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Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi

Year 2022, Volume: 23 Issue: 1, 21 - 29, 29.03.2022
https://doi.org/10.18182/tjf.1053870

Abstract

Sedir (Cedrus libani A. Rich.) ekonomik ve ekolojik açıdan Türkiye’deki en önemli asli ağaç türlerinden birisidir. Doğal sedir ormanlarının bugün ve geleceğe dönük yönetim ve planlanması ile ilgili stratejilerinin geliştirilmesinde, bu ormanların büyüme ve hasılatına ilişkin bilgiler son derece önemlidir. Çap dağılımı modelleri, yatay meşcere yapısı hakkında ve birim alandaki hacim, göğüs yüzeyi ve ağaç sayısı gibi her çap sınıfı için bilgilerin elde edilmesine yardımcı olmaktadır. Bu bilgiler, meşcereden elde edilecek odun ürününün farklı endüstriyel alanlardaki kullanım yeri ve elde edilmesi muhtemel parasal hasılatın ortaya konmasında önemlidir. Bu çalışmada, Antalya Yöresi doğal sedir meşcerelerinin çap dağılımının ortaya konması amaçlanmıştır. Daha önce yapılan çalışmalar incelendiğinde, çap dağılımını tanımlamak için, Log-normal, exponential, gama, beta, Weibull ve Johnson’s SB gibi birçok farklı olasılık yoğunluk fonksiyonu kullanılmıştır. Johnson’s SB fonksiyonu, ormancılık araştırmalarında teorik dağılımlara benzemedeki esnekliği nedeniyle en çok kullanılan dağılımlardan birisidir. Bu çalışmada, doğal sedir meşcerelerinin çap dağılımlarının modellenmesi amacıyla Johnson’s SB dağılım fonksiyonu kullanılmıştır. Bu amaçla, doğal sedir meşcerelerinden 109 adet örnek alan ölçülmüştür. Parametre tahmini için yüzdelik moment metodunu temel alan 3 parametreli çözüm yöntemi kullanılmıştır. Yapılan çap tahminleri ile gözlemlenen çap tahminleri arasındaki fark, hata indeksi ve Kolmogorov-Smirnov testi ile değerlendirilmiştir. İlgili yörede, Johnson’s SB dağılımı ve parametre tahmini için yüzdelik moment metodunu esas alan 3 parametreli çözüm yöntemi kullanılarak doğal sedir meşcerelerinin çap dağılımının gerçeğe yakın şekilde ortaya konabileceği görülmüştür.

Supporting Institution

Süleyman Demirel Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

BAP-4753-YL1-16

Thanks

Bu çalışmada kullanılan veriler, SDÜ Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından desteklenmekte olan BAP-4753-YL1-16 no’lu “Antalya Yöresi Doğal Sedir (Cedrus libanı A. Rich.) Meşcerelerinin Çap Dağılımının Johnson’s SB Dağılımı Kullanılarak Modellenmesi” isimli proje çalışmasında elde edilmiştir

