• Journal of the Korean Data and Information Science Society
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• 제27권4호
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• pp.1091-1100
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• 2016

This paper considers the noninformative priors for the linear function of parameters in the lognormal distribution. The lognormal distribution is applied in the various areas, such as occupational health research, environmental science, monetary units, etc. The linear function of parameters in the lognormal distribution includes the expectation, median and mode of the lognormal distribution. Thus we derive the probability matching priors and the reference priors for the linear function of parameters. Then we reveal that the derived reference priors do not satisfy a first order matching criterion. Under the general priors including the derived noninformative priors, we check the proper condition of the posterior distribution. Some numerical study under the developed priors is performed and real examples are illustrated.

• Nuclear Engineering and Technology
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• 제54권6호
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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.

• Journal of the Korean Data and Information Science Society
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• 제22권2호
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• pp.171-177
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• 2011

최근에 비약적으로 발달하는 보험 산업에 수반하여 보험금 지불 분포에 대한 연구가 활발하게 진행되고 있다. 보험금 지불금의 분포는 일반적으로 두터운 꼬리를 가지면서 좌로 치우친 왜도를 가지는 파레토 분포나 로그노말 분포로 잘 설명된다고 알려져 왔으며 Cooray와 Ananda (2005)는 이들 두 분포를 결합한 결합 로그노말-파레토분포를 제시하고 이 분포의 적합도가 높음을 보였다. 그런데 보험금 지불의 경우 보금지불 총 금액의 한도로 인하여 극단적으로 큰 보험금이나 혹은 매우 사소한 보험지불금의 경우는 옵션을 두어 예외적으로 취금하는 경우가 많다. 본 논문에서는 결합 로그노말-파레토 분포로부터 추출된 표본이 양쪽 중도 절단되어 있는 경우에 대하여 모수를 추정하는 문제를 다루어 보았다.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.311-319
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• 2013

Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

• Communications for Statistical Applications and Methods
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• 제28권4호
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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.

• 한국물환경학회지
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• 제39권6호
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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.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2001년도 추계학술발표회
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• pp.92-96
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• 2001

Although the problem of seawater intrusion at the coastal aquifer was recognized before over one hundred years at the coastal aquifer, much groundwater keep on being salinitized by several reasons such as groundwater exhaustion, coastalline change, and human activities. The horizontal and vertical electrical soundings and geostatistical methods were used to define the local characteristics of saltwater intrusion and to estimate the saltwater interface in the southeastern area of the Pusan City. The 24 points of the Schlumberger vertical electrical soundings(VES) to loom depth and the 2 lines of dipole-dipole horizontal soundings are peformed. The resistivity data have lognormal distributions. The horizontal extents of saline water intrusion were estimated from the inversion of horizontal prospecting data. Lognormal ordinary kriging is used in A-A' resistivity profiles on May and July because the data have stationary models in semivariograms. Lognormal IRF-k kriging is used for the isopleth maps using vertical resistivity data. The 10 ohm-m resistivity line on the isopleth maps of 21m, 30m, 50m, and 70m depth using resisitivity data measured in July is sifted to the east, cpomparing that of the isopleth maps measured in May. The kriged vertical and horizontal resistivity isopleth maps suggested that the geostatistical methods can be used to define the variation of earth resistivity distribution at the saltwater interface.

• Nuclear Engineering and Technology
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• 제54권5호
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• pp.1606-1615
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• 2022

For investigating whether the MARSSIM nonparametric test has sufficient statistical power when a site has a specific contamination distribution before conducting a final status survey (FSS), a novel approach was proposed to predict the release probability of the site. Five distributions were assumed: lognormal distribution, normal distribution, maximum extreme value distribution, minimum extreme value distribution, and uniform distribution. Hypothetical radioactivity populations were generated for each distribution, and Sign tests were performed to predict the release probabilities after extracting samples using Monte Carlo simulations. The designed Type I error (0.01, 0.05, and 0.1) was always satisfied for all distributions, while the designed Type II error (0.01, 0.05, and 0.1) was not always met for the uniform, maximum extreme value, and lognormal distributions. Through detailed analyses for lognormal and normal distributions which are often found for contaminants in actual environmental or soil samples, it was found that a greater statistical power was obtained from survey units with normal distribution than with lognormal distribution. This study is expected to contribute to achieving the designed decision error when the contamination distribution of a survey unit is identified, by predicting whether the survey unit passes the statistical test before undertaking the FSS according to MARSSIM.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1119-1128
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• 2005

The Bayes factors with improper noninformative priors are defined only up to arbitrary constants. So it is known that Bayes factors are not well defined due to this arbitrariness in Bayesian hypothesis testing and model selections. The intrinsic Bayes factor and the fractional Bayes factor have been used to overcome this problem. In this paper, we suggest a Bayesian hypothesis testing based on the intrinsic Bayes factor and the fractional Bayes factor for the comparison of two lognormal variances. Using the proposed two Bayes factors, we demonstrate our results with some examples.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.11-18
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• 1999

To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.