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Bivariate Analysis of Pollutants Monthly Maxima in Mexico City Using Extreme Value Distributions and Copula
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作者 Juan A. Vazquez-Morales Eliane R. Rodrigues Hortensia J. Reyes-Cervantes 《Journal of Environmental Protection》 2024年第7期796-826,共31页
In the present work, we are interested in studying the joint distributions of pairs of the monthly maxima of the pollutants used by the environmental authorities in Mexico City to classify the air quality in the metro... In the present work, we are interested in studying the joint distributions of pairs of the monthly maxima of the pollutants used by the environmental authorities in Mexico City to classify the air quality in the metropolitan area. In order to obtain the joint distributions a copula will be considered. Since we are analyzing the monthly maxima, the extreme value distributions of Weibull and Fréchet are taken into account. Using these two distributions as marginal distributions in the copula a Bayesian inference was made in order to estimate the parameters of both distributions and also the association parameters appearing in the copula model. The pollutants taken into account are ozone, nitrogen dioxide, sulphur dioxide, carbon monoxide, and particulate matter with diameters smaller than 10 and 2.5 microns obtained from the Mexico City monitoring network. The estimation was performed by taking samples of the parameters generated through a Markov chain Monte Carlo algorithm implemented using the software OpenBugs. Once the algorithm is implemented it is applied to the pairs of pollutants where one of the coordinates of the pair is ozone and the other varies on the set of the remaining pollutants. Depending on the pollutant and the region where they were collected, different results were obtained. Hence, in some cases we have that the best model is that where we have a Fréchet distribution as the marginal distribution for the measurements of both pollutants and in others the most suitable model is the one assuming a Fréchet for ozone and a Weibull for the other pollutant. Results show that, in the present case, the estimated association parameter is a good representation to the correlation parameters between the pair of pollutants analyzed. Additionally, it is a straightforward task to obtain these correlation parameters from the corresponding association parameters. 展开更多
关键词 COPULA Extreme value distribution Bayesian Inference Air Pollution Mexico City
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ON VALUE DISTRIBUTIONS OF GENERAL DIFFERENTIAL MONOMIALS
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作者 吴天毅 李伟 程英 《Transactions of Tianjin University》 EI CAS 2001年第1期68-70,共3页
Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) ... Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0】2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0. 展开更多
关键词 meromorphic function differential monomial differential polynomial value distribution
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Extreme value distribution and reliability of nonlinear stochastic structures 被引量:7
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作者 陈建兵 李杰 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2005年第2期275-286,共12页
A new approach to evaluate the extreme value distribution (EVD) of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed proba... A new approach to evaluate the extreme value distribution (EVD) of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency. 展开更多
关键词 extreme value distribution RELIABILITY NONLINEAR probability density evolution method number theoreticalmethod
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Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis 被引量:4
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作者 刘晶 史道济 吴新荣 《Transactions of Tianjin University》 EI CAS 2008年第1期50-54,共5页
This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be ... This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels. 展开更多
关键词 Poisson-generalized Pareto compound extreme value distribution probability-weightedmoment estimation maximum likelihood estimation compound moment estimation
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ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n(C) 被引量:2
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作者 涂振汉 李平丽 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期702-710,共9页
This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n(C).. An example is given to compleme... This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n(C).. An example is given to complement these results. 展开更多
关键词 Complex projective spaces holomorphic mappings normal families singular directions and value distribution theory
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Extreme value distributions of mixing two sequences with different MDA's 被引量:2
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作者 蒋岳祥 《Journal of Zhejiang University Science》 CSCD 2004年第5期509-517,共9页
Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme ... Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions. 展开更多
关键词 Extreme value distribution Maximum domain of attraction(MDA) Mixed distribution functions
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THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH (Ⅱ) 被引量:1
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作者 丁晓庆 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期504-510,共7页
This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > ... This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > 0. Suppose [h*(σ)]2 = n converges for any α > 0, and diverges for = 0. It is shown that if = ρ E (0, ), then with probability one, where β is a constant depending only upon the constant α. 展开更多
关键词 value distribution exceptional value random Dirichlet series independent random variab
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Further Extension on a Theorem of the Value Distribution of f′f^n 被引量:1
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作者 DOU Pan-ying WU Ghang-qun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期155-158,共4页
By using small function method, the following result is obtained. If f(z) is transcendental meromorphic and that ψ(z) is non-zero meromorphic and that T(r,ψ) = S(r, f), then(n+1)T(r,f)≤N^-(r,1/f'f^n... By using small function method, the following result is obtained. If f(z) is transcendental meromorphic and that ψ(z) is non-zero meromorphic and that T(r,ψ) = S(r, f), then(n+1)T(r,f)≤N^-(r,1/f'f^n-ψ)+2N^-(r,1/f)+N^-(r,f)+S(r,f). 展开更多
关键词 transcendental meromorphic value distribution small function
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THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS
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作者 张克玉 仪洪勋 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期719-728,共10页
In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomialsG(z)=(f^n(f^m(z)-1)∏j=1^d f(z+cj)^vj)^(k)-α(z),H(z)=(f^n(f(z)-1)^m∏j=1^d f(z... In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomialsG(z)=(f^n(f^m(z)-1)∏j=1^d f(z+cj)^vj)^(k)-α(z),H(z)=(f^n(f(z)-1)^m∏j=1^d f(z+cj)^vj)^(k)-α(z),where f is transcendental entire function of finite order, cj(j = 1,2,…,d), n,m,d, and vj(j = 1, 2,… , d) are integers, and obtain some theorems, which extended and improved many previous results. 展开更多
