• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.171-177
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• 2011

With the development of the actuarial and insurance industries, the distributions of the insurance payments data are deeply studied by many authors. It is known that theses types of distribution are very highly positively skewed and have a long thick upper tail such as Pareto or lognormal distribution. In 2005, Cooray and Ananda proposed a new model which is composed lognormal distribution and Pareto distribution. They said it as composite lognormal-Preto distribution. They showed that the proposed distribution was better fitted than lognormal or Pareto distribution. On the other hand many agreements about the insurance payment have some options for a trivially small payment or extremely large one because of the limits of total payment. Appling these cases, in this paper we consider the parameter estimation on the composite lognormal-Pareto distribution based on doubly censored samples.

• Journal of Food Hygiene and Safety
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• v.18 no.4
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• pp.237-242
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• 2003

Sequences of industrial microbial counts of foods shows irregular fluctuating patterns as adeinition of fluctuating microbial counts(FMC). Recently, it beame clear that the FMC was considered as having a lognormal distribution as a first order approximation. Application of lognormal distribution to the industrial microbial counts could produce useful information in practice. This study is intended to verift the application method of lognormal idstribution in FMC. The one year's records for microbial counts of frozen dumplings from two companies were obtained, and the statistical analysis was carried out to estimate the frequencies of future events where counts exceeding selected levels and to compare the sanitation level of the two companies. The results showed that this spplication method enable translation of irregular recourds of microbial counts into an useful information such as te actual probalities of outburst of a given level and the quantitative predictions of potential hazards in the processing.

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.109-122
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• 2018

The composite lognormal-generalized Pareto distribution (LN-GPD) is a mixture of right-truncated lognormal and GPD for a given threshold value. Scollnik (Scandinavian Actuarial Journal, 2007, 20-33, 2007) shows that the composite LN-GPD is adequate to describe body distribution and heavy-tailedness. This paper considers time-varying modeling of the LN-GPD based on local polynomial maximum likelihood estimation. Time-varying model provides significant detailed information of time dependent data, hence it can be applied to disciplines such as service engineering for staffing and resources management. Our work also extends to Beirlant and Goegebeur (Journal of Multivariate Analysis, 89, 97-118, 2004) in the sense of losing no data by including truncated lognormal distribution. Our proposed method is shown to perform adequately in simulation. Real data application to the service time of the Israel bank call center shows interesting findings on the staffing policy.

• 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.

• Journal of Navigation and Port Research
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• v.46 no.4
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• pp.303-312
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• 2022

Bridges across waterways act as interference factors, that reduce the navigable water area from the perspective of navigation safety. To analyze the safety navigational width of ships navigating bridges across waterways, the optimal traffic distribution based on AIS data was investigated, and ships were classified according to size through k-means clustering. As a result of the goodness-of-fit analysis of the clustered data, the lognormal distribution was found to be close to the optimal distribution for Incheon Bridge and Busan Harbor Bridge. Also, the normal distributions for Mokpo Bridge and Machang Bridge were analyzed. Based on the lognormal and normal distribution, the analysis results assumed that the safe passage range of the vessel was 95% of the confidence interval, As a result, regarding the Incheon Bridge, the difference between the normal distribution and the lognormal distribution was the largest, at 64m to 98m. The minimum difference was 10m, which was revealed for Machang Bridge. Accordingly, regarding Incheon Bridge, it was analyzed that it is more appropriate to present a safety width of traffic by assuming a lognormal distribution, rather than suggesting a safety navigation width by assuming a normal distribution. Regarding other bridges, it was analyzed that similar results could be obtained using any of the two distributions, because of the similarity in width between the normal and lognormal distributions. Based on the above results, it is judged that if a safe navigational range is presented, it will contribute to the safe operation of ships as well as the prevention of accidents.

• Journal of Soil and Groundwater Environment
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• v.8 no.4
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• pp.21-26
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• 2003

Hwang and Powers (2003) developed a simple model for estimating water retention characteristic (WRC) directly from particle-size distribution (PSD) data, by applying a lognormal distribution law to both PSD and pore-size distribution. The objective of this work was to determine if the performance of the model developed by Hwang and Powers (2003) would be affected by soil texture. The results of this research proved that the performance of the model was indeed affected by soil texture. In particular, its performance diminished with increases in the fine particle fractions. Also, the nonlinear model, which assumes a nonlinear relation between particle-size and pore-size, performed better than the linear model, regardless of soil texture classes.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.625-636
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• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.807-822
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• 2016

The composite lognormal-GPD models (LN-GPD) enjoys both merits from log-normality for the body of distribution and GPD for the thick tailedness of the observation. However, in the estimation perspective, LN-GPD model performs poorly due to numerical instability. Therefore, a two-stage procedure, that estimates threshold first then estimates other parameters later, is a natural method to consider. This paper considers five nonparametric threshold estimation methods widely used in extreme value theory and compares their performance in LN-GPD parameter estimation. A simulation study reveals that simultaneous maximum likelihood estimation performs good in threshold estimation, but very poor in tail index estimation. However, the nonparametric method performs good in tail index estimation, but introduced bias in threshold estimation. Our method is illustrated to the service time of an Israel bank call center and shows that the LN-GPD model fits better than LN or GPD model alone.

• Journal of Applied Reliability
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• v.14 no.1
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• pp.1-9
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• 2014

One important measure of performance for a repairable system is steady-state availability. In this paper, a method to estimate and establish confidence interval for the steady-state availability under Weibull lifetime and lognormal repair time distributions is proposed. Also, bias and mean squared error of a point estimator for an availability are investigated. In addition, a procedure to derive the sample size and critical value for availability demonstration test is presented and illustrated with a numerical example.

• 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.