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Table 3 Average difference between maximum likelihood (ML) estimates of \(\alpha\), \(\beta\) and \(\sigma\) and the estimates of these parameters using PRM methods and t test p values for those differences. \(PRM({\overline{D}D}_{\mathrm{g}})\): PRM system of Eqs. (8, 9) applied to the field values of \(\overline{D}\) and \({D}_{\mathrm{g}}\). \(PRM({\widehat{\overline{D}}\widehat{D}}_{\mathrm{g}})\): PRM system of Eqs. (8, 9) applied to values of \(\widehat{\overline{D}}\) and \({\widehat{D}}_{\mathrm{g}}\) obtained from age and site index using the corresponding models. \(PRM({{D}_{\mathrm{o}}D}_{\mathrm{g}})\) and \(PRM({{\widehat{D}}_{\mathrm{o}}\widehat{D}}_{\mathrm{g}})\): PRM system of Eqs. (8, 10) using the field values of \({D}_{\mathrm{o}}\), \({D}_{\mathrm{g}}\) and \(N\) and their predicted values \({\widehat{D}}_{\mathrm{o}},{\widehat{D}}_{\mathrm{g}}\) and \(N\), resp. \(\overline{D}, {D}_{\mathrm{o}}\), \({D}_{\mathrm{g}}\) and \(N\), are the mean diameter, dominant diameter, quadratic mean diameter and stand density. \(\widehat{\overline{D}}\), \({\widehat{D}}_{\mathrm{o}}\) and \({\widehat{D}}_{\mathrm{g}}\) represent predictions of \(\overline{D}, {D}_{\mathrm{o}}\) and \({D}_{\mathrm{g}}\) obtained from the yield table models

From: Comparison of two parameter recovery methods for the transformation of Pinus sylvestris yield tables into a diameter distribution model

Comparison

\(\alpha\)

\(\beta\)

\(\sigma\)

Mean difference

p value

Mean difference

p value

Mean difference

p value

ML vs \(PRM({\overline{D}D}_{\mathrm{g}})\)  

− 0.38

0.70

0.01

0.99

0.39

0.70

ML vs \(PRM({{D}_{\mathrm{o}}D}_{\mathrm{g}})\)

− 4.18

0.00

− 0.04

0.97

3.52

0.00

ML vs \(PRM({\widehat{\overline{D}}\widehat{D}}_{\mathrm{g}})\)  

− 0.03

0.97

− 0.15

0.88

− 0.08

0.94

ML vs \({PRM({\widehat{D}}_{\mathrm{o}}\widehat{D}}_{\mathrm{g}})\)

− 4.27

0.00

− 0.19

0.85

3.51

0.00