• Kyungpook Mathematical Journal
• /
• v.45 no.3
• /
• pp.339-348
• /
• 2005

In this paper, we discuss the value distribution of the derivative of a meromorphic function.

• Journal of Soil and Groundwater Environment
• /
• v.23 no.1
• /
• pp.41-53
• /
• 2018

Comprehensive statistical analysis for the 127 groundwater monitoring stations in Jeju Island during 2005~2015 was carried out for the re-establishment of management groundwater level. Three probability distribution functions such as normal distibution, GEV (General Extreme Value) distribution, and Gumbel distribution were applied and the maximum likelihood method was used for parameter estimation of each distribution. AIC (Akaike information criterion) was calculated based on the estimated parameters to determine the proper probability distribution for all 127 stations. The results showed that normal distribution and Gumble distribution were found in 11 stations. Whereas GEV distribution were found in 105 stations, which covered most of groundwater monitoring stations. Therefore, confidence levels should be established in accord with the proper probability distribution when groundwater level management is determined.

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

• The Korean Journal of Applied Statistics
• /
• v.22 no.1
• /
• pp.171-179
• /
• 2009

In this paper we studied the effective approximations to the distribution of the sum of products of normal variables. Based on the saddlepoint approximations to the quadratic forms, the suggested approximations are very accurate and easy to use. Applications to the FSK (Frequency Shift Keying) communication are also considered.

• Journal of the Korean Statistical Society
• /
• v.34 no.2
• /
• pp.125-140
• /
• 2005

In this paper, we consider the estimation of the correlation coefficient in the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) that was introduced by Al-Saleh and Al-Hadhrami (2003a). The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered under different settings. The obtained estimators are compared to their counterparts that are obtained based simple random sampling (SRS). It appears that the suggested estimators are more efficient

• Journal of the Korean Statistical Society
• /
• v.24 no.1
• /
• pp.257-266
• /
• 1995

Consider a p-variate $(p \geq 4)$ normal distribution with mean $\b{\theta}$ and identity covariance matrix. For estimating $\b{\theta}$ under a quadratic loss we investigate the behavior of risks of Stein-type estimators which shrink the usual estimator toward the mean of observations. By using concavity of the function appearing in the shrinkage factor together with new expectation identities for noncentral chi-squared random variables, a characterization of estimators with nondecreasing risk is obtained.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1996.10a
• /
• pp.95-102
• /
• 1996

In this study, a stochastic finite element model is proposed with a view to consider the uncertainty of physical properties of discontinuous rock mass in the analysis of structural behavior on underground caverns. In so doing, the LHS(Latin Hypercube sampling) technique has been applied to make up weak points of the Crude Monte Carlo technique. Concerning the effect of discontinuities, a joint finite element model is used that is known to be superior in explaining faults, cleavage, things of that nature. To reflect the uncertainty of material properties, the variables such as the the elastic modulus, the poisson's ratio, the joint shear stiffness, and the joint normal stiffness have been used, all of which can be applicable through normal distribution, log-normal distribution, and rectangulary uniform distribution. The validity of the newly developed computer program has been confirmed in terms of verification examples. And, the applicability of the program has been tested in terms of the analysis of the circular cavern in discontinuous rock mass.

• Journal of Mechanical Science and Technology
• /
• v.16 no.1
• /
• pp.60-74
• /
• 2002

In this study, normal, log-normal, triangular, uniform. Weibull, Erlang and unit beta probability density functions are tried to represent the behaviour of frequency distributions of workpiece dimensions collected from various manufacturing firms. Among the distribution functions, the unit beta distribution function is found to be the best fit using the chi-square test of fit. An attempt is made for the adoption of the unit beta model to x-bar charts of quality control in manufacturing. In this direction, upper and lower control limits (UCL and LCL) of x-bar control charts of dimension measurements are estimated for the beta model, and the observed differences between the beta and normal model control limits are discussed for the measurement sets.

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

• Communications for Statistical Applications and Methods
• /
• v.21 no.6
• /
• pp.529-538
• /
• 2014

In this paper, we consider maximum likelihood estimators of normal distribution based on type II censoring. Gupta (1952) and Cohen (1959, 1961) required a table for an auxiliary function to compute since they did not have an explicit form; however, we derive an explicit form for the estimators using a method to approximate the likelihood function. The derived estimators are a special case of Balakrishnan et al. (2003). We compare the estimators with the Gupta's linear estimators through simulation. Gupta's linear estimators are unbiased and easily calculated; subsequently, the proposed estimators have better performance for mean squared errors and variances, although they show bigger biases especially when the ratio of the complete data is small.