In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditiona...In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.展开更多
Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcom...Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.展开更多
The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1...The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.展开更多
Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a st...Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.展开更多
Leaf normal distribution is an important structural characteristic of the forest canopy. Although terrestrial laser scanners（TLS） have potential for estimating canopy structural parameters, distinguishing between le...Leaf normal distribution is an important structural characteristic of the forest canopy. Although terrestrial laser scanners（TLS） have potential for estimating canopy structural parameters, distinguishing between leaves and nonphotosynthetic structures to retrieve the leaf normal has been challenging. We used here an approach to accurately retrieve the leaf normals of camphorwood（Cinnamomum camphora） using TLS point cloud data.First, nonphotosynthetic structures were filtered by using the curvature threshold of each point. Then, the point cloud data were segmented by a voxel method and clustered by a Gaussian mixture model in each voxel. Finally, the normal vector of each cluster was computed by principal component analysis to obtain the leaf normal distribution. We collected leaf inclination angles and estimated the distribution, which we compared with the retrieved leaf normal distribution. The correlation coefficient between measurements and obtained results was 0.96, indicating a good coincidence.展开更多
The original data of Nilsson-Ehle experiment in wheat were analyzed with existent genetic knowledge. It indicated that the core of polygenic hypothesis from this experiment was that a character similarity produced by ...The original data of Nilsson-Ehle experiment in wheat were analyzed with existent genetic knowledge. It indicated that the core of polygenic hypothesis from this experiment was that a character similarity produced by additive effect of multiple genes was the basis of continuous variation. Its precondition was for effective genes to have equal effect, to show merodominance and binomial distribution and to inherit independently. In fact, quantitative characters were determined by many genes with different property, effect and behavior. So it was difficult to solve all problems of continuous variation by the aid of polygenic hypothesis. The researchers should seek new ways. With Mendelian group as research object and by means of Lyapunov central limit theorem it was proved that both genotypic value G and the environmental effect in a niche E were subordinated to the normal distribution and respectively. According to additivity of the normal distribution the phenotype P = G + E also obeyed the normal distribution P = G + E ~ and quantitative characters showed continuous variation, whether or not the linkage was presented, whether or not every gene effect was equal, whether or not there were dominance and what kind of dominance between alleles. Moreover it was discussed that the quantitative characters in self-fertilized organism and clone were submitted to the normal distribution and presented continuous variation too.展开更多
Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to p...Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.展开更多
The calculation of the mean difference for the inverse normal distribution can be obtained by a transformation of variable or a hard integration by parts. This paper shows a simpler formula of the mean difference of t...The calculation of the mean difference for the inverse normal distribution can be obtained by a transformation of variable or a hard integration by parts. This paper shows a simpler formula of the mean difference of the inverse normal distribution that highlights the role of the two parameters on the mean difference of the model. It makes it easier to study the relation of the mean difference with the other indexes of variability for the inverse normal distribution.展开更多
This paper proposes a new pre-processing technique to separate the most effective features from those that might deteriorate the performance of the machine learning classifiers in terms of computational costs and clas...This paper proposes a new pre-processing technique to separate the most effective features from those that might deteriorate the performance of the machine learning classifiers in terms of computational costs and classification accuracy because of their irrelevance,redundancy,or less information;this pre-processing process is often known as feature selection.This technique is based on adopting a new optimization algorithm known as generalized normal distribution optimization(GNDO)supported by the conversion of the normal distribution to a binary one using the arctangent transfer function to convert the continuous values into binary values.Further,a novel restarting strategy(RS)is proposed to preserve the diversity among the solutions within the population by identifying the solutions that exceed a specific distance from the best-so-far and replace them with the others created using an effective updating scheme.This strategy is integrated with GNDO to propose another binary variant having a high ability to preserve the diversity of the solutions for avoiding becoming stuck in local minima and accelerating convergence,namely improved GNDO(IGNDO).The proposed GNDO and IGNDO algorithms are extensively compared with seven state-of-the-art algorithms to verify their performance on thirteen medical instances taken from the UCI repository.IGNDO is shown to be superior in terms of fitness value and classification accuracy and competitive with the others in terms of the selected features.Since the principal goal in solving the FS problem is to find the appropriate subset of features that maximize classification accuracy,IGNDO is considered the best.展开更多
