A percentile-based estimator for the log-logistic function: Application to forestry

Friday Nwabueze Ogana

doi:10.2478/fsmu-2020-0009

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A percentile-based estimator for the log-logistic function: Application to forestry

Forestry Studies

Volume 72 (2020): Issue 1 (September 2020)

By: Friday Nwabueze Ogana

Open Access

|Sep 2020

Figures & Tables

Observed and fitted LogL diameter distributions of the natural forests and plantations.

The observed and predicted diameter distributions from PRM and PPM models.

Descriptive statistics of the inventoried data from natural forests and plantations_

Forest	Statistics	Dbh (cm)	Ht (m)	dg (cm)	Ho (m)	G (m²ha⁻¹)	N (trees ha⁻¹)	A (years)
Ikrigon Natural Forest	Mean	30.0	24.1	33.8	31.9	28.0	310.4	na^*
63 species	Min	10.0	5.7	29.4	27.6	16.9	184.0
776 trees	Max	125.0	43.8	39.6	35.9	40.9	440.0
	SD	15.9	7.5	3.5	2.5	8.3	72.8

Oluwa Natural Forest	Mean	25.1	16.9	29.6	25.7	19.4	227.1	na^*
58 species	Min	10.0	4.8	26.1	22.0	14.5	200.0
486 trees	Max	118.5	63.7	34.5	33.0	31.7	352.0
	SD	16.7	9.0	2.7	3.7	6.7	56.6

G. arborea	Mean	21.2	13.9	22.3	21.6	30.5	710.3	26.6
486 trees	Min	3.0	1.6	14.7	8.8	6.2	300.0	11.0
	Max	54.5	42.7	31.0	34.5	72.9	1525.0	39.0
	SD	9.8	5.8	3.7	4.5	19.5	308.6	7.7

T. grandis	Mean	17.9	16.7	18.5	21.3	24.2	877.6	19.8
1,916 trees	Min	6.0	6.6	14.3	17.9	11.5	624.0	13.0
	Max	37.9	26.5	22.4	24.0	50.8	1744.0	27.0
	SD	5.3	3.5	2.2	1.9	8.9	198.6	5.2

Models for the percentiles, scale and shape parameters and their cross-validation indices_

Species	DV^*	Parameter	Estimate	SE	5-fold Cross-validation

					RMSE	CV	AICc	BIC	R¯2{\bar R^2}
G. arborea	P25	b₀	−0.590	1.570	4.830	4.801	116.937	123.460	0.533
	P25	b₁	0.632	0.069	4.830	4.801	116.937	123.460	0.533
	P40	b₀	−2.975	1.676	5.539	5.441	126.491	133.015	0.677
	P40	b₁	0.912	0.074	5.539	5.441	126.491	133.015	0.677
	P60	b₀	−0.768	1.159	2.519	2.615	72.663	79.186	0.854
	P60	b₁	1.050	0.051	2.519	2.615	72.663	79.186	0.854
	P75	b₀	−0.677	1.116	2.446	2.418	67.149	73.672	0.897
	P75	b₁	1.232	0.049	2.446	2.418	67.149	73.672	0.897
	P80	b₀	−0.468	1.148	2.567	2.561	71.250	77.774	0.900
	P80	b₁	1.288	0.051	2.567	2.561	71.250	77.774	0.900
	Shape	b₀	1.952	0.124	0.138	0.147	−146.720	−140.196	0.764
	Shape	b₁	−0.826	0.054	0.138	0.147	−146.720	−140.196	0.764
	Scale	b₀	−0.753	0.955	1.803	1.768	44.331	50.855	0.860
	Scale	b₁	0.888	0.042	1.803	1.768	44.331	50.855	0.860

T. grandis	P25	b₀	−3.885	1.374	0.917	0.874	−1.105	2.556	0.844
	P25	b₁	0.975	0.074	0.917	0.874	−1.105	2.556	0.844
	P40	b₀	1.562	1.189	0.668	0.652	−10.687	−7.025	0.874
	P40	b₁	0.951	0.064	0.668	0.652	−10.687	−7.025	0.874
	P60	b₀	0.263	1.016	0.495	0.475	−21.063	−17.401	0.912
	P60	b₁	0.995	0.055	0.495	0.475	−21.063	−17.401	0.912
	P75	b₀	2.704	1.232	0.671	0.704	−8.334	−4.672	0.873
	P75	b₁	0.982	0.066	0.671	0.704	−8.334	−4.672	0.873
	P80	b₀	4.946	1.331	0.786	0.829	−3.200	0.461	0.833
	P80	b₁	0.905	0.071	0.786	0.829	−3.200	0.461	0.833
	Shape	b₀	2.514	0.397	0.368	0.378	−30.438	−26.776	0.773
	Shape	b₁	−1.028	0.098	0.368	0.378	−30.438	−26.776	0.773
	Scale	b₀	−1.306	0.625	0.186	0.181	−53.142	−49.480	0.965
	Scale	b₁	1.002	0.033	0.186	0.181	−53.142	−49.480	0.965

