Nonlinear Height-DBH Growth Models for Larix kaempferi in Gangwon and North Gyeongsang Province
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This study was conducted to estimate the best-fit nonlinear height-DBH growth models for Larix kaempferi in Gangwon and North Gyeongsang province in South Korea. Exponential, Modified Logistic, Chapman-Richards, and Weibull function were used for estimating height-DBH models. To evaluate the selected models, Keywords:
Larix kaempferi
Logistic function
The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.
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Abstract Weibull renewal function has attracted a lot of attention because the Weibull distribution describes in a relatively simple analytical manner a wide range of realistic behavior and its shape and scale parameters can be readily determined with graphical or statistical procedure. On the other hand, there are no closed form analytical solutions for the Weibull renewal function except for the special case of exponential distribution. Bounds, approximations, and tables are usually used. In this article, some approximations based on Normal approximation of Weibull distribution are studied. Such a procedure, which is different from that in the existing literature, is shown to be good for Weibull renewal function when the shape parameter is of moderate or large size. Series truncation expression and approximation bounds can be obtained as well. Numerical examples and comparisons are shown to illustrate the procedure.
Truncation (statistics)
Weibull modulus
Shape parameter
Exponentiated Weibull distribution
Scale parameter
Expression (computer science)
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Weibull modulus
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A simple yet accurate approximation method is proposed to solve the Weibull renewal function (RF) when the shape parameter β is between 0 and 1. The idea is to find a simple mixture model, constructed by two exponential functions, to approximate the Weibull distribution function. Parameters of the mixture model can be determined using minimum mean square errors (MMSEs) or moment match. Now finding the Weibull RF becomes the problem to find the RF for the mixture model. The mixture model allows the Laplace transform that significantly simplifies the computation of the RF. Numerical data show that the new analytical RF model is mathematically accurate and computationally convenient to approximate the actual Weibull RF for 0<β<1. The primary contribution of this paper is that the Weibull RF with decreasing failure rate can be directly approximated by the combination of two exponential functions.
Weibull modulus
Shape parameter
Exponentiated Weibull distribution
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Taken the different site types and different clones of Larix kaempferi Carr.as the research objects,through the continuous observation and analysis on height,diameter and volume for 32 years,the excellent clones suited to be planted in Chifeng have been determined,in order to realize the forestation with the excellent clones of Larix kaempferi Carr.
Larix kaempferi
Carr
Afforestation
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Based on the comparison in volume of Larix kaempferi prediction model,the study showed that SSE of the Logistic function was less than the GM(1,1) model,R2 of the Logistic function was more than that of GM(1,1) model,and according to the criteria in model evaluation,the Logistic model was more suitable to forecast growth of Larix kaempferi.From the graphical analysis,the study showed that GM(1,1) model was applicable to exponential sequence with strong regularity,so GM(1,1) model was more suitable for the short-term prediction in forest growth.The Logistic function graphic was closer to the volume of the trend,so it can be more accurate to predict forecast growth,and it also provides a scientific theory for reasonable business using in Larix kaempferi plantation.
Larix kaempferi
Logistic function
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Larix kaempferi
Larix gmelinii
Compensation point
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We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation.
Exponentiated Weibull distribution
Weibull modulus
Weibull fading
Representation
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It chose 6 vertical factors and utilized the method of quantification theory I in the foundation of analyzing comprehensively the influence of Larch-tree(Larix kaempferi) growth environment factors.This paper constructed the model of eastern part of Liaoning province.Using this model to appraise the eastern part of Liaoning province area Larch-tree(Larix kaempferi) vertical quality.
Larix kaempferi
Tree (set theory)
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У Західному Лісостепу України Larix kaempferi відзначається дуже високими інтенсивністю росту (Id-Ie класи бонітету) та конкурентоздатністю в молодому віці, переважно витісняючи зі складу насаджень інші деревні види.
У чистих насадженнях L. kaempferi нагромаджує найвищі запаси стовбурової деревини, хоча її середні висота та діаметр тут помітно менші, ніж у мішаних деревостанах. Водночас, у разі встановлення в чистих культурах модрини густоти, близької до оптимальної, середні таксаційні показники хвойної породи наближаються до таких у мішаних насадженнях.
Збереженість модрини навіть і в початково чистих насадженнях характеризується високою варіабельністю, причиною чого є різні підходи до інтенсивності проведення рубок догляду. Відсутність конкретної програми вирощування модринових насаджень щодо встановлення близької до оптимальної густоти у різні вікові періоди є причиною неповного використання едафічного потенціалу типів лісорослинних умов, недоотримання значних обсягів деревини.
Доцільно на території лісового фонду Західного Лісостепу та прилеглих територій створювати чисті насадження модрини Кемпфера з рівномірним розміщенням садивних місць та постійним підтримуванням високої зімкнутості деревостану. Створювати плантаційні насадження цього деревного виду доцільно в умовах дібров і судібров, бучин і субучин, яличин і суяличин.
Як об’єкт плантаційного лісовирощування, L. kaempferi задовольняє низку важливих вимог: інтенсивний ріст та швидке нагромадження стовбурової деревини; проста технологія вирощування; відносно широка екологічна амплітуда, можливість успішного культивування в чистих насадженнях, цінна деревина; стійкість проти шкідників і хвороб; широкий діапазон застосування деревини; можливість ведення інтенсивного проміжного користування.
Larix kaempferi
Carr
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