• Journal of Forest and Environmental Science
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• 제36권1호
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• The Korean Journal of Ecology
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• 제23권6호
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• pp.435-438
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• 2000

Diameter distributions describe forest stand structure information. Prediction equations for percentiles of diameter distribution and parameter recovery procedures for the Weibull distribution function based on four percentile equations were applied to develop prediction system of even-aged slash pine stand structure development in terms of the number of stems per diameter class changes. Four percentiles of the cumulative diameter distribution were predicted as a function of stand characteristics. The predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level. Statistically, no significant differences were detected based on the data from 236 evaluation data sets. This stand level diameter distribution prediction system will be useful in slash pine stand structure modeling and in updating forest inventories for the long-term forest management planning.

• Communications for Statistical Applications and Methods
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• 제28권1호
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Structural Engineering and Mechanics
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• 제28권3호
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• pp.263-280
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• 2008

Information on the distribution of the basic random variable is essential for the accurate analysis of structural reliability. The usual method for determining the distributions is to fit a candidate distribution to the histogram of available statistical data of the variable and perform approximate goodness-of-fit tests. Generally, such candidate distribution would have parameters that may be evaluated from the statistical moments of the statistical data. In the present paper, a cubic normal distribution, whose parameters are determined using the first four moments of available sample data, is investigated. A parameter table based on the first four moments, which simplifies parameter estimation, is given. The simplicity, generality, flexibility and advantages of this distribution in statistical data analysis and its significance in structural reliability evaluation are discussed. Numerical examples are presented to demonstrate these advantages.

• 물과 미래
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• 제29권1호
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• pp.129-139
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• 1996

수공구조물의 계획과 설계에 있어서 수문자료에 대한 적정분포형을 선정하는 것은 매우 중요하며, 선정된 분포함수가 실측자료의 통계학적 특성을 잘 나타내고 있는가를 검토하는 것은 필수적인 과제이다. 본 연구에서는 전국 22개 지점, 7개 지속기간의 강우자료에 대하여 2변수 및 3변수 gamma, 2변수 및 3변수 lognormal, Gumbel, 2변수 및 3변수 log-Gumbel, GEV, log-Pearson type III, 2변수 및 3변수 Weibull, 4변수 및 5변수 Wakeby 분포를 적용하여 모멘트법, 확률가중 모멘트법, 최우도법 등으로 각 분포형의 매개변수를 추정하고, 적합성 조건을 검사하였다. 각 매개변수 추정법에 의하여 추정된 매개변수를 이용하여 10,000번 모의 발생하여 분리효과를 검토한 결과 매개변수 적합성을 고려한 경우 모멘트법에서는 log-Pearson type III 분포, 확률가중 모멘트법에서는 log-Pearson type III와 GEV 분포, 최우도법에서는 GEV 분포가 분리효과를 가장 작게 나타냈으며, 2변수 분포형의 경우 모두 분리효과가 크게 나타났다.

• 한국생산제조학회지
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• 제18권5호
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• pp.536-543
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• 2009

In this paper the mean stress effects on the probability distribution of the random grown crack size at a specified loading cycle are studied through the fatigue crack propagation tests, which are conducted on the specimens of magnesium alloy under four different stress ratios. Through 80 replicates the probability distributions of the grown crack size are obtained. The goodness-of-fit for probability distributions of the random grown crack size are investigated by Anderson-Darling test and the best fit for those probability distributions is found to be a 3-parameter Weibull distribution. The effects of the mean stress on the probability distribution of the random grown crack size are also estimated.

• Wind and Structures
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• 제31권5호
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• pp.419-430
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• 2020

Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.

• Journal of Radiation Protection and Research
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• 제15권2호
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• pp.101-112
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• 1990

For the performance assessment of the radioactive waste disposal system (repository), a biosphere model is suggested. This biosphere model is intended to calculate the annual doses to man caused by the contaminated river water for eight pathways and four radionuclides. This model can also be applied to assess the radiological effects of contaminated well water. To account for the uncertainties on the model parameter values, parameter distributions are assigned to these model parameters. Then, Monte Carlo simulation method with Latin Hypercube sampling technique is used. Also, sensitivity analysis is performed by using the Spearman rank correlation coefficients. It is found that these methods are a very useful tool to treat uncertainties and sensitivities on the model parameter values and to analyze the biosphere model. A conversion factor is proposed to calculate the annual dose rate to humans arising from a unit radionuclide concentration in river water. This conversion factor allows for the substitution of the biosphere model in a probabilistic performance assessment computer code by one single variable.

• 한국산림과학회지
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• 제90권2호
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• pp.176-183
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• 2001

본(本) 연구(硏究)에서는 목재(木材)의 다목적(多目的) 생산량(生産量)(multiple-product yield) 예측(豫測)에 대한 해결책(解決策)으로서 테다소나무(Pinus taeda L.) 조림지(造林地)를 대상으로 하여 Weibull 직경분포(直徑分布) 수확예측(收穫豫測) 시스템을 개발(開發)하였다. 직경분포(直徑分布) 수확예측(收穫豫測) 모형(模型)을 개발(開發)하기 위하여, 4개의 백분위수(百分位數) 식(式)들을 근거(根據)로 한 모수(母數) 회복(回復)(parameter recovery) 절차법(節次法)을 적용(適用)하였다. 또한 직경급(直徑級)에 대한 수확량(收穫量) 계산(計算)을 위하여 단목(單木) 수고(樹高) 예측식(豫測式)을 개발(開發)하였으며, 그리고 단목(單木) 재적(材積) 예측식(豫測式)을 이용(利用)함으로써 직경급(直徑級)에 대해 기대되는 재적량(材積量)을 계산(計算)할 수가 있다. 본(本) 연구(硏究)에서 사용(使用)된 직경급(直徑級)에 대한 Weibull 누적함수(累積函數)의 상한선(上限線) 차이(差異) 방법(方法)이 기존(旣存)의 상한선(上限線)과 하한선(下限線)의 절차법(節次法)보다도 괄약오차(括約誤差)를 줄 일수 있는 보다 나은 절차법(節次法)이였다. 본(本) 연구(硏究)에서 제시(提示)된 Weibull 직경분포(直徑分布) 수적예측(收積豫測) 시스템에 대한 타당성(妥當性) 검정(檢定)의 한 방법(方法)으로서 Kolmogorov-Smirnov test 결과(結果), 각(各) plot당 예측(豫測)된 직경분포(直徑分布)와 관측(觀測)된 직경(直徑) 분포급(分布級) 사이에서 통계적(統計的) 유의성(有意性)이 없는 것으로 나타났다. 이와 같은 직경분포(直徑分布) 수확예측(收穫豫測) 시스템은 다목적(多目的) 목재(木材) 생산량(生産量) 예측(豫測)과 임분(林分) 구조(構造) 모형(模型) 및 임분(林分)의 경영(經營)에 유용(有用)한 정보(情報)를 제공(提供)할 것이다.