• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.125-134
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• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.243-247
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• 2014

Let {$X_n$, $n{\geq}1$} be a sequence of i.i.d. random variables with absolutely continuous cumulative distribution function(cdf) F(x) and the corresponding probability density function(pdf) f(x). In this paper, we give characterizations of Pareto and Weibull distribution by considering conditional expectations of record values.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.399-409
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• 2016

Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modified Weibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modified Weibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.3
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• pp.1-8
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• 2016

We propose an adaptive histogram stretching algorithm for application to a car's personal recorder. The algorithm was used for pre-processing to detect the license plate region in an image from a personal recorder. The algorithm employs a Probability Density Function (PDF) and Cumulative Distribution Function (CDF) to analyze the distribution diagram of the images. These two functions are calculated using an image obtained by sampling at a certain pixel interval. The images were subjected to different levels of stretching, and experiments were done on the images to extract their characteristics. The results show that the proposed algorithm provides less deterioration than conventional algorithms. Moreover, contrast is enhanced according to the characteristics of the image. The algorithm could provide better performance than existing algorithms in applications for detecting search regions for license plates.

• The KIPS Transactions:PartA
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• v.9A no.2
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• pp.267-270
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• 2002

The evaluation of the cumulative distribution function of the noncentral $\chi^2$ distribution is required in approximate determination of the power of the $\chi^2$ test. This article provides an algorithm for evaluating the noncentral $\chi^2$ distribution function in terms of a single "central" $\chi^2$ distribution function and compared various approximations.ximations.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.445-459
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• 2014

As a certain job is repeatedly done by a worker, the outcome comparative to the effort to complete the job gets more remarkable. The outcome may be the time required and fraction defective. This phenomenon is referred to a learning-curve effect. We focus on the parametric modeling of the learning-curve effects on count data using a logistic cumulative distribution function and some probability mass functions such as a Poisson and negative binomial. We conduct various simulation scenarios to clarify the characteristics of the proposed model. We also consider a real application to compare the two discrete-type distribution functions.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.459-465
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• 2009

For an inverse double Weibull distribution which is symmetric about zero, we obtain distribution and moment of ratio of independent inverse double Weibull variables, and also obtain the cumulative distribution function and moment of a skew-symmetric inverse double Weibull distribution. And we introduce a skew-symmetric inverse double Weibull generated by a double Weibull distribution.

• International Journal of Automotive Technology
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• v.6 no.1
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• pp.53-63
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• 2005

We propose a fuzzy neural network (FNN) theory capable of deciding the quality of a road image prior to extracting lane-related information. The accuracy of lane-related information obtained by image processing depends on the quality of the raw images, which can be classified as good or bad according to how visible the lane marks on the images are. Enhancing the accuracy of the information by an image-processing algorithm is limited due to noise corruption which makes image processing difficult. The FNN, on the other hand, decides whether road images are good or bad with respect to the degree of noise corruption. A cumulative distribution function (CDF), a function of edge histogram, is utilized to extract input parameters from the FNN according to the fact that the shape of the CDF is deeply correlated to the road image quality. A suitability analysis shows that this deep correlation exists between the parameters and the image quality. The input pattern vector of the FNN consists of nine parameters in which eight parameters are from the CDF and one is from the intensity distribution of raw images. Experimental results showed that the proposed FNN system was quite successful. We carried out simulations with real images taken in various lighting and weather conditions, and obtained successful decision-making about $99\%$ of the time.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.6
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• pp.468-476
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• 2002

The confidence of information from image processing depends on the original image quality. Enhancing the confidence by an algorithm has an essential limitation. Especially, road images are exposed to lots of noisy sources, which makes image processing difficult. We, in this paper, propose a FNN (fuzzy-neural network) capable oi deciding the quality of a road image prior to extracting lane-related information. According to the decision by the FNN, road images are classified into good or bad to extract lane-related information. A CDF (cumulative distribution function), a function of edge histogram, is utilized to construct input parameters of the FNN, it is based on the fact that the shape of the CDF and the image quality has large correlation. Input pattern vector to the FNN consists of ten parameters in which nine parameters are from the CDF and the other one is from intensity distribution of raw image. Correlation analysis shows that each parameter represents the image quality well. According to the experimental results, the proposed FNN system was quite successful. We carried out simulations with real images taken by various lighting and weather conditions and achieved about 99% successful decision-making.