• 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.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2003년도 추계학술발표회
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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.

• 한국농공학회지
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• 제31권4호
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• pp.31-49
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• 1989

It is of the most urgent necessity to get hydrological time series of long duration for the establishment of rational design and operation criterion for the Agricultural hydraulic structures. This study was conducted to select best fitted frequency distribution for the monthly runoff and to simulate long series of generated flows by multi-season first order Markov model with comparison of statistical parameters which are derivated from observed and sy- nthetic flows in the five watersheds along Geum river basin. The results summarized through this study are as follows. 1. Both two parameter gamma and two parameter lognormal distribution were judged to be as good fitted distributions for monthly discharge by Kolmogorov-Smirnov method for goodness of fit test in all watersheds. 2. Statistical parameters were obtained from synthetic flows simulated by two parameter gamma distribution were closer to the results from observed flows than those of two para- meter lognormal distribution in all watersheds. 3. In general, fluctuation for the coefficient of variation based on two parameter gamma distribution was shown as more good agreement with the observed flow than that of two parameter lognormal distribution. Especially, coefficient of variation based on two parameter lognormal distribution was quite closer to that of observed flow during June and August in all years. 4. Monthly synthetic flows based on two parameter gamma distribution are considered to give more reasonably good results than those of two parameter lognormal distribution in the multi-season first order Markov model in all watersheds. 5. Synthetic monthly flows with 100 years for eack watershed were sjmulated by multi- season first order Markov model based on two parameter gamma distribution which is ack- nowledged to fit the actual distribution of monthly discharges of watersheds. Simulated sy- nthetic monthly flows may be considered to be contributed to the long series of discharges as an input data for the development of water resources. 6. It is to be desired that generation technique of synthetic flow in this study would be compared with other simulation techniques for the objective time series.

• 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.

• Asian Pacific Journal of Cancer Prevention
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• 제13권5호
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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.

• 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.

• 한국지하수토양환경학회지:지하수토양환경
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• 제8권4호
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• pp.21-26
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• 2003

황과 Powers(2003)는 입도분포와 공극크기분포에 로그분포함수를 적용하여, 입도분포로부터 토양수분특성을 직접 추정하는 간단한 모형을 개발하였다. 본 연구의 목적은 황과 Powers(2003)가 개발한 모형의 추정능력이 토성에 의해 영향을 받는가를 밝히는 것이다. 연구결과, 모형은 토성에 의해 영향을 받았고, 특히 토양내 세립질 분율이 커질수록 모형의 추정능력은 감소하였다. 또한 입도와 공극크기사이의 관계를 비선형으로 가정한 비선형모형이 선형모형보다 토성에 관계없이 그 추정능력이 크게 나타났다.

• 대한교통학회지
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• 제4권2호
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• pp.3-14
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• 1986

This study was undertaken to develop the gap acceptance model of left-turn drivers on the major road at intersections. Typical unsignalized intersections on the two-lane and four-lane streets in Masan City were selected for the study intersection. For the gap distribution model, the lognormal, negative exponential, shifted negative exponential, and Gamma distributions were tested using the x2 and K-S tests. Based on the results for both streets, it was concluded that among the distributions tested the lognormal distribution represented the gap distribution best, followed by the shifted negative exponential distribution. Stochastic models of the gap-acceptance behavior of left-turn drivers on the major road at unsignalized intersections were programmed using SLAM Ⅱ, a simulation computer language. A stochastic model was selected for the gap-acceptance behavior to compare the results of the simulation with the observed data. The model assumes that a fixed critical acceptance gap is assigned to each left-turn driver based on a normal distribution and the gap distribution of the opposing traffic stream follows the shifted negative exponential distribution.

• 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.

• 품질경영학회지
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• 제34권3호
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• pp.19-30
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• 2006

For highly reliable products, it is difficult to assess the lifetime of the products with traditional life tests. Accordingly, a recent approach is to observe the performance degradation of product during the test rather than regular failure time. This study compares performances of three methods(i.e. the approximation, analytical and numerical methods) to estimate the parameters and quantiles of the lifetime when the time-to-failure distribution follows Weibull and lognormal distributions under a random coefficient degradation rate model. Numerical experiments are also conducted to investigate the effects of model error such as measurements in a random coefficient model.