• 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 Korean Statistical Society
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• v.23 no.1
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.317-320
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• 2002

In this paper, an automatic histogram specification method is proposed for image enhancement, Fuzzy membership value is adopted for the representation of image histogram. The desired PDF is automatically constructed by the fuzzy membership value. Fuzzy membership value is extracted from dark membership, bright membership function and original histogram. The effectual results are demonstrated by desired PDF which meet the image enhancement requirements. The performance and effectiveness are shown by the analysis and the resultant image in comparison with histogram equalization method.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.1-9
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• 1987

In this paper, the acquisition performance of a receiver that utilizes a non-coherent digital correlator is analyzed. In order to analyze the acquisition performance, the probability density function of a receiver output random variable has been derived approximately. Using this function, the acquisition performance of the coarse acquisition code receiver in a global positioning system is analyzed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.11
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• pp.1691-1696
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• 2010

The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliabilitybased design optimization are examples of the most famous methodologies. The statistical moments of a performance function and the constraints corresponding to probability conditions are involved in the formulation of these methodologies. Therefore, it is essential to effectively and accurately calculate them. The sensitivities of these methodologies have to be determined when nonlinear programming is utilized during the optimization process. The sensitivity of statistical moments and probability constraints is expressed in the integral form and limited to the normal random variable; we aim to expand the sensitivity formulation to nonnormal variables. Additional functional calculation will not be required when statistical moments and failure or satisfaction probabilities are already obtained at a design point. On the other hand, the accuracy of the sensitivity results could be worse than that of the moments because the target function is expressed as a product of the performance function and the explicit functions derived from probability density functions.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.26-29
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• 2002

Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2073-2081
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• 2002

In product design and manufacturing, axiomatic design provides a systematic approach for the decision-making process. Two axioms have been defined such as the Independence Axiom and the Information Axiom. The Information Axiom states that the best design among those that satisfy the independence axiom is the one with the least information content. In other words, the best design is the one that has the highest probability of success. On the other hand, the Taguchi robust design is used in the two-step process; one is "reduce variability," and the other is "adjust the mean on the target." The two-step can be interpreted as a problem that has two FRs (functional requirements). Therefore, the Taguchi method should be used based on the satisfaction of the Independence Axiom. Common aspects exist between the Taguchi method and Axiomatic Design in that a robust design is induced. However, different characteristics are found as well. The Taguchi method does not have the design range, and the probability of success may not be enough to express robustness. Our purpose is to find the one that has the highest probability of success and the smallest variation. A new index is proposed to satisfy these conditions. The index is defined by multiplication of the robustness weight function and the probability density function. The robustness weight function has the maximum at the target value and zero at the boundary of the design range. The validity of the index is proved through various examples.gh various examples.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.10a
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• pp.440-447
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• 2000

In order to evaluate the cost effectiveness of seismic isolation for bridges in low and moderate seismic region, a method of calculation minimum life-cycle cost of seismic-isolated bridges under specific acceleration level and soil condition is developed. Input ground motion is modeled as spectral density function compatible with response spectrum for combination of acceleration coefficient and site coefficient. Failure probability is calculated by spectrum analysis based on random vibration theories to simplify repetitive calculations in the minimization procedure. Ductility of piers and its effects on cost effectiveness are considered by stochastic linearization method. Cost function and cost effectiveness index are defined by taking into consideration the characteristics of seismic isolated bridges. Limit states for calculation of failure probability are defined on superstructure, isolator and pier, respectively. The results of example design and analysis show that seismic isolation is more cost-effective in low and moderate seismic region than in high seismic region.