• Communications for Statistical Applications and Methods
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• v.28 no.4
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• pp.351-368
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• 2021

For a probabilistic model with positively skewed data, a lognormal distribution is one of the key distributions that play a critical role. Several lognormal models can be found in various areas, such as medical science, engineering, and finance. In this paper, we propose a new estimator for a lognormal mean and depict the performance of the proposed estimator in terms of the relative mean squared error (RMSE) compared with Shen's estimator (Shen et al., 2006), which is considered the best estimator among the existing methods. The proposed estimator includes a tuning parameter. By finding the optimal value of the tuning parameter, we can improve the average performance of the proposed estimator over the typical range of σ². The bias reduction of the proposed estimator tends to exceed the increased variance, and it results in a smaller RMSE than Shen's estimator. A numerical study reveals that the proposed estimator has performance comparable with Shen's estimator when σ² is small and exhibits a meaningful decrease in the RMSE under moderate and large σ² values.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Journal of Korea Water Resources Association
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• v.53 no.10
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• pp.917-928
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• 2020

The purpose of this study is to find the appropriate probability distribution representing the size distribution of suspended cohesive sediment. Based on goodness-of-fit test for a significance level of 5% using the Kolmogorov-Smirnov test, it is found that the floc size distributions measured in laboratory experiment and field study show different results. In the case of sample data collected from field experiments, the Gamma distribution is the best fitting form. In the case of laboratory experiment results, the sample data shows the positively-skewed distribution and the GEV distribution is the best fitted. The lognormal distribution, which is generally assumed to be a floc size distribution, is not suitable for both field and laboratory results. By using 3-parameter lognormal distribution, it is shown that similar size distribution with floc size distribution can be simulated.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.09a
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• pp.99-101
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• 2003

Unsaturated hydraulic conductivity models have been widely used for the numerical modeling of water flow and contaminant transport in soils. In this study, a simple hydraulic conductivity model is developed by using information of particle-size distribution from the lognormal distribution model and its results are compared with those from the Kosugi-Mualem (KM) model. The accuracy of the proposed model is verified for observed data chosen from the international UNSODA database. Results showed that the proposed model produces adequate predictions of hydraulic conductivities. Performance of this model is generally better than the KM function.

• Journal of Applied Reliability
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• v.4 no.1
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• pp.15-26
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• 2004

Life test is performed to set a confidence (lower) limit on the mean or median life of items if the number of failures at the end of the fixed time t does not exceed a given number c. Gupta(1962) propose a sampling plan for truncated life tests when the life distribution of an item is normal or lognormal distribution. In this paper, based on the result of Gupta(1962), we propose a sampling plan for failure rate test when an item has normal or lognormal life distribution. We assume that the shape parameter is known while the location parameter is unknown.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.227-237
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• 2004

In this paper we presented a Bayesian inference approach for estimating the location and scale parameters of the lognormal distribution using iterative Gibbs sampling algorithm. We also presented estimation of location parameter by two non iterative methods, importance sampling and weighted bootstrap assuming scale parameter as known. The estimates by non iterative techniques do not depend on the specification of hyper parameters which is optimal from the Bayesian point of view. The estimates obtained by more sophisticated Gibbs sampler vary slightly with the choices of hyper parameters. The objective of this paper is to illustrate these tools in a simpler setup which may be essential in more complicated situations.

• Journal of Plant Biology
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• v.27 no.1
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• pp.25-32
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• 1984

