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Diameter-Distribution Models for Even-Aged Stands

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Abstract

Overall stand volume is sufficient for many purposes, but effective forest management and planning often requires information about the distribution of volume by size and product classes. This chapter provides an in-depth treatment of techniques for estimating yields by size class using a distribution function approach. In typical applications, the total number of trees per unit area is distributed through the use of a probability density function, which provides the relative frequency of trees by diameters. Mean total tree heights are predicted for trees of given diameters growing under specified stand conditions. Volume per diameter class is calculated by substituting the predicted mean tree heights and the diameter class midpoints into tree volume equations. Yield estimates are obtained by summing the diameter classes of interest. Detailed treatment is provided on selecting a distribution function, characterizing diameter distributions using parameter prediction and parameter recovery, modeling height-diameter relationships, and predicting unit area tree survival.

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References

  • Affleck DLR (2006) Poisson mixture models for regression analysis of stand-level mortality. Can J For Res 36:2994–3006

    Article  Google Scholar 

  • Amateis RL, Burkhart HE, Knoebel BR, Sprinz PT (1984) Yields and size class distributions for unthinned loblolly pine plantations on cutover site-prepared lands. Virginia Polytechnic Institute and State University, Blacksburg, Pub. FWS-2–84

    Google Scholar 

  • Amateis RL, Burkhart HE, Burk TE (1986) A ratio approach to predicting merchantable yields of unthinned loblolly pine plantations. For Sci 32:287–296

    Google Scholar 

  • Amateis RL, Burkhart HE, Liu J (1997) Modeling survival in juvenile and mature loblolly pine plantations. For Ecol Manage 90:51–58

    Article  Google Scholar 

  • Arabatzis AA, Burkhart HE (1992) An evaluation of sampling methods and model forms for estimating height-diameter relationships in loblolly pine plantations. For Sci 38:192–198

    Google Scholar 

  • Avery TE, Burkhart HE (2002) Forest measurements, 5th edn. McGraw-Hill, New York

    Google Scholar 

  • Bailey RL (1980) Individual tree growth derived from diameter distribution models. For Sci 26:626–632

    Google Scholar 

  • Bailey RL, Dell TR (1973) Quantifying diameter distributions with the Weibull function. For Sci 19:97–104

    Google Scholar 

  • Bailey RL, Burgan TM, Jokela EJ (1989) Fertilized mid-rotation-aged slash pine plantations- stand structure and yield prediction models. South J Appl For 13:76–80

    Google Scholar 

  • Baldwin VC Jr, Feduccia DP (1987) Loblolly pine growth and yield prediction for managed west Gulf plantations. USDA Forest Service, New Orleans, Research Paper SO-236

    Google Scholar 

  • Beck DE, Della-Bianca L (1970) Yield of unthinned yellow-poplar. USDA Forest Service, Asheville, Research Paper SE-58

    Google Scholar 

  • Bennett FA, Clutter JL (1968) Multiple-product yield estimates for unthinned slash pine plantations – pulpwood, sawtimber, gum. USDA Forest Service, Asheville, Research Paper SE-35

    Google Scholar 

  • Bliss CI, Reinker KA (1964) A lognormal approach to diameter distributions in even-aged stands. For Sci 10:350–360

    Google Scholar 

  • Borders BE (1989) Systems of equations in forest stand modeling. For Sci 35:548–556

    Google Scholar 

  • Borders BE, Patterson WD (1990) Projecting stand tables: a comparison of the Weibull diameter distribution method, a percentile-based projection method, and a basal area growth projection method. For Sci 36:413–424

    Google Scholar 

  • Borders BE, Souter RA, Bailey RL, Ware KD (1987) Percentile-based distributions characterize forest stand tables. For Sci 33:570–576

    Google Scholar 

  • Bowling EH, Burkhart HE, Burk TE, Beck DE (1989) A stand-level multispecies growth model for Appalachian hardwoods. Can J For Res 19:405–412