References

  • Bailey, R.L., Dell. T., 1973. Quantifying diameter distributions with the Weibull function. Forest Sciences, 19(2): 97-104.
  • Bankston, J.B., Sabatia, C.O., Poudel, K.P., 2021. Effects of sample plot size and prediction models on diameter distribution recovery. Forest Science, 67(3): 245-255.
  • Bolat, I., 2014. The effect of thinning on microbial biomass C, N and basal respiration in black pine forest soils in Mudurnu, Turkey. European Journal of Forest Research, 133(1): 131-139.
  • Borders, B.E., Souter, R., Bailey., R., Ware., K., 1987. Percentile-based distributions characterize forest stand tables. Forest Sciences, 33(2): 570-576.
  • Borders, B.E., Wang., M., Zhao., D., 2008. Problems of scaling plantation plot diameter distributions to stand level. Forest Sciences, 54(3): 349-355.
  • Boydak, M., 2003. Regeneration of Lebanon cedar (Cedrus libani A. Rich.) on karstic lands in Turkey. Forest ecology and Management, 178(3): 231-243.
  • Boydak, M., 20014. Toros sedirinin ekolojisi, doğal gençleştirilmesi ve bu türle karstik alan ağaçlandırmaları. II. Ulusal Akdeniz Orman ve Çevre Sempozyumu, 22-24 Ekim, Isparta, s. 1-25.
  • Cao, Q.V., Yao., F., Qinglin., W., 2010. Effectd of sample size on characterization of wood-particle length distribution. Wood and Fiber Science, 42(1): 46-50.
  • Diamantopoulou, M.J., Özçelik, R., Crecente-Campo, F., Eler, Ü., 2015. Estimation of Weibull function parameters for modelling tree diameter distribution using least squares and artificial neural networks methods. Biosystems Engineering, 133: 33-45.
  • Ercanlı, İ., Yavuz, H., 2010. The probability density functions to diameter distributions for oriental spruce and Scots pine mixed stands. Kastamonu Üniversitesi Orman Fakültesi Dergisi, 10(1): 68-83.
  • Fischer, R., Lorenz, M., Köhl., M., Becher., G., Granke., O., Christou., A., 2008. The conditions of Forests in Europe: 2008 executive report. United Nations Economic Commission for Europe, Convention on Long-range Trans boundary Air Pollution, International Co-operative Programme on Assessment And Monitoring of Air Pollution Effects on Forests (ICP Forests), 23 p. Fonseca, T.F., 2004. Modelação do crescimento, mortalidade e distribuiçao, do pinhal bravo no Vale do Tamega. Ph.D. dissertation, Univ. of Trás-os-Montese e Alto Douro, Vila Real, Portugal.
  • Fonseca, T.F., Marques., C.P., Parresol., B.R., 2009. Describing Maritime pine diameter distributions with Johnson's sB distribution using a new all-parameter recovery approach. Forest Sciences, 55(4): 367-373.
  • Furtado, A.X., 2006. Modelação da estrutura dinâmica de povoamentos de Eucalyptus globulus em primeira rotação. Tese de Doutoramento, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Lisbon.
  • Gorgoso, J., González, J.Á., Rojo., A., Grandas-Arias., J., 2007. Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Forest Systems, 16(2): 113-123.
  • Gorgoso, J., Rojo, A., Cámara-Obregón., A., Diéguez-Aranda., U., 2012. A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain. Forest Systems, 21(3): 446-459.
  • Hafley, W., Schreuder., H., 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research, 7(3): 481-487.
  • Johnson, N.L., 1949. Systems of frequency curves generated by methods of translation. Biometrika, 36(1-2): 149-176.
  • Johnson, N.L., Kotz., S., 1970. Continuous Univariate Distribitions. Vol. 1. John Viley & Sons, New York, NY.
  • Kahriman, A., Yavuz, H. 2011. Sarıçam (Pinus sylvestris L.)-Doğu kayını (Fagus orientalis Lipsky) karışık meşcerelerinde çap dağılımlarının olasılık yoğunluk fonksiyonları ile belirlenmesi. Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi, 12 (2): 109-125.
  • Kiviste, A., Nilson, A., Hordo., M., Merenäkk., M., 2003. Diameter distribution models and height-diameter equations for Estonian forests. In: Modelling Forest Systems (Ed: Amaro, A., Reed, D., Soares, P.), CABI Publishing, Portugal, pp. 169-179.
  • Knoebel, B.R., Burkhart, H.E., 1991. A bivariate distribution approach to modeling forest diameter distributions at two points in time. Biometrics, 47: 241–253.
  • Lei, Y., 2008. Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis). Journal of Forest Science, 54(12): 566-571.
  • 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. Scandinavian Journal of Forest Research, 10(1-4):284-295.
  • 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. Annals of Forest Science, 68(2):325-335.
  • Ogana, F.N., 2018. Evaluation of four methods of fitting Johnson’s SBB for height and volume predictions. Journal of Forest Science, 64(4): 187-197.
  • Özçelik, R., Fidalgo Fonseca, T. J., Parresol, B.R., Eler, Ü., 2016. Modeling the Diameter Distributions of Brutian Pine Stands Using Johnson's SB Distribution. Forest Science, 62(6): 587-593.
  • Palahí, M., Pukkala, T., Blasco., E., Trasobares., A., 2007. Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain). European Journal of Forest Research, 126(4): 563-571. Palahí, M., Pukkala., T., Trasobares., A., 2006. Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function. Forestry, 79(5): 553-562.
  • Parresol, B.R., 2003. Recovering parameters of Johnson’s SB distribution. US For. Serv. Res. Paper SRS-31, 9 .
  • Parresol, B.R., Fonseca., T.F., Marques., C.P., 2010. Numerical details and SAS programs for parameter recovery of the SB distribution. US For. Serv. Gen. Tech. Rep. SRS-122. USDA, USA.
  • Qin, J., Cao, Q.V., Blouin, D.C., 2006. Projection of a diameter distribution through time. Canadian Journal of Forest Research, 37(1): 188-194.
  • Reynolds, M.R., Burk, T.E., Huang., W.C., 1988. Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Sciences, 34(2): 373-399.
  • Sakıcı, O.E., Dal, E., 2021. Kastamonu yöresi sarıçam meşcereleri için çap dağılımlarının modellenmesi ve çeşitli meşcere özellikleri ile ilişkilerinin belirlenmesi. Bartın Orman Fakültesi Dergisi, 23(3): 1026-1041. DOI: 10.24011/barofd.1015603
  • SAS Institute Inc., 2014. SAS/OR(R) 9.2 User's Guide: Mathematical Programming. <http://support.sas.com/documentation/cdl/en/ormpug/59679/HTML/default/viewer.htm#optmodel.htm, Accessed: May 2014.
  • Schreuder, H.T., Hafley., W.L., 1977. A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics, 33: 471-478.
  • Scolforo, J.R.S., Tabai, F.C.V., de Macedo, R.L.S.G., Acerbi., F.W., de Assis., A.L., 2003. S B distribution’s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods. Forest Ecology and Management, 175(1): 489-496.
  • Scolforo, J.R.S., Thierschi., A., 1998. Estimativas e testes da distibuiçao de frequencia diametrica para Eucalytus camaldulensis, atraves da distribuiçao SB De Johnson, por diferentes metodos de ajuste. Scientia Forestalis, 54(1): 93-106.
  • Siipilehto, J., 1999. Improving the accuracy of predicted basal-area diameter distribution in advanced stands by determining stem number. Silva Fennica, 33(4): 281-301.
  • Siipilehto, J., Siitonen., J., 2004. Degree of previous cutting in explaining the differences in diameter distributions between mature managed and natural Norway spruce forests. Silva Fennica, 38(4): 425-435.
  • Tham, A., 1988. Estimate and test frequency distributions with the Johnson SB Function from stand parameters in young mixed stands after different thinning treatments. P.255-262 in Forest growth modeling and prediction: Proc. IUFRO Conference. US For. Serv. Gen. Tech. Rep. NC-120. North Central Forest Experiment Station, Minneapolis, MN.
  • Von Gadow, K., 1983. The Development of Diameter Distributions in Unthinned Stands of Pinus radiata. South African Forestry Journal, 124(1): 63-67.
  • Zhang, L., Packard., K.C., 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. Canadian Journal of Forest Research, 33(7): 1340-1347.

