• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.195-209
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• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.11
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• pp.506-513
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• 2001

The islanding detection for distributed resources (DR) becomes an important and emerging issue in power system protection since the distributed generator installations are rapidly increasing and most of the installed systems are interconnected with distribution network. In order to avoid the negative impacts from islanding operations of DR on protection, operation and management of distribution system, it is necessary to effectively detect the islanding operations of DR and rapidly disconnect it from distribution network. Generally, it is difficult to detect islanding operation by monitoring only one system parameter This paper presents a new logic based islanding detection method for distributed resources(DR) which are interconnected with distribution network. The proposed method detects the islanding operation by monitoring four system parameter: voltage variation, phase displacement, frequency variation, and the variation of total harmonic distortion(THD) of current; therefore, it effectively detects island operation of DR unit operating in parallel with the distribution network. We also verified the efficiency of the proposed algorithm using the radial distribution network of IEEE 34 bus model.

• Journal of Ocean Engineering and Technology
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• v.17 no.2
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• pp.54-59
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• 2003

The characteristics of the parameters for the probability distribution of fatigue crack growth life, using the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length equals the number of cycle curves that are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratios of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Wiubull,, showing a slight dependence on specimen thickness and stress intensity level. The shape parameter, $\alpha$, does not show the dependency of thickness and stress intensity level, but the scale parameter, $\beta$, and location parameter, ${\gamma}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.10a
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• pp.301-306
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• 2002

The characteristics of parameters for the probability distribution of fatigue crack growth lives by the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length - the number of cycles curves are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratio of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth lives seems to follow the 3-parameter Wiubull and shows a slight dependence on specimen thickness and stress intensity level. The shape parameter, ${\alpha}$, does not show the dependency of thickness and stress intensity level, but the scale parameter, ${\beta}$, and location parameter, ${\upsilon}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• Journal of the Korea Safety Management & Science
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• v.9 no.5
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• pp.43-48
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• 2007

This paper is to present linkage parameter to integrate statistical models and physical models for accelerated life test. Statistical models represent the relationship of probability distribution and life. Physical models show the relationship of life and stress. Moreover, this study proposes the four steps for construction of integrated models for accelerated life test using linkage parameter. Finally, this paper develops new integrated models such as extreme value distribution-general Eyring, linearly increasing failure rate function-general Eyring, etc., and estimates various reliability measures.

• Communications for Statistical Applications and Methods
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• v.23 no.4
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• pp.321-334
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• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.397-419
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• 2017

A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.99-118
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• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

• Journal of Korean Society on Water Environment
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• v.33 no.3
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• pp.256-272
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• 2017

Extreme rainfall has become more frequent over the Korean peninsula in recent years, causing serious damages. In a changing climate, traditional approaches based on historical records of rainfall and on the stationary assumption can be inadequate and lead to overestimate (or underestimate) the design rainfalls. A main objective of this study is to develop a stochastic disaggregation method of seasonal rainfall to hourly extreme rainfall, and offer a way to derive the nonstationary IDF curves. In this study, we propose a novel approach based on a Four-Parameter Beta (4P-beta) distribution to estimate the nonstationary IDF curves conditioned on the observed (or simulated) seasonal rainfall, which becomes the time-varying upper bound of the 4P beta distribution. Moreover, this study employed a Bayesian framework that provides a better way to take into account the uncertainty in the model parameters. The proposed model showed a comparable design rainfall to that of GEV distribution under the stationary assumption. As a nonstationary rainfall frequency model, the proposed model can effectively translate the seasonal variation into the sub-daily extreme rainfall.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.