• Journal of the Korean Data and Information Science Society
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• 제27권1호
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• pp.265-274
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• 2016

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.237-244
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• 2014

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.1-19
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• 2016

The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.

• 제어로봇시스템학회논문지
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• 제2권3호
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• pp.220-228
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• 1996

This paper presents a extended stochastic Petri net (ESPN) model for CTN(Circulated Token with No duration) service in the data link layer of IEC/ISA fieldbus. It is assumed that a station on the fieldbus has a specified minimum token holding time, a finite capacity buffer, and one transmitter queue with the highest priority. The mean transmission (or service) time at a station and the mean token rotation time for the symmetric fieldbus system atr derived using the presented SPN model and the moment generating function. These performance measures are represented in terms of the minimum token holding time, the number of stations, the arrival rate of messages, and the mean length of messages. The presented performance measure are validated by computer simulations.

• Journal of Communications and Networks
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• 제11권3호
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• pp.240-247
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• 2009

The results of performance analysis by adopting the channel scenarios characterized as Weibull fading for an multicarrierdirect sequence-coded division multiple access (MC-DS-CDMA) system are proposed in this investigation. On the other hand, an approximate simple expression with the criterion of bit error rate (BER) versus signal-to-noise ratio (SNR) method is derived for an MC-DS-CDMA system combining with maximal ratio combining (MRC) diversity based on the moment generating function (MGF) formula of Weibull statistics, and it associates with an alternative expression of Gaussian Q-function. Besides, the other point of view on the BER performance evaluation of an MC-DS-CDMA system is not only the assumption of both single-user and multi-user cases applied, but the phenomena of partial band interference (PBI) is also included. Moreover, in order to validate the accuracy in the derived formulas, some of the system parameters, such as Weibull fading parameter (${\beta}$), user number (K), spreading chip number (N), branch number (L), and the PBI (JSR) values, etc., are compared with each other in the numerical results. To the best of author's knowledge, it is a brand new idea which proposes the evaluation of the system performance for an MC-DS-CDMA system over the point of view with Weibull fading channel.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.65-84
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• 2016

Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.

• 산업경영시스템학회지
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• 제12권20호
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• pp.71-76
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• 1989

In this paper, GERT network in modeled to improve the network of manufacturing process with feedback loop. A lot of Information on the GERT network can be derived from the equivalent W-function and MGF(moment generating function) using Mason's rule. These equations are used in calculating the variations of the performance measure and in improving the system performance. System improvement in manufacturing process is achieved by increasing the equivalent probabilities of each branches and by decreasing the expected equivalent time.

• International Journal of Reliability and Applications
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• 제2권1호
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• pp.49-56
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• 2001

In this paper we consider empirical Bayes estimation of the hazard rate and survival probabilities with right censored data under the assumption that the hazard function is constant over the period of observation and the prior distribution is gamma. We provide an estimator of the first derivative of the prior moment generating function that converges at each point to the true value in $L_2$ and use it to obtain, easy to compute, asymptotically optimal estimators under the squared error loss function.

• 대한전자공학회논문지TC
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• 제49권4호
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• pp.1-8
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• 2012

본 논문에서는 레일리 페이딩 환경에서 OAF (opportunistic amplify-and-forward) 릴레이 전송 기법의 정확한 성능을 제시하는 새로운 분석 기법에 대해서 알아본다. 이를 위해 집합 연산 기반의 선택될 확률을 활용한다. 이를 기반으로 OAF 릴레이 전송기법의 수정된 MGF(modified moment generating function)를 제안한다. 제안된 MGF 를 바탕으로 OAF 릴레이 전송 기법의 특성을 정확하게 표현해주는 M-ary Phase Shift Keying (MPSK) 심볼 오류 확률을 제안한다. 모의 실험 결과를 통해서 제안된 심볼 오류 확률의 정확함을 확인한다.

• 대한전자공학회논문지TC
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• 제48권8호
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• pp.1-6
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• 2011

본 논문에서는 이중 홉 증폭 후 전달(AF: Amplify-and-Forward) 릴레이 시스템에 대한 새로운 성능 분석 기법을 레일리 페이딩 채널에 대하여 제안한다. 기존의 분석 기법들에서는 S-R-D(Source-Relay-Destination) 링크의 수신 신호 대 잡음비(SNR: Signal-to-Noise Ratio)에 대한 누적 분포 함수(CDF: Cumulative Distribution Function) 혹은 확률 밀도 함수 (PDF: Probability Density Function)로부터 모멘트 발생 함수(MGF: Moment Generating Function)를 유도한 후 평균 심벌 오류율을 유도된 MGF를 이용하여 표현하였다. 본 논문에서는 기존의 분석과 다른 새로운 접근법을 제안한다. 즉, S-R(Source-Relay) 링크 및 R-D(Relay-Destination) 링크의 PDF들로부터 S-R-D 링크에 대한 MGF를 직접 유도한다. 그리고 새롭게 유도된 MGF을 기존의 연구들에서 제시한 형태와 비교 분석한다. 또한 제안된 성능분석 기법의 정확성은 모의실험을 통하여 검증한다. 이를 통하여 제안된 분석 기법이 이중 홉 증폭 후 전달 릴레이 시스템에 대한 새로운 해를 제시함을 확인한다.