• Proceedings of the Korea Water Resources Association Conference
• /
• 2008.05a
• /
• pp.173-178
• /
• 2008

확률도시위치는 주로 도시적 해석을 통한 연최대홍수량 또는 연최대강우량의 초과확률의 추정치 산정에 사용되며 빈도해석을 통해 선정된 적정 확률분포형과 표본자료의 개략적인 적합도를 도시적으로 파악할 수 있도록 해주기 때문에 오래 전부터 널리 이용되어 왔다. 본 연구에서는 Gumbel 분포에 적합한 도시위치공식을 새롭게 추정하기 위해 Gumbel 분포의 order statistic과 확률가중모멘트를 이용하여 다양한 표본크기에 대한 도시위치공식의 기본식을 유도하였고, 최적화 기법 중 하나인 유전자 알고리즘을 이용하여 유도된 도시위치공식의 매개변수를 추정하였다. 또한 본 연구에서 추정된 도시위치공식과 기존에 널리 사용되고 있는 도시 치공식의 정확도를 비교하기 위해 reduced variate 간의 오차를 계산하여 비교 검토하였다. 그 결과, 금회 추정된 도시위치공식은 높은 순위에서는 기존의 도시위치공식에 비해 더 정확도가 높은 것으로 나타났고, 표본크기에 대한 순위를 모두 고려할 경우에는 기존의 도시위치공식에 비해 정확도가 높은 것으로 나타나 Gumbel 분포에 대해서 높은 정확도를 보이는 것으로 나타났다.

• The Korean Journal of Applied Statistics
• /
• v.21 no.5
• /
• pp.739-754
• /
• 2008

Researches on conversion formulas between multiple decrement models and the associated single decrement models have focused on calculating yearly-based conversion formulas. In practice, actuaries may be more interested in monthly-based conversion formulas. Multiple decrement tables and their associated single decrement tables consist of yearly-based rates of multiple decrements and absolute rates of decrements, respectively. This paper derives conversion formulas from yearly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under the uniform distribution of decrements(UDD). Next, it suggests conversion formulas from monthly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under UDD. In addition, it calculates conversion formulas from yearly-based rates of decrement due to cause j to the corresponding absolute rates of decrements under UDD or constant force assumption. Some numerical examples are discussed.

• Communications of Mathematical Education
• /
• v.22 no.4
• /
• pp.505-514
• /
• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• The Korean Journal of Applied Statistics
• /
• v.21 no.6
• /
• pp.1045-1063
• /
• 2008

This paper derives conversion formulas from yearly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under FI (fractional age independence) assumption that is a generalization of UDD assumption. Next, it suggests conversion formulas from monthly-based absoluterates of decrements to monthly-based rates of decrement due to cause j under FI assumption. In addition, it calculates conversion formulas from yearly-based rates of decrement due to cause j to the corresponding monthly-based absolute rates of decrements under FI assumption. Some numerical examples are discussed.

• Journal of Korea Water Resources Association
• /
• v.46 no.2
• /
• pp.155-169
• /
• 2013

This study proposes proper forms of empirical formulas for the concentration time and storage coefficient based on their theoretical backgrounds and evaluates several existing empirical formulas by comparing them with the formula proposed in this study. Additionally, empirical formulas for the concentration time and storage coefficient of the Chungju Dam basin were derived using the forms proposed by considering their theoretical backgrounds, and compared with exiting empirical formulas. The results derived are summarized as follows. (1) The concentration time of a basin is proportional to the square of the main channel length, but inversely proportional to the channel slope, as the flood flow is generally turbulent. (2) The storage coefficient is proportional to the concentration time. (3) The comparison results with existing empirical formulas for the concentration time indicates that the empirical formulas like the Kirpich, Kraven (I), Kraven (II), California DoT, Kerby, SCS, and Morgali & Linsley are in line with the form proposed in this study. Among existing empirical formulas for the storage coefficient, the Clak, Russell, Sabol and Jung are found to be well matched to this study. (4) The application results to Chungju Dam basin indicates that among empirical formulas for the concentration time, the Jung, Yoon, Kraven (I), and Kraven (II) show relatively similar results to the observed in this study, but the Rziha shows abnormal results. Among the empirical formulas for the storage coefficient, the Yoon and Hong, Jung, Lee, and Yoon show somewhat reasonable results, but the Sabol shows abnormal results. In conclusion, the empirical formulas for the concentration time and storage coefficient developed in Korea are found to reflect the basin characteristics of Korea better.

