The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspend...The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.展开更多
A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of life...A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.展开更多
Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been pro...Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.展开更多
A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function...A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.展开更多
Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct ...Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.展开更多
The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual serve...The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.展开更多
In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip...In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.展开更多
This article develops a beta-exponentiated Ishita distribution that extends the exponentiated Ishita distribution. Expansions for the cumulative distribution and probability density functions are given. Various proper...This article develops a beta-exponentiated Ishita distribution that extends the exponentiated Ishita distribution. Expansions for the cumulative distribution and probability density functions are given. Various properties of the new distribution such as hazard function, moments, cumulants, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, Rényi and Tsallis entropies, and stress-strength reliability are discussed. Moment generating function and characteristic function of the new model were derived. Distribution and the moment of order statistic have been derived. The method of maximum likelihood was used for estimation of parameters. The new model is quite flexible in analysing positively skewed data. Two real datasets are used to demonstrate the flexibility of the new distribution.展开更多
基金National Natural Science Foundation of China,Grant/Award Number:U2243218。
文摘The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.
基金The National Natural Science Foundation of China(No. 10801032)
文摘A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.
基金supported by the Natural Science Foundation of China(32071758 and U21A20244)the Fundamental Research Funds for the Central Universities of China(No.2572020BA01)。
文摘Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.
基金Supported by Natural Science Foundation of Tianjin(No.09JCYBJC07700)
文摘A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.
文摘Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.
基金supported by the National Development and Reform Commission of China (CNGI-04-12-1D).
文摘The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.
文摘In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
文摘This article develops a beta-exponentiated Ishita distribution that extends the exponentiated Ishita distribution. Expansions for the cumulative distribution and probability density functions are given. Various properties of the new distribution such as hazard function, moments, cumulants, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, Rényi and Tsallis entropies, and stress-strength reliability are discussed. Moment generating function and characteristic function of the new model were derived. Distribution and the moment of order statistic have been derived. The method of maximum likelihood was used for estimation of parameters. The new model is quite flexible in analysing positively skewed data. Two real datasets are used to demonstrate the flexibility of the new distribution.