Development of diameter distribution model for natural cedar stands in Antalya region using Johnson’s Sb Distribution

Year 2022, Volume: 23 Issue: 1, 21 - 29, 29.03.2022
https://doi.org/10.18182/tjf.1053870

Abstract

Taurus cedar (Cedrus libani A. Rich.) forests are economically and ecologically one of the most important forests in Turkey. In this context, knowing the state and limitations of growth and yield of Cedar forests is necessary and important for improving future management and planning strategies. Diameter distribution models are provide information for data about horizontal stand structure and each diameter class: number of trees, basal area, and volume per unit area. These predictions is used to predict volume yield and to forecast the range of products. In this study, diameter distribution models were developed for natural cedar stands in Antalya Region. Many different probability density functions such as log-normal, exponential, gamma, beta, Weibull, and Johnson’s SB have been used to describe diameter distributions. Johnson’s SB function are among the most commonly used in forest research because of their flexibility in mimicking the emprical distributions. In this study, Johnson’s SB distribution was used for modeling diameter disrtributions of natural cedar stands. For this aim, 109 sample plots measured from natural distribution areas of natural cedar stands. The obtained results from observed and predicted diameter distributions of sample plots were compared using Error index and Kolmogorov-Smirnov Test. The results show good performance of three-parameter recovery method. The major advantage of 3-parameter recovery method relies on the reduced level of input information required.