In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature ...In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.展开更多
We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜...We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.展开更多
We introduce a kind of generalized Wigner operator,whose normally ordered form can lead to the bivariatenormal distribution in p-q phase space.While this bivariate normal distribution corresponds to the pure vacuum st...We introduce a kind of generalized Wigner operator,whose normally ordered form can lead to the bivariatenormal distribution in p-q phase space.While this bivariate normal distribution corresponds to the pure vacuum state inthe generalized Wigner function phase space,it corresponds to a mixed state in the usual Wigner function phase space.展开更多
Microlatex particles of emulsion explosives determined by microphotography were studied with the law of logarithmic Gauss normal distribution, and results obtained showed that the microlatex particle just possessed th...Microlatex particles of emulsion explosives determined by microphotography were studied with the law of logarithmic Gauss normal distribution, and results obtained showed that the microlatex particle just possessed the law of logarithmic Gauss normal distribution. The particle diameter in statistical average value, such as DNL, DNS, DLS, DSV and DVM was calculated through the diagram of logarithmic Gauss normal distribution of microlatex particles of emulsion explosives, so was SW.展开更多
The purpose of this paper is to broaden the knowledge of mean difference and, in particular, of an important distribution model known as truncated normal distribution, which is widely used in applied sciences and econ...The purpose of this paper is to broaden the knowledge of mean difference and, in particular, of an important distribution model known as truncated normal distribution, which is widely used in applied sciences and economics. In this work, we obtained the general formula of mean difference, which is not yet reported in literature, for the aforementioned distribution model and also for particular truncated cases.展开更多
In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become i...In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.展开更多
The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineer...The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6展开更多
In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the vari...In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l<sub>2</sub> penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.展开更多
Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, t...Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.展开更多
Aiming at the limitation of traditional normal distribution structure is put forward. With strength-strain model, an improved algorithm for this method, the reliability coefficient of non-linear limit status function ...Aiming at the limitation of traditional normal distribution structure is put forward. With strength-strain model, an improved algorithm for this method, the reliability coefficient of non-linear limit status function is solved by developing Taylor progression, and the distribution parameters of random variables are estimated with experimental sample data. Therefore, the estimation of reliability confidence interval on certain confidence level can be solved when distribution parameters are unknown and limit status function is non-linear.展开更多
文摘In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.
基金Supported by the National Natural Science Foundation of China(11261025,11201412)the Natural Science Foundation of Yunnan Province(2011FB016)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.
文摘The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.
基金Project (50378036) supported by the National Natural Science Foundation of China Project (03JJY5024) supported by the Natural Science Foundation of Hunan Province, China
文摘Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.
文摘Leaf normal distribution is an important structural characteristic of the forest canopy. Although terrestrial laser scanners（TLS） have potential for estimating canopy structural parameters, distinguishing between leaves and nonphotosynthetic structures to retrieve the leaf normal has been challenging. We used here an approach to accurately retrieve the leaf normals of camphorwood（Cinnamomum camphora） using TLS point cloud data.First, nonphotosynthetic structures were filtered by using the curvature threshold of each point. Then, the point cloud data were segmented by a voxel method and clustered by a Gaussian mixture model in each voxel. Finally, the normal vector of each cluster was computed by principal component analysis to obtain the leaf normal distribution. We collected leaf inclination angles and estimated the distribution, which we compared with the retrieved leaf normal distribution. The correlation coefficient between measurements and obtained results was 0.96, indicating a good coincidence.
