Pekka Kilkki, Matti Maltamo, Reijo Mykkänen, Risto Päivinen. (1989). Use of the Weibull function in estimating the basal area dbh-distribution. Silva Fennica vol. 23 no. 4 article id 5392. https://doi.org/10.14214/sf.a15550

Keywords: Picea abies; distribution; diameter; Weibull function; maximum likelihood; estimation

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The paper continues an earlier study by Kilkki and Päivinen concerning the use of the Weibull function in modelling the diameter distribution. The data consists of spruces (Picea abies (L.) H. Karst.) measured on angle count sample points of the National Forest Inventory of Finland. First, maximum likelihood estimation method was used to derive the Weibull parameters. Then, regression models to predict the values of these parameters with stand characteristics were calculated. Several methods to describe the Weibull function by a tree sample were tested. It is more efficient to sample the trees at equal frequency intervals than at equal diameter intervals. It also pays to take separate samples for pulpwood and saw timber.

The PDF includes an abstract in Finnish.

Kilkki, E-mail: pk@mm.unknown
Maltamo, E-mail: mm@mm.unknown
Mykkänen, E-mail: rm@mm.unknown
Päivinen, E-mail: rp@mm.unknown

article id 5270, category Article

Pekka Kilkki, Risto Päivinen. (1986). Weibull function in the estimation of the basal area dbh-distribution. Silva Fennica vol. 20 no. 2 article id 5270. https://doi.org/10.14214/sf.a15449

Keywords: Pinus sylvestris; diameter distribution; beta function; nonlinear regression; maximum likelihood; initial parameter estimates; relascope sample plot

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The paper demonstrates the possibility of using data from small relascope sample plots in the derivation of the regression models which predict the Weibull function parameters for the dbh-distribution. The Weibull parameters describing the basal area dbh-distribution were estimated for relascope sample plots from the Finnish National Forest Inventory. In the first stage of the estimation nonlinear regression analysis was employed to derive initial parameter estimates for the second stage, in which the maximum likelihood method was used. The parameter estimates were employed as dependent variables for the derivation of the regression models; the independent variables comprised of the compartment-wise stand variables generally estimated in ocular inventories.

The PDF includes an abstract in Finnish.

Kilkki, E-mail: pk@mm.unknown
Päivinen, E-mail: rp@mm.unknown

Category : Research article

article id 956, category Research article

Michał Zasada. (2013). Evaluation of the double normal distribution for tree diameter distribution modeling. Silva Fennica vol. 47 no. 2 article id 956. https://doi.org/10.14214/sf.956

Keywords: diameter distribution; simulated annealing; goodness-of-fit; Weibull distribution; maximum likelihood method; method of moments

Abstract | Full text in HTML | Full text in PDF | Author Info

The double normal distribution consists of two normal distributions truncated at their means and then combined in such a way, that points of truncation now become the overall distribution mode. So far, parameters of the double normal distribution have been estimated exclusively using the method of moments. This study evaluates the maximum likelihood method for the estimation of the double normal distribution parameters in Scots pine stands in Poland, and compares it to the results of the method of moments and the two-parameter Weibull distribution fitted using the maximum likelihood method and the method of moments. Presented results show that it is not recommended to use the maximum likelihood method of parameter fitting with Nelder-Mead and quasi-Newton optimization algorithms for the double normal distribution for small samples. However, it can be used for large samples, giving the fit comparable to the two-parameter Weibull distribution and providing parameters having sound practical and biological meaning. In the case of smaller samples for the double normal distribution it is recommended to apply the maximum likelihood method with the alternative simulated annealing optimization algorithm, use the method of moments or substitute the described distribution with more the flexible and robust Weibull distribution. For the smaller samples, the method of moments was superior to the maximum likelihood method.

Zasada, Warsaw University of Life Sciences, Faculty of Forestry, Laboratory of Dendrometry and Forest Productivity, Nowoursynowska 159, 02-776 Warsaw, Poland E-mail: michal.zasada@wl.sggw.pl

article id 618, category Research article

Steen Magnussen, Paul Boudewyn, Mike Wulder, David Seemann. (2000). Predictions of forest inventory cover type proportions using Landsat TM. Silva Fennica vol. 34 no. 4 article id 618. https://doi.org/10.14214/sf.618

Keywords: neural net; maximum likelihood classification; agreement of predictions

Abstract | View details | Full text in PDF | Author Info

The feasibility of generating via Landsat TM data current estimates of cover type proportions for areas lacking this information in the national forest inventory was explored by a case study in New Brunswick. A recent forest management inventory covering 4196 km2 in south-eastern New Brunswick (the test area) and a coregistered Landsat TM scene was used to develop predictive models of 12 cover type proportions in an adjacent 4525 km2 region (the validation area). Four prediction models were considered, one using a maximum likelihood classifier (MLC), and three using the proportions of 30 TM clusters as predictors. The MLC was superior for non-vegetated cover types while a neural net or a prorating of cluster proportions was chosen for predicting vegetated cover types. Most predictions generated for national inventory photo-plots of 2 x 2 km were closer to the most recent inventory results than estimates extrapolated from the test area. Agreement between predictions and current inventory results varied considerably among cover types with model-based predictions outperforming, on average, the simple spatial extensions by about 14%. In this region, an 11-year-old forest inventory for the validation area provided estimates that in half the cases were closer to current inventory estimates than predictions using the optimal Landsat TM model. A strong temporal correlation of photo-plot-level cover type proportions made old-values more consistent than predictions using the optimal Landsat TM model in all but three cases. Prorating of cluster proportions holds promise for large-scale multi-sensor predictions of forest inventory cover types.

Magnussen, Canadian Forest Service, 506 West Burnside Road, Victoria B.C., Canada V8Z 1M5 E-mail: smagnussen@pfc.forestry.ca
Boudewyn, Canadian Forest Service, 506 West Burnside Road, Victoria B.C., Canada V8Z 1M5 E-mail: pb@nn.ca
Wulder, Canadian Forest Service, 506 West Burnside Road, Victoria B.C., Canada V8Z 1M5 E-mail: mw@nn.ca
Seemann, Canadian Forest Service, 506 West Burnside Road, Victoria B.C., Canada V8Z 1M5 E-mail: ds@nn.ca

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