摘A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.
基金The NNSF(10571073)of china,and 985 project of Jilin University.
文摘In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081).
文摘The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.
基金Supported by the National Natural Science Foundation of China (No.10071081) & Special Foundation of USTC.
文摘Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.
基金Project supported by the National Natural Science Foundation of China(No.11071182)
文摘Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ： k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P（X〉x）/P（τ〉x）→0 as x →∞.
基金supported by the National Natural Science Foundation of China (No. 11171179)the Research Fund for the Doctoral Program of Higher Education of China (No. 20093705110002)
文摘Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {Xk, k 〉 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = fi Xk and S（n） =∑ k=1 n 〉 1, and their randomized versions ST and S（τ） are studied. Some risk theory are presented. max Sk for 1〈k〈n applications to the
基金supported by the National Natural Science Foundation of China(Grant No.10471005).
文摘We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
基金Supported by Ferdowsi University of Mashhad(Grant No.MS88076AMI)
文摘Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.
基金Project supported by the National Natural Science Foundationof China (Nos. 61103010,61103190,and 60803100)the National Basic Research Program (973) of China (No. 2012CB933500)the High-Tech R&D Program (863) of China (No.2012AA011001)
文摘The error patterns of a wireless channel can be represented by a binary sequence of ones(burst) and zeros(run),which is referred to as a trace.Recent surveys have shown that the run length distribution of a wireless channel is an intrinsically heavy-tailed distribution.Analytical models to characterize such features have to deal with the trade-off between complexity and accuracy.In this paper,we use an independent but not identically distributed(inid) stochastic process to characterize such channel behavior and show how to parameterize the inid bit error model on the basis of a trace.The proposed model has merely two parameters both having intuitive meanings and can be easily figured out from a trace.Compared with chaotic maps,the inid bit error model is simple for practical use but can still be deprived from heavy-tailed distribution in theory.Simulation results demonstrate that the inid model can match the trace,but with fewer parameters.We then propose an improvement on the inid model to capture the 'bursty' nature of channel errors,described by burst length distribution.Our theoretical analysis is supported by an experimental evaluation.
基金Supported by the 333 High Level Talent Training Project of Jiangsu Provincethe National Natural Science Foundation of China(71871046)Science and Technology Projects of Sichuan Province(2021YFQ0007)。
文摘This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 0 87)
文摘Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subclass DKc and subclass DK 1 are obtained.