Project Number

BAP-4753-YL1-16

References

  • Bailey, R.L., Dell. T., 1973. Quantifying diameter distributions with the Weibull function. Forest Sciences, 19(2): 97-104.
  • Bankston, J.B., Sabatia, C.O., Poudel, K.P., 2021. Effects of sample plot size and prediction models on diameter distribution recovery. Forest Science, 67(3): 245-255.
  • Bolat, I., 2014. The effect of thinning on microbial biomass C, N and basal respiration in black pine forest soils in Mudurnu, Turkey. European Journal of Forest Research, 133(1): 131-139.
  • Borders, B.E., Souter, R., Bailey., R., Ware., K., 1987. Percentile-based distributions characterize forest stand tables. Forest Sciences, 33(2): 570-576.
  • Borders, B.E., Wang., M., Zhao., D., 2008. Problems of scaling plantation plot diameter distributions to stand level. Forest Sciences, 54(3): 349-355.
  • Boydak, M., 2003. Regeneration of Lebanon cedar (Cedrus libani A. Rich.) on karstic lands in Turkey. Forest ecology and Management, 178(3): 231-243.
  • Boydak, M., 20014. Toros sedirinin ekolojisi, doğal gençleştirilmesi ve bu türle karstik alan ağaçlandırmaları. II. Ulusal Akdeniz Orman ve Çevre Sempozyumu, 22-24 Ekim, Isparta, s. 1-25.
  • Cao, Q.V., Yao., F., Qinglin., W., 2010. Effectd of sample size on characterization of wood-particle length distribution. Wood and Fiber Science, 42(1): 46-50.
  • Diamantopoulou, M.J., Özçelik, R., Crecente-Campo, F., Eler, Ü., 2015. Estimation of Weibull function parameters for modelling tree diameter distribution using least squares and artificial neural networks methods. Biosystems Engineering, 133: 33-45.
  • Ercanlı, İ., Yavuz, H., 2010. The probability density functions to diameter distributions for oriental spruce and Scots pine mixed stands. Kastamonu Üniversitesi Orman Fakültesi Dergisi, 10(1): 68-83.
  • Fischer, R., Lorenz, M., Köhl., M., Becher., G., Granke., O., Christou., A., 2008. The conditions of Forests in Europe: 2008 executive report. United Nations Economic Commission for Europe, Convention on Long-range Trans boundary Air Pollution, International Co-operative Programme on Assessment And Monitoring of Air Pollution Effects on Forests (ICP Forests), 23 p. Fonseca, T.F., 2004. Modelação do crescimento, mortalidade e distribuiçao, do pinhal bravo no Vale do Tamega. Ph.D. dissertation, Univ. of Trás-os-Montese e Alto Douro, Vila Real, Portugal.
  • Fonseca, T.F., Marques., C.P., Parresol., B.R., 2009. Describing Maritime pine diameter distributions with Johnson's sB distribution using a new all-parameter recovery approach. Forest Sciences, 55(4): 367-373.
  • Furtado, A.X., 2006. Modelação da estrutura dinâmica de povoamentos de Eucalyptus globulus em primeira rotação. Tese de Doutoramento, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Lisbon.
  • Gorgoso, J., González, J.Á., Rojo., A., Grandas-Arias., J., 2007. Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Forest Systems, 16(2): 113-123.
  • Gorgoso, J., Rojo, A., Cámara-Obregón., A., Diéguez-Aranda., U., 2012. A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain. Forest Systems, 21(3): 446-459.
  • Hafley, W., Schreuder., H., 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research, 7(3): 481-487.
  • Johnson, N.L., 1949. Systems of frequency curves generated by methods of translation. Biometrika, 36(1-2): 149-176.
  • Johnson, N.L., Kotz., S., 1970. Continuous Univariate Distribitions. Vol. 1. John Viley & Sons, New York, NY.
  • Kahriman, A., Yavuz, H. 2011. Sarıçam (Pinus sylvestris L.)-Doğu kayını (Fagus orientalis Lipsky) karışık meşcerelerinde çap dağılımlarının olasılık yoğunluk fonksiyonları ile belirlenmesi. Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi, 12 (2): 109-125.
  • Kiviste, A., Nilson, A., Hordo., M., Merenäkk., M., 2003. Diameter distribution models and height-diameter equations for Estonian forests. In: Modelling Forest Systems (Ed: Amaro, A., Reed, D., Soares, P.), CABI Publishing, Portugal, pp. 169-179.
