Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR p...Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.展开更多
Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, ...Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).展开更多
Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades...Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.展开更多
The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west. A positive temperature skewness appears in the equatorial eastern Pacific, while ...The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west. A positive temperature skewness appears in the equatorial eastern Pacific, while the temperature skewness in the western and central Pacific is primarily negative. There is also an asymmetry of the temperature skewness above and below the climatological mean therrnocline in the central and western Pacific. A positive skewness appears below the thermocline, but the skewness is negative above the thermocline. The distinctive vertical asymmetry of the temperature skewness is argued to be attributed to the asymmetric temperature response to upward and downward thermocline displacement in the presence of the observed upper-ocean vertical thermal structure. Because of positive （negative） second derivative of temperature with respect to depth below （above） the thermocline, an upward and a downward shift of the thermocline with equal displacement would lead to a negative temperature skewness above the thermocline but a positive skewness below the thermocline. In the far eastern equatorial Pacific, the thermocline is close to the base of the mixed layer, the shape of the upper-ocean vertical temperature profile cannot be kept. Positive skewness appears in both below the thermocline and above the thermocline in the far eastern basin. Over the central and eastern Pacific, the anomalies of the subsurface waters tend to entrain into the surface mixed layer （by climatological mean upwelling） and then affect the SST. Hence, the positive （negative） subsurface skewness in the far eastern （central） Pacific may favor positive （negative） SST skewness, which is consistent with the observational fact that more La Nina （EI Nino） occur in the central （eastern） Pacific. The present result implies a possible new paradigm for EI Nino and La Nina amplitude asymmetry in the eastern Pacific.展开更多
The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Her...The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.展开更多
In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fi...In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.展开更多
Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely...Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.展开更多
Regarding the scale effects on propeller＇s noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respec...Regarding the scale effects on propeller＇s noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes （ URANS ） simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency （APF） and the blade passing frequency （BPF）, and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.展开更多
基金The National Natural Science Foundation of China (No.70671025)
文摘Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.
基金The project supported by the National Basic Research Program "Non-linear Science"
文摘Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).
基金Supported by the National Natural Science Foundation of China(11261025,11561075)the Natural Science Foundation of Yunnan Province(2016FB005)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.
基金Supported by the National Basic Research Program of China (973 Program)(No 2007CB816005)the National Natural Science Foundation of China (No 40706003)+1 种基金International S&T Cooperation Project of the Ministry of Science and Technology of China (No2009DFA21430)the COPES in China (GYHY200706005)
文摘The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west. A positive temperature skewness appears in the equatorial eastern Pacific, while the temperature skewness in the western and central Pacific is primarily negative. There is also an asymmetry of the temperature skewness above and below the climatological mean therrnocline in the central and western Pacific. A positive skewness appears below the thermocline, but the skewness is negative above the thermocline. The distinctive vertical asymmetry of the temperature skewness is argued to be attributed to the asymmetric temperature response to upward and downward thermocline displacement in the presence of the observed upper-ocean vertical thermal structure. Because of positive （negative） second derivative of temperature with respect to depth below （above） the thermocline, an upward and a downward shift of the thermocline with equal displacement would lead to a negative temperature skewness above the thermocline but a positive skewness below the thermocline. In the far eastern equatorial Pacific, the thermocline is close to the base of the mixed layer, the shape of the upper-ocean vertical temperature profile cannot be kept. Positive skewness appears in both below the thermocline and above the thermocline in the far eastern basin. Over the central and eastern Pacific, the anomalies of the subsurface waters tend to entrain into the surface mixed layer （by climatological mean upwelling） and then affect the SST. Hence, the positive （negative） subsurface skewness in the far eastern （central） Pacific may favor positive （negative） SST skewness, which is consistent with the observational fact that more La Nina （EI Nino） occur in the central （eastern） Pacific. The present result implies a possible new paradigm for EI Nino and La Nina amplitude asymmetry in the eastern Pacific.
基金Project supported by the National Natural Science Foundation of China(Grant No.11772032)the Science Foundation of North University of China(Grant No.11026829).
文摘The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.
文摘In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.
基金supported by the National Natural Science Foundation of China(12131015,12071422).
文摘Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.
基金The National Natural Science Foundation of China(No.51009144)
文摘Regarding the scale effects on propeller＇s noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes （ URANS ） simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency （APF） and the blade passing frequency （BPF）, and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.