Estimated parameters, goodness-of-fits and the relative rank sum (R) of the percentiles and MLE in natural forest_

Natural Forest	Percentiles	Parameters		Goodness-of-fit			R

		Shape	Scale	KS	AD	W²
Ikrigon	M1	2.6293	26.2730	0.0736	8.4744	0.6452	7.29
	M2	3.4970	23.7620	0.1263	21.5400	3.4572	27.00
	M3	3.2008	24.5129	0.0889	10.3310	1.5687	12.34
	M4	2.7855	26.1412	0.0648	5.9910	0.4154	4.49
	M5	2.6278	26.3674	0.0731	8.5303	0.6549	7.29
	M6	2.5619	26.2305	0.0785	9.9085	0.8018	8.97
	M7	2.7658	26.1683	0.0658	6.2362	0.4338	4.77
	M8	2.5572	26.3818	0.0778	10.0510	0.8231	9.00
	MLE	3.2957	26.2105	0.0547	5.2472	0.7167	3.79

Oluwa	M1	3.0771	20.2929	0.1061	6.5088	0.6674	7.29
	M2	3.0150	21.6576	0.0988	8.5493	1.3996	21.48
	M3	2.9375	20.7274	0.1089	7.0406	0.8385	11.56
	M4	2.7995	20.1118	0.1299	8.6210	0.9602	22.20
	M5	3.0966	19.8522	0.1125	7.3039	0.7098	11.73
	M6	3.0229	19.8817	0.1172	7.5092	0.7532	13.74
	M7	3.2683	19.6982	0.1037	7.5823	0.6984	11.12
	M8	3.0186	19.8512	0.1180	7.6141	0.7661	14.41
	MLE	3.3928	20.4790	0.0827	6.4187	0.6964	3.32

Estimated parameters, goodness-of-fits and the relative rank sum (R) of the percentiles and MLE in plantations_

Plantation	Percentiles	Parameters		Goodness-of-fit			R

		Shape	Scale	KS	AD	W²
G. arborea	M1	2.9081	19.2593	0.0739	19.0410	2.0426	4.13
	M2	3.7818	16.2732	0.2120	182.6300	33.5450	27.00
	M3	3.5858	17.7908	0.1325	60.1980	11.6370	11.50
	M4	3.3184	19.8874	0.0598	19.9870	2.0377	3.47
	M5	2.8103	19.6023	0.0853	22.5520	2.1931	4.91
	M6	2.8513	19.8796	0.0862	22.9980	2.1995	4.98
	M7	3.0304	20.1196	0.0773	21.7450	2.0812	4.44
	M8	2.8908	19.8028	0.0824	21.2250	1.9992	4.66
	MLE	3.3267	19.4248	0.0526	18.0290	2.1989	3.05

T. grandis	M1	5.0963	17.4920	0.0593	8.5247	0.7829	6.42
	M2	6.0548	16.5020	0.1084	33.8000	6.4582	27.00
	M3	6.1169	16.9031	0.0840	16.3320	2.8739	14.37
	M4	5.3251	17.2658	0.0415	5.2366	0.5085	3.00
	M5	5.1543	17.5622	0.0594	8.9145	0.8782	6.67
	M6	4.9264	17.4620	0.0657	10.6700	1.0045	8.08
	M7	4.8683	17.3897	0.0657	11.1180	1.0443	8.26
	M8	4.9804	17.5226	0.0655	10.5200	1.0175	8.03
	MLE	5.6892	17.2884	0.0436	5.4299	0.6729	3.52

References

Authors

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Articles in this issue

DOI: https://doi.org/10.2478/fsmu-2020-0009 | Journal eISSN: 1736-8723 | Journal ISSN: 1406-9954

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Language: English

Page range: 107 - 120

Submitted on: Mar 26, 2020

Accepted on: Jun 19, 2020

Published on: Sep 18, 2020

Published by: Estonian University of Life Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

percentile method,

parameter prediction model,

Related subjects:

Ecology,

© 2020 Friday Nwabueze Ogana, published by Estonian University of Life Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 72 (2020): Issue 1 (September 2020)

A percentile-based estimator for the log-logistic function: Application to forestry

Figures & Tables

Figure 1

Figure 2

Descriptive statistics of the inventoried data from natural forests and plantations_

Models for the percentiles, scale and shape parameters and their cross-validation indices_

Estimated parameters, goodness-of-fits and the relative rank sum (R) of the percentiles and MLE in natural forest_

Estimated parameters, goodness-of-fits and the relative rank sum (R) of the percentiles and MLE in plantations_

Paradigm

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