A study on the dominance-diversity of forest vegetation in Mt. Seolag was conducted from May 1981 to Aug. 1983. Based on the field data, the dominance-diversity curves were for 16 sites including slopes and vallies. The curves are grouped in two types, lognormal distribution at the sites of mature vegetation and geometric series at the disturbed or rocky sites. It seems that the curves express the nature of their ecocline, by the hypotheses of some investigators, i.e. Random Niche hypothesis, Niche Pre-emption hypothesis, Lognormal distribution and Logarithmic series. The dominance concentration among the southern, northern and western slope, H'=1.282 at southern slope and H'=1.385 at western slope. Dominance-diversity curves of 16 sites showed Preston's lognormal distribution with small variations among them. It seems that the dominance diversity reflects the differences in the coenocline of their sites. The top 10 dominant species in species sequence of 113 tree species in whole the mountain, were noticed: Quercus mongolica, Pinus densiflora, Acer pseudo-siebold anum, Quercus serrata, Carpinus laxiflora, Styrax obassia, Fraxinus rhynchophylla, Tilia amurensis, Lindera obtusiloba and Abies holophylla in order.

• Journal of Applied Reliability
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• v.12 no.1
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• pp.47-56
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• 2012

Reliability demonstration tests with zero-failure acceptance criterion are most commonly used in the field of reliability application since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. For products with lognormal lifetime distribution, an economic zero-failure test plan is developed that minimizes the total cost related to perform a life test to guarantee a specified reliability of a product with a given confidence level. A numerical example is provided to illustrate the use of the proposed test plan.

• Journal of Korean Society on Water Environment
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• v.39 no.6
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• pp.475-490
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• 2023

Chemical water quality suitability for species (Ephemera strigata, Ephemera separigata, and Ephemera orientalis-sachalinensis group) of the mayfly genus Ephemera (Order Ephemeroptera) was analyzed with probability distribution models (Exponential, Normal, Lognormal, Logistic, Weibull, Gamma, Beta, Gumbel). Data was collected from 23,957 sampling units of 6,664 sites in Korea from 2010 to 2021. E. orientalis-sachalinensis occurred at the range of BOD₅ 0.3~11.1 mg/L (the best-fit Lognormal model); T-P 0.007~0.769 mg/L (the Gumbel model); TSS 0.4~142.2 mg/L (the Lognormal model). E. strigata occurred at the range of BOD₅ 0.4~7.4 mg/L (the Gumbel model); T-P 0.007~0.254 mg/L (the Lognormal model); TSS 0.4~17.1 mg/L (the Lognormal model). E. separigata occurred at the range of BOD₅ 0.4~2.6 mg/L (the R-Weibull model); T-P 0.007~0.134 mg/L (the Lognormal model); TSS 0.7~10.0 mg/L (the Lognormal model). Habitat suitability range of E. orientalis-sachalinensis was estimated to be 0.4~1.9 mg/L (BOD₅), 0.024~0.086 mg/L (T-P), 2.5~22.4 mg/L (TSS); that of E. strigata was 0.4~0.7 mg/L (BOD₅), 0.007~0.018 mg/L (T-P), 0.0~1.7 mg/L (TSS); that of E. separigata was 0.0~0.4 mg/L (BOD₅), 0.000~0.015 mg/L (T-P), 0.5~3.1 mg/L (TSS). In a relative comparision, E. orientalis-sachalinensis was estimated to be eurysaprobic, and narrowly adapted in high levels of T-P and TSS, E. strigata was estimated to be oligosaprobic and adapted in low levels of T-P and TSS, and E. separigata was estimated to be stenooligosaprobic and widely adapted in low level of T-P and TSS.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2084-2093
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• 2022

Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is approximated with the sum of lognormal random variables after minimal cutsets are obtained, and rare-event approximation is applied. As handling complicated analytic expressions for the sum of lognormal random variables is challenging, several approximation methods, especially Monte Carlo simulation, are widely used in practice for uncertainty analysis. In this study, a theoretical approach for analyzing the sum of lognormal random variables using an efficient numerical integration method is proposed for uncertainty analysis in probability safety assessments. The change of variables from correlated random variables with a complicated region of integration to independent random variables with a unit hypercube region of integration is applied to obtain an efficient numerical integration. The theoretical advantages of the proposed method over other approximation methods are shown through a benchmark problem. The proposed method provides an accurate and efficient approach to calculate the uncertainty of the top event in probabilistic safety assessment when the uncertainties of basic events are described with lognormal random variables.