• International Journal of Reliability and Applications
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• 제4권3호
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Journal of the Korean Statistical Society
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• 제17권1호
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• pp.46-55
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• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.887-889
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• 1996

This paper presents Variance Reduction Techniques of the Monte Carlo Simulation considering Non-Exponential Distribution for Power System Reliability Evaluation. Generally, the components consisting of power system are assumed to be exponentially distributed in their state residence time. Sometimes, however, this assumption may cause a lot of errors in the reliability index evaluation. Non-exponential distribution can be approximated by a sum of several Erlangian distributions, whose inverse transform is easily calculated by using composition method. This paper proposes a new approach to deal with the non-exponential distribution and to reduce the simulation time by virtue of Variance Reduction Techniques such as Control Variate and Antithetic Variate.

• 충청수학회지
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• 제25권3호
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• 제3권3호
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• pp.149-153
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• 2022

The degree distribution of the plant-pollinator network was identified by analyzing the data in the ecosystem and reproduced by a model of the growing bipartite mutualistic networks. The degree distribution of pollinator shows power law or stretched exponential distribution, while plant usually shows stretched exponential distribution. In the growth model, the plant and the pollinator are selected with probability P_p and P_A=1-P_p, respectively. The number of incoming links for the plant and the pollinator is l_p and l_A, respectively. The probability that the link of the plant selects the pollinator of the existing network given as $A_{k_i}=k^{{\lambda}_A}_i/{\sum}_i\;k^{{\lambda}_A}_i$, and the probability that the pollinator selects the plant is $P_{k_i}=k^{{\lambda}_p}_i/{\sum}_i\;k^{{\lambda}_p}_i$. When the nonlinear growth index is 𝛌_X=1 (X=A or P), the degree distribution follows a power law, and if 0≤𝛌_X<1, the degree distribution follows a stretched exponential distribution. The cumulative degree distributions of plants and pollinators of 14 empirical plant-pollinators included in Interaction Web Database were calculated. A set of parameters (P_A,P_P,l_A,l_P) that reproduces these cumulative degree distributions and a growth index 𝛌_X (X=A or P) were obtained. We found that animal takes very heterogenous connections, whereas plant takes a more flexible connection network.

• 생태와환경
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• 제45권4호
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• pp.420-443
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• 2012

An Individual-Based Model (IBM) was developed by employing natural and toxic survival rates of individuals to elucidate the community responses of benthic macroin-vertebrates to anthropogenic disturbance in the streams. Experimental models (dose-response and relative sensitivity) and mathematical models (power law and negative exponential distribution) were applied to determinate the individual survival rates due to acute toxicity in stressful conditions. A power law was additionally used to present the natural survival rate. Life events, covering movement, exposure to contaminants, death and reproduction, were simulated in the IBM at the individual level in small (1 m) and short (1 week) scales to produce species abundance distributions (SADs) at the community level in large (5 km) and long (1~2 years) scales. Consequently, the SADs, such as geometric series, log-series, and log-normal distribution, were accordingly observed at severely (Biological Monitoring Working Party (BMWP<10), intermediately (BMWP<40) and weakly (BMWP${\geq}50$) polluted sites. The results from a power law and negative exponential distribution were suitably fitted to the field data across the different levels of pollution, according to the Kolmogorov-Smirnov test. The IBMs incorporating natural and toxic survival rates in individuals were useful for presenting community responses to disturbances and could be utilized as an integrative tool to elucidate community establishment processes in benthic macroin-vertebrates in the streams.

• 품질경영학회지
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• 제25권2호
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• pp.1-14
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• 1997

This paper considers maximum likelihood (ML) estimation of lifetime distribution under stress bounded ramp tests in which the stress is increased linearly from used condition stress to the stress u, pp.r bound. The following assumptions are used: exponential lifetime distribution under a constant stress, an inverse power law relationship between stress and mean of exponential lifetime distribution, and a cumulative exposure model for the effect of changing stress. Likelihood equations for the parameters involved in the model and asymptotic distribution of the estimators are obtained, and a numerical example is given.

• International Journal of Reliability and Applications
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• 제9권2호
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• pp.141-152
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• 2008

This paper presents equations, which can be used to evaluate the failure frequency and the failure rate of a two identical component parallel redundant system in which each component can operate in its wear out period, and the failure rate of each component is exponential power distribution. The optimum maintenance interval for a two identical component parallel redundant system can be obtained using these equations. The proposed approach is presented and illustrated using several numerical examples. The optimum maintenance interval for each component in a two identical parallel redundant system will depend on factors such as: failure rate, repair and maintenance times of each component in the parallel redundant systems.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.899-910
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• 2004

In this paper we have proposed a new loss function, namely, non-linear exponential(NLINEX) loss function, which is quite asymmetric in nature. We obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions. Moreover, a numerical comparison among the Bayes estimators of power function distribution under SE, LINEX, and NLINEX loss function have been made.

• 응용통계연구
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• 제27권6호
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• pp.1039-1047
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• 2014

시계열 자료를 위한 가장 기본적인 모형인 자기회귀모형을 고려한다. 흔히 시계열 자료에서 정규성 가정이 위배되는 경우가 발생하며, 정규성 가정을 완화하기 위한 방법으로 두꺼운 꼬리를 가지는 분포 또는 비대칭 분포를 고려할 수 있다. 비대칭 지수멱 분포의 사용은 비뚤림이 있는 두꺼운 꼬리를 가지는 자기회귀모형의 이상치의 영향을 줄이고 로버스트한 추론을 할 수 있도록 한다. 본 논문에서는 자기회귀모형에 대한 오차항에 정규분포 보다 첨도와 왜도에 유연함을 가지는 분포를 고려함으로써 정규성 가정을 완화하여 추론하고자 하였다. 정규분포의 대안으로 비대칭 지수멱 분포를 고려하였으며 정규분포의 결과와 비교 하여 비대칭 지수멱 분포의 로버스트함을 보였다. 또한 주어진 분포에 대한 효율적인 베이지안 추론을 하기 위하여 SIR 알고리즘과 격자망 방법을 고려하였다.