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
Managing mature Douglas-fir[Pseudotsuga menziesii(Mirb.)Franco]stands to emulate the structural complexity of natural old-growth forest requires identifying structural targets at the sub-stand level at which neighborh...Managing mature Douglas-fir[Pseudotsuga menziesii(Mirb.)Franco]stands to emulate the structural complexity of natural old-growth forest requires identifying structural targets at the sub-stand level at which neighborhood dynamics and patchy disturbance shape structure.We therefore sought to describe the archetypal shapes of predominant sub-stand diameter distribution types(DDTs)observed in natural tree neighborhoods in stands comprising a chronosequence(ca.120-450+yrs)encompassing mature,vertical diversification,and horizontal diversification development stages.The ten 1.0 ha stands are located in the southcentral Oregon Cascades,USA.Building on the known spatial position of each tree,natural tree neighborhoods were identified using the floating neighborhood approach based on spatial tessellation connecting neighboring trees at the first-(mean 61 m2)through fifth-(mean 2058 m2)order scales.Cluster analysis was then used to objectively identify the most predominant DDTs among the relative tree size distributions observed in the trans-scale neighborhoods within each stand.Repeated measures regression was used to classify each DDT to one of six observed archetypal shapes:negative exponential,unimodal,rotated sigmoid,bimodal,concave,or multi-modal.Only three of the 81 observed DDTs deviated by<10%from the stand average,while every stand had at least one DDT that deviated by>50%(maximum 83%).Within each stand,five to ten predominant DDTs were observed,which deviated from the stand average by 30-48%and were characterized by two to five different archetypal shapes.Consequently,in some stands the majority of tree neighborhoods were best characterized by a different shape from that assigned at the stand level.Deviation from the stand average increased from the youngest stand in the mature development stage through the middle stands in the vertical diversification stage to the oldest stands in the horizontal diversification stage.The complexity of DDT shapes tended to increase along the chronosequence(from negative exponential and uniform toward concave and multi-modal),with shape richness highest mid-sequence and evenness peaking in the oldest stands.The high diversity of sub-stand structural complexity reduces the utility of standlevel diameter distributions as old-growth restoration targets.However,the presence in early-sequence stands of sub-stand diameter distributions common to later-sequence stands may facilitate active management at the neighborhood level to promote future old-growth condition.Restoration of substand diameter structures would likely require combining spatial perspectives,such as by augmenting tree-level croptree management with diameter distribution targets for the resulting tree neighborhoods.展开更多
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 Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the es...The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.展开更多
We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and ...We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.展开更多
Multi-cohort management （MCM） that retains a range of stand structures （age and size class） has been proposed to emulate natural disturbance and improve management in the Nearctic boreal forest. Although MCM fores...Multi-cohort management （MCM） that retains a range of stand structures （age and size class） has been proposed to emulate natural disturbance and improve management in the Nearctic boreal forest. Although MCM forests contain both single- and multi-aged stands of mixed tree sizes, little is known about how variable stand structure affects associated fauna and biodiversity. Here, we examine the relationship between ground beetle （Coleoptera, Carabidae） communities and stand characteristics across a range of forest structure （=cohort classes）. Given that MCM classes are defined by the distribution of their tree-stem diameters, we ask whether parameters associated with these distributions （Weibull） could explain observed variation in carabid communities, and if so, how this compares to traditional habitat variables such as stand age, foliage complexity or volume of downed woody debris. We sampled carabids using weekly pitfall collections and compared these with structural habitat variables across a range of cohort classes （stand structure and age since disturbance） in 18 sites of upland mixed boreal forests from central Canada. Results showed that richness and diversity of carabid communities were similar among cohort classes. Weibull parameters from the diameter distribution of all stems were the strongest predictors of variation in carabid communities among sites, but vertical foliage complexity, understory thickness, and percentage of deciduous composition were also significant. The abundance of several carabid forest specialists was strongly correlated with tree canopy height, the presence of large trees, and high vertical foliage complexity. Our results demonstrate that variable forest structure, as expected under MCM, may be useful in retaining the natural range of ground beetle species across the central Nearctic boreal forest.展开更多