关键词 MEROMORPHIC UNIQUENESS value distribution differential-difference
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THE VALUE DISTRIBUTION OF GAUSS MAPS OF IMMERSED HARMONIC SURFACES WITH RAMIFICATION
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作者 Zhixue LIU Yezhou LI Xingdi CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2022年第1期172-186,共15页
Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a... Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a generalization of the results in the case of the minimal surfaces.In addition,we give an estimate of the Gauss curvature for the K-quasiconfomal harmonic surfaces whose generalized Gauss map is ramified over a set of hyperplanes. 展开更多
关键词 value distribution harmonic surfaces quasiconformal mappings conformal metric Gauss map
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More general results on mixed extreme value distributions
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作者 蒋岳祥 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第7期769-774,共6页
The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of ... The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz(x) does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases. 展开更多
关键词 Extreme value distribution Maximum domain of attraction (MDA) Mixed distribution functions
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A class of not max-stable extreme value distributions
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作者 蒋岳祥 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第4期315-321,共7页
The sequences {Zi , 1≤i≤n}, n≥1 have multi-nomial distribution among i.i.d. random variables {X1, , i≥1}, {X2, , ,n i i i≥1}, …, {Xm , i≥1}. The extreme value distribution GZ(x) of this particular triangular ar... The sequences {Zi , 1≤i≤n}, n≥1 have multi-nomial distribution among i.i.d. random variables {X1, , i≥1}, {X2, , ,n i i i≥1}, …, {Xm , i≥1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1, , Z2, , …, ,i n n r ?1 Zn is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) GZ (x) = ,n ∏Φα Ai(x)×Φαr (x); i i=1 r ?1 r?1 ii) GZ (x) = ∏Ψα Ai(x)×Ψαr (x); iii) GZ (x) = ∏Λ Ai(λix)×Λ(x), r≥2, 0<α1≤α2≤…≤αr and λi∈(0,1] for i, 1≤i≤r?1 which occur if i i=1 i=1 Fj, …, Fm belong to the same MDA. 展开更多
关键词 Extreme value distribution Maximum domain of attraction (MDA) Mixed distribution functions
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Value Distribution of Differential Polynomials in Meromorphic Functions
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作者 LIU Xiao-shu 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期297-300,共4页
Let f(z) be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N(r, f)+-↑N (r, 1/f) = S(r, f). We obtain several results about the zero point of the ψ and ... Let f(z) be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N(r, f)+-↑N (r, 1/f) = S(r, f). We obtain several results about the zero point of the ψ and those results extend and improve the results of Yang and Yi in this paper. 展开更多
关键词 Meromorphic function differential polynomials value distribution
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VALUE DISTRIBUTION THEORY AND DIOPHANTINE APPROXIMATION
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作者 Peichu Hu Chungchun Yang 《Analysis in Theory and Applications》 2005年第2期101-117,共17页
In this paper, we will introduce some problems and results between Diophantine approximation and value distribution theory.
关键词 value distribution Diophantine approximation
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Applications of Bootstrap in Analyzing General Extreme Value Distributions
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作者 Dang Kien Cuong Duong Ton Dam +1 位作者 Duong Ton Thai Duong Ngo Thuan Du 《Journal of Mechanics Engineering and Automation》 2019年第7期236-242,共7页
The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is con... The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions. 展开更多
关键词 Bootstrap method time series block bootstrap jackknife method generalized extreme value distributions
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General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution (Ⅰ) 被引量:3
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作者 Xiao Qian WANG Shi Hong CHENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第5期1121-1130,共10页
In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions... In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved. 展开更多
关键词 General regular variation Extreme value distribution Edgeworth expansion
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MULTIVARIATE EXTREME VALUE DISTRIBUTION AND ITS FISHER INFORMATION MATRIX 被引量:3
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作者 史道济 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1995年第4期421-428,共8页
The paper is concerned with the basic properties of multivariate extreme value distribution (in the Logistic model). We obtain the characteristic function and recurrence formula of the density function. The explicit a... The paper is concerned with the basic properties of multivariate extreme value distribution (in the Logistic model). We obtain the characteristic function and recurrence formula of the density function. The explicit algebraic formula for Fisher information matrix is indicated. A simple and accurate procedure for generating random vector from multivariate extreme value distribution is presented. 展开更多
关键词 Characteristic function Fisher information matrix Gumbel distribution multivariate extreme value distribution
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Stationary distributions for two-dimensional sticky Brownian motions:Exact tail asymptotics and extreme value distributions
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作者 Hongshuai Dai Yiqiang Q.Zhao 《Science China Mathematics》 SCIE CSCD 2021年第11期2539-2562,共24页
Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stati... Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis. 展开更多
关键词 sticky Brownian motion queueing model stationary distribution exact tail asymptotic kernel method extreme value distribution
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General Regular Variation of the n-th Order and 2nd Order Edgeworth Expansions of the Extreme Value Distribution (Ⅱ)
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作者 Xiao Qian WANG Shi Hong CHENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第1期27-40,共14页
In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.
关键词 General regular variation Extreme value distribution Edgeworth Expansion
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On Value Distribution of Δ~nf
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作者 Shuang Ting LAN Zong Xuan CHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第10期1795-1809,共15页
In this paper, we mainly study zeros and poles of the forward differences △nf(z), where f(z) is a finite order meromorphic function with two Borel exceptional values.
关键词 Borel exceptional value deficient value value distribution
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