  • Knoebel, B.R., Burkhart, H.E., 1991. A bivariate distribution approach to modeling forest diameter distributions at two points in time. Biometrics, 47: 241–253.
  • Lei, Y., 2008. Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis). Journal of Forest Science, 54(12): 566-571.
  • 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. Scandinavian Journal of Forest Research, 10(1-4):284-295.
  • 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. Annals of Forest Science, 68(2):325-335.
  • Ogana, F.N., 2018. Evaluation of four methods of fitting Johnson’s SBB for height and volume predictions. Journal of Forest Science, 64(4): 187-197.
  • Özçelik, R., Fidalgo Fonseca, T. J., Parresol, B.R., Eler, Ü., 2016. Modeling the Diameter Distributions of Brutian Pine Stands Using Johnson's SB Distribution. Forest Science, 62(6): 587-593.
  • Palahí, M., Pukkala, T., Blasco., E., Trasobares., A., 2007. Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain). European Journal of Forest Research, 126(4): 563-571. Palahí, M., Pukkala., T., Trasobares., A., 2006. Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function. Forestry, 79(5): 553-562.
  • Parresol, B.R., 2003. Recovering parameters of Johnson’s SB distribution. US For. Serv. Res. Paper SRS-31, 9 .
  • Parresol, B.R., Fonseca., T.F., Marques., C.P., 2010. Numerical details and SAS programs for parameter recovery of the SB distribution. US For. Serv. Gen. Tech. Rep. SRS-122. USDA, USA.
  • Qin, J., Cao, Q.V., Blouin, D.C., 2006. Projection of a diameter distribution through time. Canadian Journal of Forest Research, 37(1): 188-194.
  • Reynolds, M.R., Burk, T.E., Huang., W.C., 1988. Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Sciences, 34(2): 373-399.
  • Sakıcı, O.E., Dal, E., 2021. Kastamonu yöresi sarıçam meşcereleri için çap dağılımlarının modellenmesi ve çeşitli meşcere özellikleri ile ilişkilerinin belirlenmesi. Bartın Orman Fakültesi Dergisi, 23(3): 1026-1041. DOI: 10.24011/barofd.1015603
  • SAS Institute Inc., 2014. SAS/OR(R) 9.2 User's Guide: Mathematical Programming. <http://support.sas.com/documentation/cdl/en/ormpug/59679/HTML/default/viewer.htm#optmodel.htm, Accessed: May 2014.
  • Schreuder, H.T., Hafley., W.L., 1977. A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics, 33: 471-478.
  • Scolforo, J.R.S., Tabai, F.C.V., de Macedo, R.L.S.G., Acerbi., F.W., de Assis., A.L., 2003. S B distribution’s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods. Forest Ecology and Management, 175(1): 489-496.
  • Scolforo, J.R.S., Thierschi., A., 1998. Estimativas e testes da distibuiçao de frequencia diametrica para Eucalytus camaldulensis, atraves da distribuiçao SB De Johnson, por diferentes metodos de ajuste. Scientia Forestalis, 54(1): 93-106.
  • Siipilehto, J., 1999. Improving the accuracy of predicted basal-area diameter distribution in advanced stands by determining stem number. Silva Fennica, 33(4): 281-301.
  • Siipilehto, J., Siitonen., J., 2004. Degree of previous cutting in explaining the differences in diameter distributions between mature managed and natural Norway spruce forests. Silva Fennica, 38(4): 425-435.
  • Tham, A., 1988. Estimate and test frequency distributions with the Johnson SB Function from stand parameters in young mixed stands after different thinning treatments. P.255-262 in Forest growth modeling and prediction: Proc. IUFRO Conference. US For. Serv. Gen. Tech. Rep. NC-120. North Central Forest Experiment Station, Minneapolis, MN.
  • Von Gadow, K., 1983. The Development of Diameter Distributions in Unthinned Stands of Pinus radiata. South African Forestry Journal, 124(1): 63-67.
  • Zhang, L., Packard., K.C., 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. Canadian Journal of Forest Research, 33(7): 1340-1347.
There are 41 citations in total.