Quadratic mean diameter is the most frequently reported descriptor of the diameter distribution of forests.As such,it is often used as an indicator of forest stand structure,developmental stage,and ecological and econ...Quadratic mean diameter is the most frequently reported descriptor of the diameter distribution of forests.As such,it is often used as an indicator of forest stand structure,developmental stage,and ecological and economic potential.However,quadratic mean diameter can be heavily influenced by the presence or absence of large numbers of small stems in lower canopy strata,and it is also sensitive to left-truncation of the diameter distribution,making its interpretation across inventories with different protocols challenging.Here,we examine three alternative expressions of stand diameter:the arithmetic and quadratic mean diameter of the thickest 100 trees per hectare,and the basal area-weighted mean diameter.Using data from the United States Forest Inventory and Analysis program for New York and New England,these alternative expressions showed closer correlation with multiple stand structural variables than did quadratic mean diameter,including merchantable cubic and board foot volume per hectare,aboveground live tree carbon per hectare,and total number of live and dead standing trees greater than 40 cm diameter at breast height per hectare(previously proposed as an index of old-growth structure).Arithmetic and quadratic mean diameter of the thickest 100 trees per hectare showed nearly identical performance,and the strongest correlations across the board.We develop closed-form expressions for these variables when the diameter distribution is a Weibull,and illustrate their behavior relative to quadratic mean diameter for that situation.While the reasons for prevalence of quadratic mean diameter as an indicator remain valid,we suggest that these alternative measures should be more widely reported and analyzed to give a more informative depiction of stand structure and development in complex forests.展开更多
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.
基金funded by USDA National Institute of Food and Agriculture Hatch Appropriations[#PEN04639,Accession#1015105,EZ]。
文摘Managing mature Douglas-fir[Pseudotsuga menziesii(Mirb.)Franco]stands to emulate the structural complexity of natural old-growth forest requires identifying structural targets at the sub-stand level at which neighborhood dynamics and patchy disturbance shape structure.We therefore sought to describe the archetypal shapes of predominant sub-stand diameter distribution types(DDTs)observed in natural tree neighborhoods in stands comprising a chronosequence(ca.120-450+yrs)encompassing mature,vertical diversification,and horizontal diversification development stages.The ten 1.0 ha stands are located in the southcentral Oregon Cascades,USA.Building on the known spatial position of each tree,natural tree neighborhoods were identified using the floating neighborhood approach based on spatial tessellation connecting neighboring trees at the first-(mean 61 m2)through fifth-(mean 2058 m2)order scales.Cluster analysis was then used to objectively identify the most predominant DDTs among the relative tree size distributions observed in the trans-scale neighborhoods within each stand.Repeated measures regression was used to classify each DDT to one of six observed archetypal shapes:negative exponential,unimodal,rotated sigmoid,bimodal,concave,or multi-modal.Only three of the 81 observed DDTs deviated by<10%from the stand average,while every stand had at least one DDT that deviated by>50%(maximum 83%).Within each stand,five to ten predominant DDTs were observed,which deviated from the stand average by 30-48%and were characterized by two to five different archetypal shapes.Consequently,in some stands the majority of tree neighborhoods were best characterized by a different shape from that assigned at the stand level.Deviation from the stand average increased from the youngest stand in the mature development stage through the middle stands in the vertical diversification stage to the oldest stands in the horizontal diversification stage.The complexity of DDT shapes tended to increase along the chronosequence(from negative exponential and uniform toward concave and multi-modal),with shape richness highest mid-sequence and evenness peaking in the oldest stands.The high diversity of sub-stand structural complexity reduces the utility of standlevel diameter distributions as old-growth restoration targets.However,the presence in early-sequence stands of sub-stand diameter distributions common to later-sequence stands may facilitate active management at the neighborhood level to promote future old-growth condition.Restoration of substand diameter structures would likely require combining spatial perspectives,such as by augmenting tree-level croptree management with diameter distribution targets for the resulting tree neighborhoods.
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 Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.
文摘We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.