    Article  Google Scholar 

  • Brooks JR, Borders BE, Bailey RL (1992) Predicting diameter distributions for site-prepared loblolly and slash pine plantations. South J Appl For 16:130–133

    Google Scholar 

  • Budhathoki CB, Lynch TB, Guldin JM (2008) A mixed-effects model for the dbh-height relationship of shortleaf pine (Pinus echinata Mill.). South J Appl For 32:5–11

    Google Scholar 

  • Bullock BP, Boone EL (2007) Deriving tree distributions using Bayesian model averaging. For Ecol Manage 242:127–132

    Article  Google Scholar 

  • Bullock BP, Burkhart HE (2005) Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function. New For 29:233–244

    Article  Google Scholar 

  • Burk TE, Burkhart HE (1984) Diameter distributions and yields of natural stands of loblolly pine. Virginia Polytechnic Institute and State University, Blacksburg, Pub FWS-1–84

    Google Scholar 

  • Burk TE, Newberry JD (1984) A simple algorithm for moment-based recovery of Weibull distribution parameters. For Sci 30:329–332

    Google Scholar 

  • Burkhart HE (1971) Slash pine plantation yield estimates based on diameter distribution: An evaluation. For Sci 17:452–453

    Google Scholar 

  • Burkhart HE, Strub MR (1974) A model for simulation of planted loblolly pine stands. In: Fries J (ed) Growth models for tree and stand simulation, Research notes 30. Royal College of Forestry, Stockholm, pp 128–135

    Google Scholar 

  • Calama R, Montero G (2004) Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Can J For Res 34:150–163

    Article  Google Scholar 

  • Cao QV (2004) Predicting parameters of a Weibull function for modeling diameter distribution. For Sci 50:682–685

    Google Scholar 

  • Cao QV, Burkhart HE (1984) A segmented distribution approach for modeling diameter frequency data. For Sci 30:129–137

    Google Scholar 

  • Cao QV, Burkhart HE, Lemin RC Jr (1982) Diameter distributions and yields of thinned loblolly pine plantations. Virginia Polytechnic Institute and State University, Blacksburg, Pub FWS-1–82

    Google Scholar 

  • Chen W (2004) Tree size distribution functions of four boreal forest types for biomass mapping. For Sci 50:436–449

    Google Scholar 

  • Clutter JL, Bennett FA (1965) Diameter distributions in old-field slash pine plantations. Georgia Forest Research Council, Macon. Report 13

    Google Scholar 

  • Clutter JL, Jones EP Jr (1980) Prediction of growth after thinning in old-field slash pine plantations. USDA Forest Service, Asheville, Research Paper SE-217

    Google Scholar 

  • Clutter JL, Harms WR, Brister GH, Rheney JW (1984) Stand structure and yields of site-prepared loblolly pine plantations in the lower coastal plain of the Carolinas, Georgia, and north Florida. USDA Forest Service, Asheville, General Technical Report SE-27

    Google Scholar 

  • Coble DW, Lee Y-J (2011) A mixed-effects height-diameter model for individual loblolly and slash pine trees in East Texas. South J Appl For 35:12–17

    Google Scholar 

  • Crecente-Campo F, Tomé M, Soares P, Diéguez-Aranda U (2010) A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globules L. in northwestern Spain. For Ecol Manage 256:943–952

    Article  Google Scholar 

  • Curtis RO (1967) Height-diameter and height-diameter-age equations for second-growth Douglas-fir. For Sci 13:365–375

    Google Scholar 

  • Dell TR, Fedducia DP, Campbell TE, Mann WF Jr, Polmer BH (1979) Yields of unthinned slash pine plantations on cutover sites in the west Gulf region. USDA Forest Service, New Orleans, Research Paper SO-147

    Google Scholar 

  • Devine JO, Clutter JL (1985) Prediction of survival in slash pine plantations infected with fusiform rust. For Sci 31:88–94

