• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.687-705
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• 2006

In this paper we consider GPH distribution that is defined as a distribution for sum of random number of random variables following exponential distribution. We establish approximation process of general distributions to GPH distributions and offer numerical results for various cases to show the accuracy of the approximation. We also propose analysis method of delay distribution of queueing systems using approximation to GPH distributions and offer numerical results for various queueing systems to show applicability of GPH approximation.

• 한국경영과학회지
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• 제19권1호
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• pp.85-98
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• 1994

The distribution of random sum of i. i. d. exponential random variables is called GHP (Generalized Phase-Type) distribution. The class of GPH distributions is large enough to include PH (Phase-Type) distributions and has several properties which can be applied conveniently for computational purposes. In this paper, we show that any distribution difined on R$^{+}$ can be app-roximated by the GPH distribution and demonstrate the accuracy of the approximation through various numerical examples. Also, we introduce an efficient way to compute the delay and waiting various numerical examples. Also, we introduce an efficient way to compute the delay and waiting time distributions of the GPH/GPH/1 queueing system which can be used as an approximation model for the GI/G/1 system, and validate its accuracy through numerical examples. The theoretical and experimental results of this paper help us accept the usefulness of the approximations based on GPH distribution.n.

• 한국국방경영분석학회지
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• 제22권1호
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• pp.114-128
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• 1996

In this paper, a life distribution fitting method based on generalized phase-type distributions(GPH) is presented. By fitting the life distribution to a GPH, we can utilize various useful properties of the GPH. Two different approaches are used according to the properties of the given failure time data. One is an approximation to a GPH through the piecewise Weibull failure rate(PWF) model and the other is a direct approximation to a GPH using the empirical distribution function. Two numerical examples are also presented. In the first example, both of the two approaches are utilized and compared for an incomplete data set. And in the second example, the direct approximation method from an empirical distribution is utilized for the analysis of a complete data set. In both cases, we could confirm the validity of the proposed method.

• 한국경영과학회지
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• 제40권3호
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• pp.39-48
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• 2015

Even though ruin probability is a fundamental value to determine the insurance premium and policy, the complexity involved in computing its exact value forced us resort to an approximate method. In this paper, we first present an exact method to compute ruin probability under the assumption that the claim size has a GPH distribution, Then, for the arbitrary claim size distribution, we provide a method computing ruin probability quite accurately by approximating the distribution as a GPH. The validity of the proposed method demonstrated by a numerical example. The GPH approach seems to be valid for heavy-tailed claims as well as usual light-tailed claims.

• 한국시뮬레이션학회:학술대회논문집
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• 한국시뮬레이션학회 2001년도 The Seoul International Simulation Conference
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• pp.359-364
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• 2001

In this study, we try to improve the accuracy of QN-GPH by the help of simulation approach. We first establish an estimation method for GPH distributions with sufficient accuracy based on empirical distribution, and then perform a brief trial run to find appropriate empirical distributions. After getting GPH form of distributions, we continue the QN-GPH analytic steps and compute necessary performance measures. We apply the method to find sojourn time distributions in a 8-node queueing system and compare the results with the whole simulation and the original two-parametric approximation.

• 유통과학연구
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• 제14권1호
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• pp.93-102
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• 2016

Purpose - The purpose of paper is studying the static and dynamic side for long-term memory storage properties, and increase the explanatory power regarding the long-term memory process by looking at the long-term storage attributes, Korea Composite Stock Price Index. The reason for the use of GPH statistic is to derive the modified statistic Korea's stock market, and to research a process of long-term memory. Research design, data, and methodology - Level shifts were subjected to be an empirical analysis by applying the GPH method. It has been modified by taking into account the daily log return of the Korea Composite Stock Price Index a. The Data, used for the stock market to analyze whether deciding the action by the long-term memory process, yield daily stock price index of the Korea Composite Stock Price Index and the rate of return a log. The studies were proceeded with long-term memory and long-term semiparametric method in deriving the long-term memory estimators. Chapter 2 examines the leading research, and Chapter 3 describes the long-term memory processes and estimation methods. GPH statistics induced modifications of statistics and discussed Whittle statistic. Chapter 4 used Korea Composite Stock Price Index to estimate the long-term memory process parameters. Chapter 6 presents the conclusions and implications. Results - If the price of the time series is generated by the abnormal process, it may be located in long-term memory by a time series. However, test results by price fixed GPH method is not followed by long-term memory process or fractional differential process. In the case of the time-series level shift, the present test method for a long-term memory processes has a considerable amount of bias, and there exists a structural change in the stock distribution market. This structural change has implications in level shift. Stratum level shift assays are not considered as shifted strata. They exist distinctly in the stock secondary market as bias, and are presented in the test statistic of non-long-term memory process. It also generates an error as a long-term memory that could lead to false results. Conclusions - Changes in long-term memory characteristics associated with level shift present the following two suggestions. One, if any impact outside is flowed for a long period of time, we can know that the long-term memory processes have characteristic of the average return gradually. When the investor makes an investment, the same reasoning applies to him in the light of the characteristics of the long-term memory. It is suggested that when investors make decisions on investment, it is necessary to consider the characters of the long-term storage in reference with causing investors to increase the uncertainty and potential. The other one is the thing which must be considered variously according to time-series. The research for price-earnings ratio and investment risk should be composed of the long-term memory characters, and it would have more predictability.

• 태양에너지
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• 제11권3호
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• pp.62-73
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• 1991

본 연구는 주어진 기름노즐의 분무특성을 실험적으로 조사하고 아울러 적정 가동조건을 설정하기 위하여 수행하였다. 실험에 공시한 노즐은 Delalvan과 Hago(압력분무 Simplex 1.25GPH)로서 각종 압력하에서 분무 각 $60^{\circ}$와 $80^{\circ}$에 대하여 조사하고 분무특성을 기술함에 있어서는 사우터 평균입경의 개념을 사용하였다. 포집된 모든 분무입자는 고감도 필름을 사용하여 50배로 확대 촬영하고, 이들을 Nukiyama-Tanazawa의 분포함수를 도입하여 해석하였다. 결론적으로 $80^{\circ}$의 경우가 $60^{\circ}$의 경우보다 분무특성이 양호하며, 적정 가동조건은 분무압 $8kg/cm^2$ 부근에서 정착됨을 알 수 있었다.