Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptio...Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.展开更多
The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric p...The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.展开更多
为精确表述公共交通资源的分布特征,进而准确衡量公共交通服务的公平性,以公交可达性作为公共交通资源度量指标,考虑可达性数据统计特性,选取对数正态(Logarithmic Normal,Lognormal)、对数Logistic(Fisk)、伽玛(Gamma)、韦伯(Weibull)...为精确表述公共交通资源的分布特征,进而准确衡量公共交通服务的公平性,以公交可达性作为公共交通资源度量指标,考虑可达性数据统计特性,选取对数正态(Logarithmic Normal,Lognormal)、对数Logistic(Fisk)、伽玛(Gamma)、韦伯(Weibull)、Singh-Maddala(SM)、Dagum、第二类Beta(Beta of the Second Kind, B2)和广义第二类Beta(Generalized Beta of the Second Kind,GB2)8种分布函数对公交可达性数据进行拟合,并检验各分布函数的拟合效果,从而寻找对公交可达性数据拟合效果最佳的分布函数。计算结果显示,各分布函数拟合效果从优至劣排序为:GB2> B2> Dagum>SM>Fisk>Lognormal>Weibull>Gamma,即四参数分布函数的拟合效果优于三参数分布函数,三参数分布函数的拟合效果优于两参数分布函数。研究表明:四参数GB2分布函数对公交可达性数据的拟合效果最佳,可更准确地体现出公共交通资源的分配情况。展开更多
对广义极值(GEV)分布的参数进行了ML、GML和BAYBETA估计.利用R统计软件,通过用Markov Chain Monte Carlo(MCMC)方法与Metroplis-Hastings算法产生服从参数后验分布的模拟样本,进而对GEV分布的参数进行估计,并对上述几种估计的偏差和均...对广义极值(GEV)分布的参数进行了ML、GML和BAYBETA估计.利用R统计软件,通过用Markov Chain Monte Carlo(MCMC)方法与Metroplis-Hastings算法产生服从参数后验分布的模拟样本,进而对GEV分布的参数进行估计,并对上述几种估计的偏差和均方误差进行了模拟.对澳大利亚南部的Pirie港海平面年最大海平面高度建立GEV模型,并对T年一遇的最高水位进行了估计.实例研究表明,用BAY BETA方法估计的最高水位稍高于用极大似然估计得到的结果.展开更多
基金partially supported by the USDA National Institute of Food and Agriculture,Mc Intire Stennis Project OKL0 3063the Division of Agricultural Sciences and Natural Resources at Oklahoma State Universityprovided by the USDA Forest Service,Research Joint Venture 17-JV-11242306045,Old-Growth Forest Dynamics and Structure,to Mark Ducey
文摘Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.
文摘The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.
基金Supported by the Scientific Research Funds for Forestry Public Welfare of China(201004026)Ministry of Education “Overseas Experts and Scholars” project
文摘为精确表述公共交通资源的分布特征,进而准确衡量公共交通服务的公平性,以公交可达性作为公共交通资源度量指标,考虑可达性数据统计特性,选取对数正态(Logarithmic Normal,Lognormal)、对数Logistic(Fisk)、伽玛(Gamma)、韦伯(Weibull)、Singh-Maddala(SM)、Dagum、第二类Beta(Beta of the Second Kind, B2)和广义第二类Beta(Generalized Beta of the Second Kind,GB2)8种分布函数对公交可达性数据进行拟合,并检验各分布函数的拟合效果,从而寻找对公交可达性数据拟合效果最佳的分布函数。计算结果显示,各分布函数拟合效果从优至劣排序为:GB2> B2> Dagum>SM>Fisk>Lognormal>Weibull>Gamma,即四参数分布函数的拟合效果优于三参数分布函数,三参数分布函数的拟合效果优于两参数分布函数。研究表明:四参数GB2分布函数对公交可达性数据的拟合效果最佳,可更准确地体现出公共交通资源的分配情况。
文摘对广义极值(GEV)分布的参数进行了ML、GML和BAYBETA估计.利用R统计软件,通过用Markov Chain Monte Carlo(MCMC)方法与Metroplis-Hastings算法产生服从参数后验分布的模拟样本,进而对GEV分布的参数进行估计,并对上述几种估计的偏差和均方误差进行了模拟.对澳大利亚南部的Pirie港海平面年最大海平面高度建立GEV模型,并对T年一遇的最高水位进行了估计.实例研究表明,用BAY BETA方法估计的最高水位稍高于用极大似然估计得到的结果.