    Google Scholar 

  • Droessler TD, Burk TE (1989) A test of nonparametric smoothing of diameter distributions. Scand J For Res 4:407–415

    Article  Google Scholar 

  • Ek AR, Issos JN, Bailey RL (1975) Solving for Weibull diameter distribution parameters to obtain specified mean diameters. For Sci 21:290–292

    Google Scholar 

  • Farrar RM Jr, Matney TG (1994) A dual growth simulator for natural even-aged stands of longleaf pine in the South’s East Gulf region. South J Appl For 18:147–155

    Google Scholar 

  • Fast AJ, Ducey MJ (2011) Height-diameter equations for select New Hampshire tree species. North J Appl For 28:157–160

    Google Scholar 

  • Feduccia DP, Dell TR, Mann WF Jr, Campbell TE, Polmer BH (1979) Yields of unthinned loblolly pine plantations on cutover sites in the west Gulf region. USDA Forest Service, New Orleans, Research Paper SO-148

    Google Scholar 

  • Garcia O (1981) Simplified method-of-moments for the Weibull distribution. NZ J For Sci 11:304–306

    Google Scholar 

  • Gertner G, Cao X, Zhu H (1995) A quality assessment of a Weibull based growth projection system. For Ecol Manage 71:235–250

    Article  Google Scholar 

  • Green EJ, Burkhart HE, Clason TR (1984) A model for basal area distribution in loblolly pine. For Sci 30:617–628

    Google Scholar 

  • Haara A, Maltamo M, Tokola T (1997) The k-nearest-neighbor method for estimating basal area diameter distribution. Scand J For Res 12:200–208

    Article  Google Scholar 

  • Hafley WL, Buford MA (1985) A bivariate model for growth and yield prediction. For Sci 31:237–247

    Google Scholar 

  • Hafley WL, Schreuder HT (1977) Statistical distributions for fitting diameter and height data in even-aged stands. Can J For Res 7:481–487

    Article  Google Scholar 

  • Huang S, Titus SJ, Wiens DP (1992) Comparison of nonlinear height-diameter functions for major Alberta tree species. Can J For Res 22:1297–1304

    Article  Google Scholar 

  • Huang S, Price D, Titus S (2000) Development of ecoregion-based height-diameter models for white spruce in boreal forests. For Ecol Manage 129:125–141

    Article  Google Scholar 

  • Hyink DM (1980) Diameter distribution approaches to growth and yield modeling. In: Brown KM, Clarke FR (eds) Forecasting forest stand dynamics. Lakehead University School of Forestry, Thunderbay, pp 138–163

    Google Scholar 

  • Hyink DM, Moser JW Jr (1983) A generalized framework for projecting forest yield and stand structure using diameter distributions. For Sci 29:85–95

    Google Scholar 

  • Jiang L, Brooks JR (2009) Predicting diameter distributions for young longleaf pine plantations in southwest Georgia. South J Appl For 33:25–28

    Google Scholar 

  • Johnson NL (1949a) Systems of frequency curves generated by methods of translation. Biometrika 36:149–176

    PubMed  CAS  Google Scholar 

  • Johnson NL (1949b) Bivariate distributions based on simple translation systems. Biometrika 36:297–304

    PubMed  CAS  Google Scholar 

  • Kangas A, Maltamo M (2000) Calibrating predicted diameter distribution with additional information. For Sci 46:390–396

    Google Scholar 

  • Knoebel BR, Burkhart HE (1991) A bivariate distribution approach to modeling Forest diameter distributions at two points in time. Biometrics 47:241–253

    Article  Google Scholar 

  • Knoebel BR, Burkhart HE, Beck DE (1986) A growth and yield model for thinned stands of yellow-poplar. For Sci Monogr 27:64

    Google Scholar 

  • Knowe SA (1992) Basal area and diameter distribution models for loblolly pine plantations with hardwood competition in the Piedmont and upper coastal plain. South J Appl For 16:93–98