Details

Primary Language Turkish
Journal Section Orijinal Araştırma Makalesi
Authors

Burak Baş This is me 0000-0002-1149-2501

Ramazan Özçelik 0000-0003-2132-2589

Project Number BAP-4753-YL1-16
Publication Date March 29, 2022
Acceptance Date February 7, 2022
Published in Issue Year 2022 Volume: 23 Issue: 1

Cite

APA Baş, B., & Özçelik, R. (2022). Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi. Turkish Journal of Forestry, 23(1), 21-29. https://doi.org/10.18182/tjf.1053870
AMA Baş B, Özçelik R. Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi. Turkish Journal of Forestry. March 2022;23(1):21-29. doi:10.18182/tjf.1053870
Chicago Baş, Burak, and Ramazan Özçelik. “Antalya yöresi doğal Sedir meşcereleri için çap dağılım Modelinin Johnson’s SB Dağılımı Ile geliştirilmesi”. Turkish Journal of Forestry 23, no. 1 (March 2022): 21-29. https://doi.org/10.18182/tjf.1053870.
EndNote Baş B, Özçelik R (March 1, 2022) Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi. Turkish Journal of Forestry 23 1 21–29.
IEEE B. Baş and R. Özçelik, “Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi”, Turkish Journal of Forestry, vol. 23, no. 1, pp. 21–29, 2022, doi: 10.18182/tjf.1053870.
ISNAD Baş, Burak - Özçelik, Ramazan. “Antalya yöresi doğal Sedir meşcereleri için çap dağılım Modelinin Johnson’s SB Dağılımı Ile geliştirilmesi”. Turkish Journal of Forestry 23/1 (March 2022), 21-29. https://doi.org/10.18182/tjf.1053870.
JAMA Baş B, Özçelik R. Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi. Turkish Journal of Forestry. 2022;23:21–29.
MLA Baş, Burak and Ramazan Özçelik. “Antalya yöresi doğal Sedir meşcereleri için çap dağılım Modelinin Johnson’s SB Dağılımı Ile geliştirilmesi”. Turkish Journal of Forestry, vol. 23, no. 1, 2022, pp. 21-29, doi:10.18182/tjf.1053870.
Vancouver Baş B, Özçelik R. Antalya yöresi doğal sedir meşcereleri için çap dağılım modelinin Johnson’s SB Dağılımı ile geliştirilmesi. Turkish Journal of Forestry. 2022;23(1):21-9.