The Chapman-Richards Distribution and its Relationship to the Generalized Beta

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. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Gove, Jeffrey H. [verfasserIn] Lynch, Thomas B. Ducey, Mark J.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Diameter distributions Chapman-Richards growth Generalized beta distribution of the first kind Maximum likelihood McKendrick-Von Foerster equation Physiologically structured population model Size-structured distributions

Anmerkung:	© The Author(s) 2019

Übergeordnetes Werk:	Enthalten in: Forest Ecosystems - Berlin : SpringerOpen, 2014, 6(2019), 1 vom: 21. Mai
Übergeordnetes Werk:	volume:6 ; year:2019 ; number:1 ; day:21 ; month:05

Links:	Volltext

DOI / URN:	10.1186/s40663-019-0184-0

Katalog-ID:	SPR037138650

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245	1	4	\|a The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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520			\|a 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.
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650		4	\|a Physiologically structured population model \|7 (dpeaa)DE-He213
650		4	\|a Size-structured distributions \|7 (dpeaa)DE-He213
700	1		\|a Lynch, Thomas B. \|4 aut
700	1		\|a Ducey, Mark J. \|4 aut
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allfields	10.1186/s40663-019-0184-0 doi (DE-627)SPR037138650 (SPR)s40663-019-0184-0-e DE-627 ger DE-627 rakwb eng Gove, Jeffrey H. verfasserin aut The Chapman-Richards Distribution and its Relationship to the Generalized Beta 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 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. Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213 Lynch, Thomas B. aut Ducey, Mark J. aut Enthalten in Forest Ecosystems Berlin : SpringerOpen, 2014 6(2019), 1 vom: 21. Mai (DE-627)780378881 (DE-600)2760380-5 2197-5620 nnns volume:6 year:2019 number:1 day:21 month:05 https://dx.doi.org/10.1186/s40663-019-0184-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 6 2019 1 21 05
spelling	10.1186/s40663-019-0184-0 doi (DE-627)SPR037138650 (SPR)s40663-019-0184-0-e DE-627 ger DE-627 rakwb eng Gove, Jeffrey H. verfasserin aut The Chapman-Richards Distribution and its Relationship to the Generalized Beta 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 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. Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213 Lynch, Thomas B. aut Ducey, Mark J. aut Enthalten in Forest Ecosystems Berlin : SpringerOpen, 2014 6(2019), 1 vom: 21. Mai (DE-627)780378881 (DE-600)2760380-5 2197-5620 nnns volume:6 year:2019 number:1 day:21 month:05 https://dx.doi.org/10.1186/s40663-019-0184-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 6 2019 1 21 05
allfields_unstemmed	10.1186/s40663-019-0184-0 doi (DE-627)SPR037138650 (SPR)s40663-019-0184-0-e DE-627 ger DE-627 rakwb eng Gove, Jeffrey H. verfasserin aut The Chapman-Richards Distribution and its Relationship to the Generalized Beta 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 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. Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213 Lynch, Thomas B. aut Ducey, Mark J. aut Enthalten in Forest Ecosystems Berlin : SpringerOpen, 2014 6(2019), 1 vom: 21. Mai (DE-627)780378881 (DE-600)2760380-5 2197-5620 nnns volume:6 year:2019 number:1 day:21 month:05 https://dx.doi.org/10.1186/s40663-019-0184-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 6 2019 1 21 05
allfieldsGer	10.1186/s40663-019-0184-0 doi (DE-627)SPR037138650 (SPR)s40663-019-0184-0-e DE-627 ger DE-627 rakwb eng Gove, Jeffrey H. verfasserin aut The Chapman-Richards Distribution and its Relationship to the Generalized Beta 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 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. Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213 Lynch, Thomas B. aut Ducey, Mark J. aut Enthalten in Forest Ecosystems Berlin : SpringerOpen, 2014 6(2019), 1 vom: 21. Mai (DE-627)780378881 (DE-600)2760380-5 2197-5620 nnns volume:6 year:2019 number:1 day:21 month:05 https://dx.doi.org/10.1186/s40663-019-0184-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 6 2019 1 21 05