    Google Scholar 

  • Knowe SA, Stein WI (1995) Predicting the effects of site preparation on development of young Douglas-fir plantations. Can J For Res 25:1538–1547

    Article  Google Scholar 

  • Knowe SA, Foster GS, Rousseau RJ, Nance WL (1994) Eastern cottonwood clonal mixing study: predicted diameter distributions. Can J For Res 24:405–414

    Article  Google Scholar 

  • Krug AG, Nordheim EV, Giese RL (1984) Determining initial values for parameters of a Weibull model: case study. For Sci 30:573–581

    Google Scholar 

  • Lane SE, Robinson AP, Baker TG (2010) The functional regression tree method for diameter distribution modelling. Can J For Res 40:1870–1877

    Article  Google Scholar 

  • Lappi J (1997) A longitudinal analysis of height/diameter curves. For Sci 43:555–570

    Google Scholar 

  • Leduc DJ, Matney TG, Belli KL, Baldwin VC Jr (2001) Predicting diameter distributions of longleaf pine plantations: a comparison between artificial neural networks and other accepted methodologies. USDA Forest Service, Asheville, Research Paper SRS-25

    Google Scholar 

  • Lei Y, Parresol BR (2001) Remarks on height-diameter modeling. USDA Forest Service, Asheville, Research Note SRS-10

    Google Scholar 

  • Lemin RC Jr, Burkhart HE (1983) Predicting mortality after thinning in old-field loblolly pine plantations. South J Appl For 7:20–23

    Google Scholar 

  • Lenhart JD (1988) Diameter-distribution yield-prediction system for unthinned loblolly and slash pine plantations on non-old-fields in East Texas. South J Appl For 12:239–242

    Google Scholar 

  • Lenhart JD, Clutter JL (1971) Cubic-foot yield tables for old-field loblolly pine plantations in the Georgia Piedmont. Georgia Forest Research Council, Macon, Report 22 – Series 3

    Google Scholar 

  • Little SN (1983) Weibull diameter distributions for mixed stands of western conifers. Can J For Res 13:85–88

    Article  Google Scholar 

  • Liu C, Zhang L, Davis CJ, Solomon DS, Gove JH (2002) A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. For Sci 48:653–661

    Google Scholar 

  • Liu C, Zhang SY, Lei Y, Newton PF, Zhang L (2004) Evaluation of three methods for predicting diameter distributions of black spruce (Picea mariana) plantations in central Canada. Can J For Res 34:2424–2432

    Article  Google Scholar 

  • Liu C, Beaulieu J, Prégent G, Zhang SY (2009) Applications and comparison of six methods for predicting parameters of the Weibull function in unthinned Picea glauca plantations. Scand J For Res 24:67–75

    Article  Google Scholar 

  • Lu J, Zhang L (2011) Modeling and prediction of tree height-diameter relationships using spatial autoregressive models. For Sci 57:252–264

    Google Scholar 

  • Lynch TB, Murphy PA (1995) A compatible height prediction and projection system for individual trees in natural, even-aged shortleaf pine stands. For Sci 41:194–209

    Google Scholar 

  • Magnussen S (1986) Diameter distributions in Picea abies described by the Weibull model. Scand J For Res 1:493–502

    Article  Google Scholar 

  • Maltamo M (1997) Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand. Silva Fenn 31:53–65

    Google Scholar 

  • Maltamo M, Kangas A (1998) Methods based on k-nearest neighbor regression in estimation of basal area diameter distribution. Can J For Res 28:1107–1115

    Article  Google Scholar 

  • Maltamo M, Puumalainen J, Päivinen R (1995) Comparison of beta and Weibull functions for modelling basal area diameter distribution in stands of Pinus sylvestris and Picea abies. Scand J For Res 10:284–295

    Article  Google Scholar 

  • Maltamo M, Kangas A, Uuttera J, Torniainen T, Saramäki J (2000) Comparison of percentile based prediction methods and the Weibull distribution in describing the diameter distribution of heterogeneous Scots pine stands. For Ecol Manage 133:263–274