文摘The original data of Nilsson-Ehle experiment in wheat were analyzed with existent genetic knowledge. It indicated that the core of polygenic hypothesis from this experiment was that a character similarity produced by additive effect of multiple genes was the basis of continuous variation. Its precondition was for effective genes to have equal effect, to show merodominance and binomial distribution and to inherit independently. In fact, quantitative characters were determined by many genes with different property, effect and behavior. So it was difficult to solve all problems of continuous variation by the aid of polygenic hypothesis. The researchers should seek new ways. With Mendelian group as research object and by means of Lyapunov central limit theorem it was proved that both genotypic value G and the environmental effect in a niche E were subordinated to the normal distribution and respectively. According to additivity of the normal distribution the phenotype P = G + E also obeyed the normal distribution P = G + E ~ and quantitative characters showed continuous variation, whether or not the linkage was presented, whether or not every gene effect was equal, whether or not there were dominance and what kind of dominance between alleles. Moreover it was discussed that the quantitative characters in self-fertilized organism and clone were submitted to the normal distribution and presented continuous variation too.
基金the financial support from the National Natural Science Foundation of China (No. 51221462)
文摘Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.
文摘The calculation of the mean difference for the inverse normal distribution can be obtained by a transformation of variable or a hard integration by parts. This paper shows a simpler formula of the mean difference of the inverse normal distribution that highlights the role of the two parameters on the mean difference of the model. It makes it easier to study the relation of the mean difference with the other indexes of variability for the inverse normal distribution.
基金This work has supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.NRF-2021R1A2C1010362)and the Soonchunhyang University Research Fund.
文摘This paper proposes a new pre-processing technique to separate the most effective features from those that might deteriorate the performance of the machine learning classifiers in terms of computational costs and classification accuracy because of their irrelevance,redundancy,or less information;this pre-processing process is often known as feature selection.This technique is based on adopting a new optimization algorithm known as generalized normal distribution optimization(GNDO)supported by the conversion of the normal distribution to a binary one using the arctangent transfer function to convert the continuous values into binary values.Further,a novel restarting strategy(RS)is proposed to preserve the diversity among the solutions within the population by identifying the solutions that exceed a specific distance from the best-so-far and replace them with the others created using an effective updating scheme.This strategy is integrated with GNDO to propose another binary variant having a high ability to preserve the diversity of the solutions for avoiding becoming stuck in local minima and accelerating convergence,namely improved GNDO(IGNDO).The proposed GNDO and IGNDO algorithms are extensively compared with seven state-of-the-art algorithms to verify their performance on thirteen medical instances taken from the UCI repository.IGNDO is shown to be superior in terms of fitness value and classification accuracy and competitive with the others in terms of the selected features.Since the principal goal in solving the FS problem is to find the appropriate subset of features that maximize classification accuracy,IGNDO is considered the best.
文摘In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.
基金supported by National Natural Science Foundation of China under Grant No.10574647
文摘We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.
基金National Natural Science Foundation of China under Grant Nos.10775097 and 10874174
文摘We introduce a kind of generalized Wigner operator,whose normally ordered form can lead to the bivariatenormal distribution in p-q phase space.While this bivariate normal distribution corresponds to the pure vacuum state inthe generalized Wigner function phase space,it corresponds to a mixed state in the usual Wigner function phase space.
文摘Microlatex particles of emulsion explosives determined by microphotography were studied with the law of logarithmic Gauss normal distribution, and results obtained showed that the microlatex particle just possessed the law of logarithmic Gauss normal distribution. The particle diameter in statistical average value, such as DNL, DNS, DLS, DSV and DVM was calculated through the diagram of logarithmic Gauss normal distribution of microlatex particles of emulsion explosives, so was SW.
文摘The purpose of this paper is to broaden the knowledge of mean difference and, in particular, of an important distribution model known as truncated normal distribution, which is widely used in applied sciences and economics. In this work, we obtained the general formula of mean difference, which is not yet reported in literature, for the aforementioned distribution model and also for particular truncated cases.
文摘In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
文摘In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.
文摘The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6
文摘In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l<sub>2</sub> penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.
文摘Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.
文摘Aiming at the limitation of traditional normal distribution structure is put forward. With strength-strain model, an improved algorithm for this method, the reliability coefficient of non-linear limit status function is solved by developing Taylor progression, and the distribution parameters of random variables are estimated with experimental sample data. Therefore, the estimation of reliability confidence interval on certain confidence level can be solved when distribution parameters are unknown and limit status function is non-linear.