基金provided by the Forestry Futures Trust,Tembec,Inc.,Lake Abitibi Model Forest,Ontario Ministry of Natural Resources,National Science and Engineering Research Council of Canada,and the University of Toronto
文摘Multi-cohort management （MCM） that retains a range of stand structures （age and size class） has been proposed to emulate natural disturbance and improve management in the Nearctic boreal forest. Although MCM forests contain both single- and multi-aged stands of mixed tree sizes, little is known about how variable stand structure affects associated fauna and biodiversity. Here, we examine the relationship between ground beetle （Coleoptera, Carabidae） communities and stand characteristics across a range of forest structure （=cohort classes）. Given that MCM classes are defined by the distribution of their tree-stem diameters, we ask whether parameters associated with these distributions （Weibull） could explain observed variation in carabid communities, and if so, how this compares to traditional habitat variables such as stand age, foliage complexity or volume of downed woody debris. We sampled carabids using weekly pitfall collections and compared these with structural habitat variables across a range of cohort classes （stand structure and age since disturbance） in 18 sites of upland mixed boreal forests from central Canada. Results showed that richness and diversity of carabid communities were similar among cohort classes. Weibull parameters from the diameter distribution of all stems were the strongest predictors of variation in carabid communities among sites, but vertical foliage complexity, understory thickness, and percentage of deciduous composition were also significant. The abundance of several carabid forest specialists was strongly correlated with tree canopy height, the presence of large trees, and high vertical foliage complexity. Our results demonstrate that variable forest structure, as expected under MCM, may be useful in retaining the natural range of ground beetle species across the central Nearctic boreal forest.
基金Support was provided by the New Hampshire Agricultural Experiment Station.This is Scientific Contribution Number 2978supported by the USDA National Institute of Food and Agriculture,McIntire-Stennis Project 7003549
文摘Quadratic mean diameter is the most frequently reported descriptor of the diameter distribution of forests.As such,it is often used as an indicator of forest stand structure,developmental stage,and ecological and economic potential.However,quadratic mean diameter can be heavily influenced by the presence or absence of large numbers of small stems in lower canopy strata,and it is also sensitive to left-truncation of the diameter distribution,making its interpretation across inventories with different protocols challenging.Here,we examine three alternative expressions of stand diameter:the arithmetic and quadratic mean diameter of the thickest 100 trees per hectare,and the basal area-weighted mean diameter.Using data from the United States Forest Inventory and Analysis program for New York and New England,these alternative expressions showed closer correlation with multiple stand structural variables than did quadratic mean diameter,including merchantable cubic and board foot volume per hectare,aboveground live tree carbon per hectare,and total number of live and dead standing trees greater than 40 cm diameter at breast height per hectare(previously proposed as an index of old-growth structure).Arithmetic and quadratic mean diameter of the thickest 100 trees per hectare showed nearly identical performance,and the strongest correlations across the board.We develop closed-form expressions for these variables when the diameter distribution is a Weibull,and illustrate their behavior relative to quadratic mean diameter for that situation.While the reasons for prevalence of quadratic mean diameter as an indicator remain valid,we suggest that these alternative measures should be more widely reported and analyzed to give a more informative depiction of stand structure and development in complex forests.
文摘为探究封育保护后具有人工经营背景森林的群落结构和物种多样性在自然更替过程中的变化规律,以鄂西南地区的百户湾林场内0.01 km^(2)针阔混交林固定监测样地为研究对象,对木本植物的物种组成、群落结构和物种多样性进行调查与分析。结果表明,样地内胸径(diameter at breast height,DBH)≥1 cm的木本植物有8702株,隶属于39科66属111种;重要值排名前10位的物种中,常绿阔叶树种占明显优势;林冠层优势种为杉木(Cunninghamia lanceolata)和枹栎(Quercus serrata),灌木层优势种为翅柃(Eurya alata);样地内个体数量随DBH值增加而逐渐减少,小径级个体较多,平均DBH为5.2 cm;样地内物种较为丰富,各层级中亚乔木层的物种多样性最高。该研究为进一步探究森林群落结构和物种多样性的动态变化提供了科学依据。