    Article  Google Scholar 

  • Mateus A, Tomé M (2011) Modelling the diameter distribution of eucalyptus plantations with Johnson’s S B probability density function: parameters recovery from a compatible system of equations to predict stand variables. Ann For Sci 68:325–335

    Article  Google Scholar 

  • Matney TG, Farrar RM Jr (1992) A thinned/unthinned loblolly pine growth and yield simulator for planted cutover site-prepared land in the Mid-Gulf South. South J Appl For 16:70–75

    Google Scholar 

  • Matney TG, Sullivan AD (1982) Compatible stand and stock tables for thinned and unthinned loblolly pine stands. For Sci 28:161–171

    Google Scholar 

  • Matney TG, Ledbetter JR, Sullivan AD (1987) Diameter distribution yield systems for unthinned cutover site-prepared slash pine plantations in southern Mississippi. South J Appl For 11:32–36

    Google Scholar 

  • McGee CE, Della-Bianca L (1967) Diameter distributions in natural yellow-poplar stands. USDA Forest Service, Asheville, Research Paper SE-25

    Google Scholar 

  • McTague JP, Bailey RL (1987) Compatible basal area and diameter distribution models for thinned loblolly pine plantations in Santa Catarina. Brazil For Sci 33:43–51

    Google Scholar 

  • Mehtätalo L (2004) A longitudinal height-diameter model for Norway spruce in Finland. Can J For Res 34:131–140

    Article  Google Scholar 

  • Mehtätalo L, Gregoire TG, Burkhart HE (2008) Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics 19:529–548

    Article  Google Scholar 

  • Meng Q, Cieszewski CJ, Strub MR, Borders BE (2009) Spatial regression modeling of tree height-diameter relationships. Can J For Res 39:2283–2293

    Article  Google Scholar 

  • Meyer HA (1940) A mathematical expression for height curves. J For 38:415–420

    Google Scholar 

  • Mønness E (2011) The power-normal distribution: application to forest stands. Can J For Res 41:707–714

    Article  Google Scholar 

  • Nanang DM (1998) Suitability of the normal, log-normal and Weibull distributions for fitting diameter distributions of neem plantations in northern Ghana. For Ecol Manage 103:1–7

    Article  Google Scholar 

  • Nelson TC (1964) Diameter distribution and growth of loblolly pine. For Sci 10:105–114

    Google Scholar 

  • Newton PF, Amponsah IG (2007) Comparative evaluation of five height-diameter models developed for black spruce and jack pine stand-types in terms of goodness-of-fit, lack-of-fit and predictive ability. For Ecol Manage 247:149–166

    Article  Google Scholar 

  • Newton PF, Lei Y, Zhang SY (2005) Stand-level diameter distribution yield model for black spruce plantations. For Ecol Manage 209:181–192

    Article  Google Scholar 

  • Nordhausen K, Nummi T (2007) Estimation of the diameter distribution of a stand marked for cutting using finite mixtures. Can J For Res 37:817–824

    Article  Google Scholar 

  • Nord-Larsen T, Cao QV (2006) A diameter distribution model for even-aged beech in Denmark. For Ecol Manage 231:218–225

    Article  Google Scholar 

  • Palahí M, Pukkala T, Blasco E (2007) Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east Spain). Eur J For Res 126:563–571

    Article  Google Scholar 

  • Paulo JA, Tomé J, Tomé M (2011) Nonlinear fixed and random generalized height-diameter models for Portuguese cork oak stands. Ann For Sci 68:295–309

    Article  Google Scholar 

  • Pienaar LV, Harrison WM (1988) A stand table projection approach to yield prediction in unthinned even-aged stands. For Sci 34:804–808

    Google Scholar 

  • Pienaar LV, Shiver BD (1981) Survival functions for site-prepared slash pine plantations in the flatwoods of Georgia and northern Florida. South J Appl For 5:59–62