allfieldsSound	10.1186/s40663-019-0184-0 doi (DE-627)SPR037138650 (SPR)s40663-019-0184-0-e DE-627 ger DE-627 rakwb eng Gove, Jeffrey H. verfasserin aut The Chapman-Richards Distribution and its Relationship to the Generalized Beta 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 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. Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213 Lynch, Thomas B. aut Ducey, Mark J. aut Enthalten in Forest Ecosystems Berlin : SpringerOpen, 2014 6(2019), 1 vom: 21. Mai (DE-627)780378881 (DE-600)2760380-5 2197-5620 nnns volume:6 year:2019 number:1 day:21 month:05 https://dx.doi.org/10.1186/s40663-019-0184-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 6 2019 1 21 05
language	English
source	Enthalten in Forest Ecosystems 6(2019), 1 vom: 21. Mai volume:6 year:2019 number:1 day:21 month:05
sourceStr	Enthalten in Forest Ecosystems 6(2019), 1 vom: 21. Mai volume:6 year:2019 number:1 day:21 month:05
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Diameter distributions Chapman-Richards growth Generalized beta distribution of the first kind Maximum likelihood McKendrick-Von Foerster equation Physiologically structured population model Size-structured distributions
isfreeaccess_bool	true
container_title	Forest Ecosystems
authorswithroles_txt_mv	Gove, Jeffrey H. @@aut@@ Lynch, Thomas B. @@aut@@ Ducey, Mark J. @@aut@@
publishDateDaySort_date	2019-05-21T00:00:00Z
hierarchy_top_id	780378881
id	SPR037138650
language_de	englisch
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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. 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author	Gove, Jeffrey H.
spellingShingle	Gove, Jeffrey H. misc Diameter distributions misc Chapman-Richards growth misc Generalized beta distribution of the first kind misc Maximum likelihood misc McKendrick-Von Foerster equation misc Physiologically structured population model misc Size-structured distributions The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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topic_title	The Chapman-Richards Distribution and its Relationship to the Generalized Beta Diameter distributions (dpeaa)DE-He213 Chapman-Richards growth (dpeaa)DE-He213 Generalized beta distribution of the first kind (dpeaa)DE-He213 Maximum likelihood (dpeaa)DE-He213 McKendrick-Von Foerster equation (dpeaa)DE-He213 Physiologically structured population model (dpeaa)DE-He213 Size-structured distributions (dpeaa)DE-He213
topic	misc Diameter distributions misc Chapman-Richards growth misc Generalized beta distribution of the first kind misc Maximum likelihood misc McKendrick-Von Foerster equation misc Physiologically structured population model misc Size-structured distributions
topic_unstemmed	misc Diameter distributions misc Chapman-Richards growth misc Generalized beta distribution of the first kind misc Maximum likelihood misc McKendrick-Von Foerster equation misc Physiologically structured population model misc Size-structured distributions
topic_browse	misc Diameter distributions misc Chapman-Richards growth misc Generalized beta distribution of the first kind misc Maximum likelihood misc McKendrick-Von Foerster equation misc Physiologically structured population model misc Size-structured distributions
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title	The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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title_full	The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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author_browse	Gove, Jeffrey H. Lynch, Thomas B. Ducey, Mark J.
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title_sort	chapman-richards distribution and its relationship to the generalized beta
title_auth	The Chapman-Richards Distribution and its Relationship to the Generalized Beta
abstract	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. © The Author(s) 2019
abstractGer	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. © The Author(s) 2019
abstract_unstemmed	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. © The Author(s) 2019
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title_short	The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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up_date	2024-07-03T21:20:41.998Z
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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. 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The Chapman-Richards Distribution and its Relationship to the Generalized Beta

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