• Magazine of the Korean Society of Agricultural Engineers
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• v.35 no.3
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• pp.100-116
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• 1993

It is experienced fact that unreasonable design criterion and unsitable operation management for the agricultural structures including reservoirs based on short terms data of monthly flows have been brought about not only loss of lives, but also enormous property damage. For the solution of this point at issue, this study was conducted to simulate long series of synthetic monthly flows by multi-season first order Markov model with selection of best fitting frequency distribution and to make a comparison of statistical parameters between observed and synthetic flows of six watersheds in Yeong San and Seom Jin river systems. The results obtained through this study can be summarized as follows. 1.Both Gamma and two parameter lognormal distribution were found to be suitable ones for monthly flows in all watersheds by Kolmogorov-Smirnov test while those distributions were judged to be unfitness in Nam Pyeong of Yeong San and Song Jeong and Ab Rog watersheds of Seom Jin river systems in the $\chi$$^2$ goodness of fit test. 2.Most of the arithmetic mean values for synthetic monthly flows simulated by Gamma distribution are much closer to the results of the observed data than those of two parameter lognomal distribution in the applied watersheds. 3.Fluctuation for the coefficient of variation derived by Gamma distribution was shown in general as better agreement with the results of the observed data than that of two parameter lognormal distribution in the applied watersheds both in Yeong San and Seom Jin river systems. Especially, coefficients of variation calculated by Gamma distribution are seemed to be much closer to those of the observed data during July and August. 4.It can be concluded that synthetic monthly flows simulated by Gamma distribution are seemed to be much closer to the observed data than those by two parameter lognormal distribution in the applied watersheds. 5.It is to be desired that multi-season first order Markov model based on Gamma distribution which is confirmed as a good fitting one in this study would be compared with Harmonic synthetic model as a continuation follows.

• Journal of Radiation Protection and Research
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• v.31 no.1
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• pp.17-23
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• 2006

The purpose of this study is to provide the guidance necessary for making a selection of error distributions by analyzing influence of statistical distribution for a type of bioassay measurement error on the intake estimation. For this purpose, intakes were estimated using maximum likelihood method for cases that error distributions are normal and lognormal, and comparisons between two distributions for the estimated intakes were made. According to the results of this study, in case that measurement results for lung retention are somewhat greater than the limit of detection it appeared that distribution types have negligible influence on the results. Whereas in case of measurement results for the daily excretion rate, the results obtained from assumption of a lognormal distribution were 10 % higher than those obtained from assumption of a normal distribution. In view of these facts, in case where uncertainty component is governed by counting statistics it is considered that distribution type have no influence on intake estimation. Whereas in case where the others are predominant, it is concluded that it is clearly desirable to estimate the intake assuming a lognormal distribution.

• Journal of Applied Reliability
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• v.2 no.2
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• pp.63-83
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• 2002

Degradation data can provide more reliability information than traditional failure-time data, especially products with few or no failures. This paper is concerned with a method of estimating lifetime distribution from field data with supplementary information on degradation data and covariates. When a distribution of degradation rate obtained by follow-up study for a portion of products that survive after-warranty follows a reciprocal-Weibull or lognormal distribution. A time-to-failure distribution of the product follows Weibull or lognormal distribution, respectively. A method of estimating lifetime parameters for this kind of data and their asymptotic properties are studied. Effects of after-warranty report probability, follow-up rate, and proportion of degradation data on pseudo maximum likelihood estimators of these parameters are investigated.

• IE interfaces
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• v.22 no.3
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• pp.214-222
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• 2009

In the early design stage, system reliability must be estimated from life testing data at the component level. Previously, a point estimate of system reliability was obtained from the unbiased estimate of the component reliability after assuming that the number of failed components for a given time followed a binomial distribution. For deriving the confidence interval of system reliability, either the lognormal distribution or the normal approximation of the binomial distribution was assumed for the estimator of system reliability. In this paper, a new estimator is used for the component level reliability, which is biased but has a smaller mean square error than the previous one. We propose to use the beta distribution rather than the lognormal or approximated normal distribution for developing the confidence interval of the system reliability. A numerical example based on Monte Carlo simulation illustrates advantages of the proposed approach over the previous approach.

• Korean Journal of Construction Engineering and Management
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• v.6 no.1 s.23
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• pp.49-57
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• 2005

Construction labor productivity, which is the greatest source of variation in overall construction productivity, is the critical factor for determining the project performance in terms of time and cost, especially during scheduled overtime when extra time and cost are invested. The objective of this research is to select an appropriate type of probability distribution function representing the variability of daily labor productivity during overtime. Based on the results of statistical data analysis of labor performance during different weekly work hours, lognormal distribution is selected in order to take advantage of easiness of generating correlated random numbers. The selected lognormal distribution can be used for development of a simulation model in construction scheduling, cost analysis, and other applications areas where representation of the correlations between variables are essential.

• 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.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.09a
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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.

• Journal of Wetlands Research
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• v.2 no.1
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• pp.49-58
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• 2000

The frequency analysis of annual maximum rainfall data and the derivation of probable rainfall intensity formula at Masan station are performed in this study. Based on the eight different rainfall duration data from 10 minutes to 24 hours, eight types of probability distribution (Gamma, Lognormal, Log-Pearson type III, GEV, Gumbel, Log-Gumbel, Weibull, and Wakeby distributions), three types of parameter estimation scheme (moment, maximum likelihood and probability weighted methods) and three types of goodness-of-fit test (${\chi}^2$, Kolmogorov-Smirnov and Cramer von Mises tests) were considered to find an appropriate probability distribution at Masan station. The Lognormal-2 distribution was selected and the probable rainfall intensity formula was derived by regression analysis. The derived formula can be used for estimating rainfall quantiles of the Masan vicinity areas with convenience and reliability in practice.

• Magazine of the Korean Society of Agricultural Engineers
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• v.32 no.E
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• pp.20-32
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• 1990

Abstract This study was conducted to pursue the normalization of frequency distribution by making an approach to the coefficient of skewness to nearly zero through the Box-Cox transformation, to get probable flood flows can be calculated by means of the transformation equation which has been derivated by Box-Cox transformation in the annual maximum series of the applied watersheds. It has been concluded that Box-Cox transfromation is proved to be more efficient than logarithmic, square root and SMEMAX transformation which is based on the trigonometric solution of a right triangle whose three verteces repesent the smallest, median and largest observed values of a population in making the coefficient of skewness nearer to zero. Consequently it is shown that probable flood flows according to the return period based on Box-Cox transformation are closer to the observed data as compared to other methods including SMEMAX transformation and fitted probability distributions such as the three parameter lognormal and the type I extremal distribution for the applied watersheds.

• Journal of Applied Reliability
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• v.18 no.1
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• pp.80-86
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• 2018

Purpose: This article provides a mathematical model for the accelerated degradation test when the performance degradation characteristic follows the lognormal distribution. Method: For developing test plans, the total number of test units and the test time are determined based on the minimization of the asymptotic variance of the q-th quantile of the lifetime distribution at the use condition. Results: The mathematical model for the accelerated degradation test is provided. Conclusion: Accelerated degradation test method is widely used to evaluate the product lifetime within a resonable amount of cost and time. In this article. a mathematical model for the accelerated degradation test method is newly developed for this purposes.