    Google Scholar 

  • Pienaar LV, Page HH, Rheney JW (1990) Yield prediction for mechanically site-prepared slash pine plantations. South J Appl For 14:104–109

    Google Scholar 

  • Podlaski R (2010) Two-component mixture models for diameter distributions in mixed-species, two-age cohort stands. For Sci 56:379–390

    Google Scholar 

  • Rennolls K, Wang M (2005) A new parameterization of Johnson’s SB distribution with application to fitting forest tree diameter data. Can J For Res 35:575–579

    Article  Google Scholar 

  • Reynolds MR Jr, Burk TE, Huang WC (1988) Goodness-of-fit tests and model selection procedures for diameter distribution models. For Sci 34:373–399

    Google Scholar 

  • Rose CE Jr, Clutter ML, Shiver BD, Hall DB, Borders B (2004) A generalized methodology for developing whole-stand survival models. For Sci 50:686–695

    Google Scholar 

  • Rupšus P, Petrauskas E (2010) The bivariate gompertz diffusion model for tree diameter and height distribution. For Sci 56:271–280

    Google Scholar 

  • Russell MB, Amateis RL, Burkhart HE (2010) Implementing regional locale and thinning response in the loblolly pine height-diameter relationship. South J Appl For 34:21–27

    Google Scholar 

  • Sarkkola S, Hökkä H, Laiho R, Päivänen J, Penttilä T (2005) Stand structural dynamics on drained peatlands dominated by Scots pine. For Ecol Manage 206:135–152

    Article  Google Scholar 

  • Schreuder HT, Hafley WL (1977) A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics 33:471–478

    Article  Google Scholar 

  • Schreuder HT, Swank WT (1974) Coniferous stands characterized with the Weibull distribution. Can J For Res 4:518–523

    Article  Google Scholar 

  • Schreuder HT, Hafley WL, Bennett FA (1979) Yield prediction for unthinned natural slash pine stands. For Sci 25:25–30

    Google Scholar 

  • Scolforo JRS, Tabai FCV, Grisi de Macedo RL, Acerbi WF Jr, Leandra de Assis A (2003) SB distribution’s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods. For Ecol Manage 175:489–496

    Article  Google Scholar 

  • Sharma M, Parton J (2007) Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. For Ecol Manage 249:187–198

    Article  Google Scholar 

  • Shiver BD (1988) Sample sizes and estimation methods for the Weibull distribution for unthinned slash pine plantation diameter distributions. For Sci 34:809–814

    Google Scholar 

  • Siipilehto J (1999) Improving the accuracy of predicted basal-area diameter distribution in advanced stands by determining stem number. Silva Fennica 33:281–301

    Google Scholar 

  • Siipilehto J, Sakari S, Mehtätalo L (2007) Comparing regression estimation techniques when predicting diameter distributions of Scots pine on drained peatlands. Silva Fennica 41:333–349

    Google Scholar 

  • Smalley GW, Bailey RL (1974a) Yield tables and stand structure for loblolly pine plantations in Tennessee, Alabama, and Georgia highlands. USDA Forest Service, New Orleans, Research Paper SO-96

    Google Scholar 

  • Smalley GW, Bailey RL (1974b) Yield tables and stand structure for shortleaf pine plantations in Tennessee, Alabama, and Georgia highlands. USDA Forest Service, New Orleans, Research Paper SO-97

    Google Scholar 

  • Soares P, Tomé M (2002) Height-diameter equation for first rotation eucalypt plantations in Portugal. For Ecol Manage 166:99–109

    Article  Google Scholar 

  • Somers GL, Oderwald RG, Harms WR, Langdon OG (1980) Predicting mortality with a Weibull distribution. For Sci 26:291–300

    Google Scholar 

  • Stankova TV, Zlatanov TM (2010) Modeling diameter distribution of Austrian black pine (Pinus nigra Arn.) plantations: a comparison of the Weibull frequency distribution function and percentile-based projection methods. Eur J For Res 129:1169–1179

