• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.227-240
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• 2017

In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.787-798
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• 2011

In this paper, we develop some characterization results in terms of survival entropy of the first order statistic. In addition, we generalize the cumulative entropy recently proposed by Di Crescenzo and Logobardi (2009) to a new measure of information (called the failure entropy) and study some properties of it and its dynamic version. Furthermore, power distribution is characterized based on dynamic failure entropy.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1276-1282
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• 2013

This paper proposes a stochastic modeling of plug-in electric vehicles (PEVs) distribution in power systems, and analyzes the corresponding clustering characteristic. It is essential for power utilities to estimate the PEV charging demand as the penetration level of PEV is expected to increase rapidly in the near future. Although the distribution of PEVs in power systems is the primary factor for estimating the PEV charging demand, the data currently available are statistics related to fuel-driven vehicles and to existing electric demands in power systems. In this paper, we calculate the number of households using electricity at individual ending buses of a power system based on the electric demands. Then, we estimate the number of PEVs per household using the probability density function of PEVs derived from the given statistics about fuel-driven vehicles. Finally, we present the clustering characteristic of the PEV distribution via case studies employing the test systems.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.6
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• pp.100-107
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• 1999

This paper describes a probabilistic remaining life assessment program for the creep crack growth. The probabilistic life assessment program is developed to increase the reliability of life assessment. The probabilistic life assessment involves some uncertainties, such as, initial crack size, material properties, and loading condition, and a triangle distribution function is used for random variable generation. The resulting information provides the engineer with an assessment of the probability of structural failure as a function of operating time given the uncertainties in the input data. This study forms basis of the probabilistic life assessment technique and will be extended to other damage mechanisms.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.3
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• pp.109-115
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• 2006

The Weibull distribution is a good candidate for accurate probabilistic model with its rich shape-forming ability and relatively simple CDF(cumulative distribution function). If there are sufficient information to get convincible mean and variance for a probabilistic event, reliable parameters of the Weibull distribution can be determined uniquely. However, sufficient information is not given as usual. There needs more deliberate model building method for that case. This Paper presents an effective parameter estimation technique for Weibull distribution with limited failure data.

• Journal of the Korean GEO-environmental Society
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• v.19 no.12
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• pp.15-23
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• 2018

The occurrence of soil erosions in Korea is mostly driven by flowing water which has a close relationship with rainfalls. The soil eroded by rainfalls flows into and deposits in the river and it polluted the water resources and making the rivers become difficult to be managed. Recently, the frequency of heavy rainfall events that are more than 30 mm/hr has been increasing in Korea due to the influence of climate change, which creating a favourable condition for the occurrence of soil erosion within a short time. In this study, we proposed a method to estimate the distribution of rainfall intensity and to calculate the energy produced by a single rainfall event using the cumulative distribution function that take into account of the physical characteristics of rainfall. The raindrops kinetic energy estimated by the proposed method are compared with the measured data from the previous studies and it is noticed that the raindrops kinetic energy estimated by the rainfall intensity variation is very similar to the results concluded from the previous studies. In order to develop an equation for estimating rainfall kinetic energy, rainfall particle size data measured at a rainfall intensity of 0.254~152.4 mm/hr were used. The rainfall kinetic energy estimated by applying the cumulative distribution function tended to increase in the form of a power function in the relation of rainfall intensity. Based on the equation obtained from this relationship, the rainfall kinetic energy of 1~80 mm/hr rainfall intensity was estimated to be $0.03{\sim}48.26Jm^{-2}mm^{-1}$. Based on the relationship between rainfall intensity and rainfall energy, rainfall kinetic energy equation is proposed as a power function form and it is expected that it can be used in the design of short-term operated facility such as the sizing of sedimentation basin that requires prediction of soil loss by a single rainfall event.

• Journal of KIEE
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• v.11 no.1
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• pp.69-77
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• 2001

This paper describes an image processing algorithm capable of recognizing road lanes by using a CDF(cumulative distribution function). The CDF is designed for the model function of road lanes. Based on the assumptions that there are no abrupt changes in the direction and location of road lanes and that the intensity of lane boundaries differs from that of the background, we formulated the CDF, which accumulates the edge magnitude for edge directions. The CDF has distinctive peak points at the vicinity of lane directions due to the directional and the positional continuities of a lane. To obtain lane-related information a scatter diagram was constructed by collecting edge pixels, of which the direction corresponds to the peak point of the CDF, then the principal axis-based line fitting was performed for the scatter diagram. Noises can cause many similar features to appear and to disappear in an image. Therefore, to reduce the noise effect a recursive estimator of the CDF was introduced, and also to prevent false alarms or miss detection a scene understanding index (DUI) was formulated by the statistical parameters of the CDF. The proposed algorithm has been implemented in real time on video data obtained from a test vehicle driven on a typical highway.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.157-163
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• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.65-82
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• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.