An approach to modeling the joint distribution of tree diameter and height data

Ogana, Friday Nwabueze; Osho, J.S.A.; Gorgoso-Varela, José Javier

doi:10.1080/10549811.2017.1422434

Cited by 15 publications

(8 citation statements)

References 22 publications

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“…Capitani et al [9] showed a bivariate Burr Type III copula to the trivariate case. Ogana et al [10] considered Frank and Plackett copulas; the two copulas were evaluated on seven distributions models using data from temperate and tropical forests where one of the seven distributions is BBIII distribution. Azizi and Sayyareh [11] constructed bivariate BBIII using Marshall and Olkin [12] technique as they presented some properties and estimated the parameters using maximum likelihood (ML) method.…”

Section: Original Research Articlementioning

confidence: 99%

Bivariate Burr Type III Distribution: Estimation and Prediction

Mahmoud

Refaey

AL-Dayian

et al. 2021

JAMCS

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In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

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Section: Original Research Articlementioning

confidence: 99%

Bivariate Burr Type III Distribution: Estimation and Prediction

Mahmoud

Refaey

AL-Dayian

et al. 2021

JAMCS

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“…More forest statisticians promote the use of bivariate distribution (diameter and height) for the derivation of the static height-diameter equation [26,27]. The mathematical description of the diameter or height distribution provides more detailed information about the stand [28].…”

Section: Sde Modelsmentioning

confidence: 99%

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

2020

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This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania.

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Section: Models Of the Number Of Trees Per Hectare Quadratic Mean DImentioning

confidence: 99%

“…This statement confirms that univariate stand size component relationships are unsatisfactory for the modeling of stand volume and biomass. The limitation of univariate methods for the frequency analysis of diameter (or height) has attracted the attention of foresters in recent decades [39,40]. Moreover, it is necessary to consider multivariate probability problems, since they can easily connect univariate marginal and conditional distribution probability density functions of stand density, quadratic mean diameter and mean height with their multivariate probability distributions.…”

Section: Models Of the Number Of Trees Per Hectare Quadratic Mean DImentioning

confidence: 99%

Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

Rupšys

2019

Forests

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Research Highlights: Today’s approaches to modeling of forest stands are in most cases based on that the regression models and they are constructed as static sub-models describing individual stands variables. The disadvantages of this method; it is laborious because too many different equations need to be assessed and empirical choices of candidate equations make the results subjective; it does not relate to the stand variables dynamics against the age dimension (time); and does not consider the underlying covariance structure driving changes in the stand variables. In this study, the dynamical model defined by a fixed-and mixed effect parameters trivariate stochastic differential equation (SDE) is introduced and described how such a model can be used to model quadratic mean diameter, mean height, number of trees per hectare, self-thinning line, stand basal area, stand volume per hectare and much more. Background and Objectives: New developed marginal and conditional trivariate probability density functions, combining information generated from an age-dependent variance-covariance matrix of quadratic mean diameter, mean height and number of trees per hectare, improve stand growth prediction, and forecast (in forecast the future is completely unavailable and must only be estimated from historical patterns) accuracies. Materials and Methods: Fixed-and mixed effect parameters SDE models were harmonized to predict and forecast the dynamics of quadratic mean diameter, mean height, number of trees per hectare, basal area, stand volume per hectare, and their current and mean increments. The results and experience from applying the SDE concepts and techniques in an extensive whole stand growth and yield analysis are described using a Scots pine (Pinus sylvestris L.) experimental dataset in Lithuania. Results: The mixed effects scenario SDE model showed high accuracy, the percentage root mean square error values for quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare predictions (forecasts) were 3.37% (10.44%), 1.82% (2.07%), 1.76% (2.93%), 6.65% (10.41%) and 6.50% (8.93%), respectively. In the same way, the quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare prediction (forecast) relationships had high values of the coefficient of determination, R2, 0.998 (0.987), 0.997 (0.992), 0.997 (0.988), 0.968 (0.984) and 0.966 (0.980), respectively. Conclusions: The approach presented in this paper can be used for developing a new generation stand growth and yield models.

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An approach to modeling the joint distribution of tree diameter and height data

Cited by 15 publications

References 22 publications

Bivariate Burr Type III Distribution: Estimation and Prediction

Bivariate Burr Type III Distribution: Estimation and Prediction

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

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