    Article  Google Scholar 

  • Staudhammer C, LeMay V (2000) Height prediction equations using diameter and stand density measures. For Chron 76:303–309

    Google Scholar 

  • Stauffer HB (1979) A derivation for the Weibull distribution. J Theor Biol 81:55–63

    Article  PubMed  CAS  Google Scholar 

  • Strub MR, Burkhart HE (1975) A class-interval-free method for obtaining expected yields from diameter distributions. For Sci 27:67–69

    Google Scholar 

  • Sullivan AD, Clutter JL (1972) A simultaneous growth and yield model for loblolly pine. For Sci 18:76–86

    Google Scholar 

  • Temesgen H, Hann DW, Monleon VJ (2007) Regional height-diameter equations for major tree species of Southwest Oregon. West J Appl For 22:213–219

    Google Scholar 

  • Temesgen H, Monleon VJ, Hann DW (2008) Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests. Can J For Res 38:553–565

    Article  Google Scholar 

  • Tewari VP, Gadow Kv (1999) Modelling the relationship between tree diameters and height using SBB distribution. For Ecol Manage 119:171–176

    Article  Google Scholar 

  • Tham Å (1988) Structure of mixed Picea abies (L.) Karst. and Betula pendula Roth and Betula pubescens Ehrh. stands in south and middle Sweden. Scand J For Res 3:355–370

    Article  Google Scholar 

  • Thomas V, Oliver RD, Lim K, Woods M (2008) LiDAR and Weibull modeling of diameter and basal area. For Chron 84:866–875

    Google Scholar 

  • Trincado G, VanderSchaaf CL, Burkhart HE (2007) Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. Eur J For Res 126:253–262

    Article  Google Scholar 

  • Wang M, Upadhyay A, Zhang L (2010) Trivariate distribution modeling of tree diameter, height, and volume. For Sci 56:290–300

    Google Scholar 

  • Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297

    Google Scholar 

  • Yang RC, Kozak A, Smith JHG (1978) The potential of Weibull-type functions as flexible growth curves. Can J For Res 8:424–431

    Article  Google Scholar 

  • Zanakis SH (1979) A simulation study of some simple estimators for the three parameter Weibull distribution. J Stat Comput Simul 9:101–116

    Article  Google Scholar 

  • Zarnoch SJ, Dell TR (1985) An evaluation of percentiles and maximum likelihood estimators of Weibull parameters. For Sci 31:260–268

    Google Scholar 

  • Zarnoch SJ, Feduccia DP, Baldwin VC Jr, Dell TR (1991) Growth and yield predictions for thinned and unthinned slash pine plantations on cutover sites in the west Gulf region. USDA Forest Service, New Orleans, Research Paper SO-264

    Google Scholar 

  • Zasada M, Cieszewski CJ (2005) A finite distribution approach for characterizing tree diameter distributions by natural social class in pure even-aged Scots pine stands in Poland. For Ecol Manage 204:145–158

    Article  Google Scholar 

  • Zeide B, Zhang Y (2000) Diameter variability in loblolly pine plantations. For Ecol Manage 128:139–143

    Article  Google Scholar 

  • Zhang L, Packard KC, Liu C (2003) A comparison of estimation methods for fitting Weibull and Johnson’s SB distributions to mixed spruce-fir stands in northeastern North America. Can J For Res 33:1340–1347

    Article  Google Scholar 

  • Zhao D, Borders B, Wang M (2006) Survival model for fusiform rust infected loblolly pine plantations with and without mid-rotation understorey vegetation control. For Ecol Manage 235:232–239

    Article  Google Scholar 

  • Zhou B, McTague JP (1996) Comparison and evaluation of five methods of estimation of the Johnson system parameters. Can J For Res 26:928–935

    Article  Google Scholar 

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Burkhart, H.E., Tomé, M. (2012). Diameter-Distribution Models for Even-Aged Stands. In: Modeling Forest Trees and Stands. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3170-9_12

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