• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.245-255
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• 2011

There are two nonparametric methods that use empirical distribution functions and probability density estimators for the test of the distribution change of data. In this paper we investigate the two methods precisely and summarize the results of previous research. We assume several probability models to make a simulation study of the change point analysis and to examine the finite sample behavior of the two methods. Empirical powers are compared to verify which is better for each model.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.1-3
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• 2009

Recently, Carlsson, Full\acute{e}$r and Majlender [1] presented the concept of possibilitic correlation representing an average degree of interaction between marginal distribution of a joint possibility distribution as compared to their respective dispersions. They also formulated the weak and strong forms of the possibilistic Cauchy-Schwarz inequality. In this paper, we define a new probability measure. Then the weak and strong forms of the Cauchy-Schwarz inequality are immediate consequence of probabilistic Cauchy-Schwarz inequality with respect to the new probability measure.

• Genomics & Informatics
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• v.20 no.2
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• pp.17.1-17.11
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• 2022

Genetic associations have been quantified using a number of statistical measures. Entropy-based mutual information may be one of the more direct ways of estimating the association, in the sense that it does not depend on the parametrization. For this purpose, both the entropy and conditional entropy of the phenotype distribution should be obtained. Quantitative traits, however, do not usually allow an exact evaluation of entropy. The estimation of entropy needs a probability density function, which can be approximated by kernel density estimation. We have investigated the proper sequence of procedures for combining the kernel density estimation and entropy estimation with a probability density function in order to calculate mutual information. Genotypes and their interactions were constructed to set the conditions for conditional entropy. Extensive simulation data created using three types of generating functions were analyzed using two different kernels as well as two types of multifactor dimensionality reduction and another probability density approximation method called m-spacing. The statistical power in terms of correct detection rates was compared. Using kernels was found to be most useful when the trait distributions were more complex than simple normal or gamma distributions. A full-scale genomic dataset was explored to identify associations using the 2-h oral glucose tolerance test results and γ-glutamyl transpeptidase levels as phenotypes. Clearly distinguishable single-nucleotide polymorphisms (SNPs) and interacting SNP pairs associated with these phenotypes were found and listed with empirical p-values.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• Journal of the Korean Solar Energy Society
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• v.33 no.2
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• pp.18-27
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• 2013

This paper presents a method for assessing the wind energy potential at complex terrain using probability distribution. And the proper probability models of the parameters estimating the wind energy are presented. Finally a mixture-Weibull determined by numerical methods procedure are proposed to assess the probability distribution of the energy potential at a site. The developed method is applied to the Kwanjungchun Bridge and compared with wind records which the neighboring weather station.

• Journal of Information Processing Systems
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• v.15 no.2
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• pp.331-343
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• 2019

Dynamic thermal rating of the overhead transmission lines is affected by many uncertain factors. The ambient temperature, wind speed and wind direction are the main sources of uncertainty. Measurement uncertainty is an important parameter to evaluate the reliability of measurement results. This paper presents the uncertainty analysis based on Monte Carlo. On the basis of establishing the mathematical model and setting the probability density function of the input parameter value, the probability density function of the output value is determined by probability distribution random sampling. Through the calculation and analysis of the transient thermal balance equation and the steady- state thermal balance equation, the steady-state current carrying capacity, the transient current carrying capacity, the standard uncertainty and the probability distribution of the minimum and maximum values of the conductor under 95% confidence interval are obtained. The simulation results indicate that Monte Carlo method can decrease the computational complexity, speed up the calculation, and increase the validity and reliability of the uncertainty evaluation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1493-1510
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• 2000

Theoretical models that can be used to predict the range of main lobe widths and the probability distribution of the peak sidelobe levels of two-dimensionally sparse arrays are presented here. The arrays are considered to comprise microphones that are randomly positioned on a segmented grid of a given size. First, approximate expressions for the expected squared magnitude of the aperture smoothing function and the variance of the squared magnitude of the aperture smoothing function about this mean are formulated for the random arrays considered in the present study. By using the variance function, the mean value and the lower end of the range i.e., the first I percent of the mainlobe distribution can be predicted with reasonable accuracy. To predict the probability distribution of the peak sidelobe levels, distributions of levels are modeled by a Weibull distribution at each peak in the sidelobe region of the expected squared magnitude of the aperture smoothing function. The two parameters of the Weibull distribution are estimated from the means and variances of the levels at the corresponding locations. Next, the probability distribution of the peak sidelobe levels are assumed to be determined by a procedure in which the peak sidelobe level is determined as the maximum among a finite number of independent random sidelobe levels. It is found that the model obtained from the above approach predicts the probability density function of the peak sidelobe level distribution reasonably well for the various combinations of two different numbers of microphones and grid sizes tested in the present study. The application of these models to the design of random, sparse arrays having specified performance levels is also discussed.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.30 no.3
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• pp.295-303
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• 2012

Clarify wind energy productivity depends on three factors: the wind probability density function(PDF), the turbine's power curve, and the air density. The wind PDF gives the probability that a variable will take on the wind speed value. Wind shear refers to the change in wind speed with height above ground. The wind speed tends to increase with the height above ground. also, Wind PDF refers to the change with height above ground. Wind analysts typically use the Weibull distribution to characterize the breadth of the distribution of wind speeds. The Weibull distribution has the two-parameter: the scale factor c and the shape factor k. We can use a linear least squares algorithm(or Ln-least method) and moment method to fit a Weibull distribution to measured wind speed data which data was located same site and different height. In this study, find that the scale factor is related to the average wind speed than the shape factor. and also different types of terrain are characterized by different the scale factor slop with height above ground. The gross turbine power output (before accounting for losses) was caculated the power curve whose corresponding air density is closest to the air density. and air desity was choose two way. one is the pressure of the International Standard Atmosphere up to an elevation, the other is the measured air pressure and temperature to calculate the air density. and then each power output was compared.

• 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.