• 대한수학회논문집
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• 제27권4호
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• pp.835-842
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• 2012

Many researchers have studied the characterizations of probability distributions based on record values. It appears from literature that not much attention has been paid to the characterizations of the Pareto distribution. In this note, some new results on the characterizations of the Pareto distribution by upper record values have been established.

• Journal of the Korean Data and Information Science Society
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• 제23권6호
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• pp.1213-1222
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• 2012

We shall derive the moment of the ratio Y/(X + Y) and the reliability P(X < Y ), and then observe the skewness of the ratio in a bivariate Pareto density function of (X, Y). And we shall consider an approximate MLE of parameters in the bivariate Pareto density function.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.791-799
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• 2005

We consider two components parallel system in which the lifetimes have the bivariate Pareto model with bivariate random censored data. We assume that bivariate Pareto model is affected by common stress which is independent of the lifetimes of the components. We obtain estimators for the system reliability based on likelihood function and relative frequency. Also we construct approximated confidence intervals for the reliability based on maximum likelihood estimator and relative frequency estimator, respectively. Finally we present a numerical study.

• 정보처리학회논문지B
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• 제11B권2호
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• pp.213-220
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• 2004

진화 알고리즘은 여러 개의 상충하는 목적을 갖는 다목적 최적화 문제를 해결하기에 적합한 방법이다. 특히, 파레토 지배관계에 기초하여 개체의 적합도를 평가하는 파레토 기반 진화알고리즘들은 그 성능에 있어서 우수한 평가를 받고 있다. 최근의 파레토 기반 진화알고리즘들은 전체 파레토 프론트에 균일하게 분포하는 해집합의 생성을 위해 개체들의 밀도를 개체의 적합도를 평가하기 위한 하나의 요소로 사용하고 있다. 그러나 밀도의 역할은 전체 진화과정에서 중요한 요소가 되기보다는 파레토 프론트에 어느 정도 수렴된 후, 개체의 균일 분포를 만들기 위해 사용된다. 본 논문에서 우리는 파레토 지배 순위와 밀도에 대한 임의가중치를 적용한 다목적 최적화 진화알고리즘을 제안한다. 제안한 알고리즘은 진화 개체의 적합도를 평가하기 위해 파레토 순위와 밀도에 대한 임의의 가중치를 적용하므로 전체 진화과정에서 파레토 순위와 밀도가 비슷한 영향을 미치도록 하였다. 또한, 제안한 방법을 6개의 다목적 최적화 문제에 적용한 결과 비교적 우수한 결과를 보였다.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.42-47
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• 1984

In this paper, the means of the estimators for the coefficient of variation (CV) in an underlying Pareto distribution are expressed in terms of confluent hypergeometric functions. The numericla values of the biases for the CV estimators in the Pareto distribution are also obtained.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.311-319
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• 2013

Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.569-575
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• 2018

Pareto distribution is important to analyze data in actuarial sciences, reliability, finance, and climatology. In general, unknown parameters of the Pareto distribution are estimated based on the maximum likelihood method that may yield inadequate inference results for small sample sizes and high percent censored data. In this paper, a new approach based on the regression framework is proposed to estimate unknown parameters of the Pareto distribution under the progressive Type-II censoring scheme. The proposed method provides a new regression type estimator that employs the spacings of exponential progressive Type-II censored samples. In addition, the provided estimator is a consistent estimator with superior performance compared to maximum likelihood estimators in terms of the mean squared error and bias. The validity of the proposed method is assessed through Monte Carlo simulations and real data analysis.

• 충청수학회지
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• 제24권1호
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• pp.85-89
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• 2011

We present characterizations of the Pareto distribution by the independent property of upper record values in such a way that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m. Futhermore, the characterizations should find that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m.

• Journal of Power Electronics
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• 제12권1호
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• pp.104-112
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• 2012

In this paper a new method for the design of a simple PI controller is presented and it has been applied in the control of a Boost based PFC rectifier. The Strength Pareto evolutionary algorithm, which is based on the Pareto Optimality concept, used in Game theory literature is implemented as a multi-objective optimization approach to gain a good transient response and a high quality input current. In the proposed method, the input current harmonics and the dynamic response have been assumed as objective functions, while the PI controller's gains of the PFC rectifier (Kpi, Tpi) are design variables. The proposed algorithm generates a set of optimal gains called a Pareto Set corresponding to a Pareto Front, which is a set of optimal results for the objective functions. All of the Pareto Front points are optimum, but according to the design priority objective function, each one can be selected. Simulation and experimental results are presented to prove the superiority of the proposed design methodology over other methods.

• 정보관리학회지
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• 제24권4호
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• pp.255-265
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• 2007

하루에도 수백만 건 이상의 방대한 질의어가 입력되는 검색엔진을 통해 인터넷 검색 패턴을 분석하는데 활용될 수 있는 질의어 분포의 정상성을, Pareto 분포와 Zipf 모형을 이용해 검토하였다. 실제2주일간의 일간 검색어 분포를 Pareto 모형으로 적합 시킨 결과, 그 기울기가 1.33에서 1.34 정도로 일관되게 측정되고 있어 Pareto 분포를 이용해 일간질의어 분포의 정상성을 평가할수 있음을 제시하였다. 이런 연구결과는 사회적 관심사와 그 변동 흐름을 해석하는데 보다 객관적이며, 효율적인 자료를 제공해 줄 수 있을 것이다.