• Journal of the Korean Society for information Management
• /
• v.5 no.2
• /
• pp.53-98
• /
• 1988

The purpose of this Study is to irwest~gate the Zipfian distribution in Har~gul literature. The result shows that the formulas derived from the liangul Ilterature are it1 accordance with the getlcra\ized Zipf's first law. The result also shows that the formulas derived from the Harlgul literature arc2 not in accordance with the Zlpf's second law and the penerali~ed Zipf's second law.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.3 no.3
• /
• pp.53-61
• /
• 1983

The Green-Ampt equation for infiltration has been intensively investigated by many researchers because of its simplicity and adequacy for fitting experimental data to theoretical one. The infiltration equation derived from the theory of two phase flow coincides with the Green-Ampt equation except the viscouse resistance correction factor. This approach clearly defines variables in the Green-Ampt equation and also encounters the effect of viscosity of two fluids. A new equation for infiltration into multilayered soil is derived from the theory of two phase flow and compared with conventional equation. The new equation shows lower infiltration rate than that of conventional one and it is believed that this caused from the inclusion of viscosity in the derivation.

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.9
• /
• pp.35-43
• /
• 2011

To develop a software, there is a relationship between development organization's productivity, effort, development schedule, and software size. It is software equation that motive these relations. Basically, relationship between size-effort and size-schedule is applied. If this relationship is not proper, there would be no effect of the cost-schedule tradeoff equation that is derived from software equation, and the manpower profile analysis, etc. To solve these unwanted problems, we presented a modified software equation and a cost-schedule tradeoff model based on the modified software equation. To improve software development success rate, applying proposed model will help in contract negotiation or bid.

• The KIPS Transactions:PartD
• /
• v.17D no.5
• /
• pp.327-336
• /
• 2010

This paper proposed software equation that is relation with effort and duration based on function point (FP) software size. Existent software equation based on lines of code (LOC). LOC sees big difference according to development language and there are a lot of difficulties in software size estimation. First, considered method that change LOC to FP. But, this method is not decided definitely conversion ratio between LOC and FP by development language. Also, failed though the conversion ratio motives software formula because was not presented about specification development language. Therefore, we derived software formula directly to large project data that was developed by FP. Firstly, datas that reasonable development period is set among development projects. Secondly, FP through regression analysis about this data and effort, motived relation with FP and duration. Finally, software equation was derived from these relation. Proposed model solves application problems that LOC-based model has and has advantage that application is possible easily in business.

• Journal of Korea Water Resources Association
• /
• v.44 no.2
• /
• pp.85-96
• /
• 2011

Probability plotting position is generally used for the graphical analysis of the annual maximum quantile and the estimation of exceedance probability to display the fitness between sample and an appropriate probability distribution. In addition, it is used to apply a specific goodness of fit test. Plotting position formula to define the probability plotting position has been studied in many researches. Especially, the GEV distribution which is an important probability distribution to analyze the frequency of hydrologic data was popular. In this study, the theoretical reduced variates are derived using the mean value of order statistics to derived an appropriate plotting position formula for the GEV distribution. In addition, various forms of plotting position formula considering various sample sizes and coefficients of skewness related with shape parameters are applied. The parameters of plotting position formulas are estimated using the genetic algorithm. The accuracy of derived plotting position formula is estimated by the errors between the theoretical reduced variates and those by various plotting position formulas including the derived ones in this study. As a result, the errors by derived plotting position formula is the smallest at the range of shape parameter with -0.25~0.10.