This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a r...This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.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 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
Surface sediment samples were collected at 21 offshore sites in western Xiamen Bay, Southeast China. Total concentrations of Li, V, Cr, Co, Ni, Cu, Zn, St, Mn, Pb, Ba, Fe, and Ti were determined by inductively coupled...Surface sediment samples were collected at 21 offshore sites in western Xiamen Bay, Southeast China. Total concentrations of Li, V, Cr, Co, Ni, Cu, Zn, St, Mn, Pb, Ba, Fe, and Ti were determined by inductively coupled plasma-optical emission spectrometry; Hg was determined by atomic fluorescence spectrometry. A modified BCR sequential extraction procedure was used to extract fractions of the above elements. Concentrations of Pb, Cr, and Hg at most sites met the primary standard criteria of Marine Sediment Quality except site S12 for Pb and S7 for Cr, while concentrations of Zn at 17 sites and Cu at seven sites exceeded the criteria. The mean concentration of Hg was three times higher than the background, with a possible source being the Jiulong River. Fe, Ti, Ba, Co, V, and Li dominated the residual phase, mainly from terrestrial input. Ni, Cr, Pb, and Hg in the non-residual phase varied largely between sites. Sr, Mn, Cu, and Zn were mainly in the non- residual fraction. Most sites showed considerable ecological risk; exceptions were site S7 （very high） and sites S10, S11, and S14 （moderate）. Cu showed moderate-to-high pollution and Pb exhibited no-to-low pollution, while other metals had a non-pollution status according to their ratios of secondary phase to primary phase （RSP）. Results of two assessment methods showed moderate pollution and a very high ecological risk for Cu, Zn, Ni, and Cr at site S7, which might be due to the local sewage treatment plant.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
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
For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove th...For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio ■equals 1 as x →∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented.展开更多
The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To ...The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L<sub>1</sub> estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ<sup>2</sup>/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.展开更多
Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, a...Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.展开更多
主要研究当汇率回报呈多元t-分布时,对于外汇期权非线性头寸的VaR(Value at Risk)度量的问题。在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上,本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的...主要研究当汇率回报呈多元t-分布时,对于外汇期权非线性头寸的VaR(Value at Risk)度量的问题。在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上,本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的值,并和基于多元正态分布Cornish-Fisher模型以及基于Delta-正态模型计算所得的VaR值了进行比较。这种方法克服了厚尾分布的VaR计算的困难。展开更多
文摘This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.
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.
基金supported by the National Natural Science Foundation of China(21177043,21077036)+1 种基金State Key Laboratory of Environmental Geochemistry(SKLEG2013801)Cultivation Project on 2014 Postgraduates’Research and Innovation Capability of Huaqiao University(426)
文摘Surface sediment samples were collected at 21 offshore sites in western Xiamen Bay, Southeast China. Total concentrations of Li, V, Cr, Co, Ni, Cu, Zn, St, Mn, Pb, Ba, Fe, and Ti were determined by inductively coupled plasma-optical emission spectrometry; Hg was determined by atomic fluorescence spectrometry. A modified BCR sequential extraction procedure was used to extract fractions of the above elements. Concentrations of Pb, Cr, and Hg at most sites met the primary standard criteria of Marine Sediment Quality except site S12 for Pb and S7 for Cr, while concentrations of Zn at 17 sites and Cu at seven sites exceeded the criteria. The mean concentration of Hg was three times higher than the background, with a possible source being the Jiulong River. Fe, Ti, Ba, Co, V, and Li dominated the residual phase, mainly from terrestrial input. Ni, Cr, Pb, and Hg in the non-residual phase varied largely between sites. Sr, Mn, Cu, and Zn were mainly in the non- residual fraction. Most sites showed considerable ecological risk; exceptions were site S7 （very high） and sites S10, S11, and S14 （moderate）. Cu showed moderate-to-high pollution and Pb exhibited no-to-low pollution, while other metals had a non-pollution status according to their ratios of secondary phase to primary phase （RSP）. Results of two assessment methods showed moderate pollution and a very high ecological risk for Cu, Zn, Ni, and Cr at site S7, which might be due to the local sewage treatment plant.
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.
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Supported by the National Natural Science Foundation of China(no.11401415)Tian Yuan Foundation(nos.11226208 and 11426139)+2 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(no.13KJB110025)Postdoctoral Research Program of Jiangsu Province of China(no.1402111C)Jiangsu Overseas Research and Training Program for Prominent University Young and Middle-aged Teachers and Presidents
文摘For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio ■equals 1 as x →∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented.
文摘The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L<sub>1</sub> estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ<sup>2</sup>/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.
文摘Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.
文摘主要研究当汇率回报呈多元t-分布时,对于外汇期权非线性头寸的VaR(Value at Risk)度量的问题。在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上,本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的值,并和基于多元正态分布Cornish-Fisher模型以及基于Delta-正态模型计算所得的VaR值了进行比较。这种方法克服了厚尾分布的VaR计算的困难。
