• Title/Summary/Keyword: density function

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Estimation of Probability Density Functions of Damage Parameter for Valve Leakage Detection in Reciprocating Pump Used in Nuclear Power Plants

  • Lee, Jong Kyeom;Kim, Tae Yun;Kim, Hyun Su;Chai, Jang-Bom;Lee, Jin Woo
    • Nuclear Engineering and Technology
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    • v.48 no.5
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    • pp.1280-1290
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    • 2016
  • This paper presents an advanced estimation method for obtaining the probability density functions of a damage parameter for valve leakage detection in a reciprocating pump. The estimation method is based on a comparison of model data which are simulated by using a mathematical model, and experimental data which are measured on the inside and outside of the reciprocating pump in operation. The mathematical model, which is simplified and extended on the basis of previous models, describes not only the normal state of the pump, but also its abnormal state caused by valve leakage. The pressure in the cylinder is expressed as a function of the crankshaft angle, and an additional volume flow rate due to the valve leakage is quantified by a damage parameter in the mathematical model. The change in the cylinder pressure profiles due to the suction valve leakage is noticeable in the compression and expansion modes of the pump. The damage parameter value over 300 cycles is calculated in two ways, considering advance or delay in the opening and closing angles of the discharge valves. The probability density functions of the damage parameter are compared for diagnosis and prognosis on the basis of the probabilistic features of valve leakage.

Analysis of Inductively Coupled Plasma using Electrostatic Probe and Fluid Simulation (정전 탐침법과 유체 시뮬레이션을 이용한 유도결합 Ar 플라즈마의 특성 연구)

  • Cha, Ju-Hong;Lee, Ho-Jun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.7
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    • pp.1211-1217
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    • 2016
  • Discharge characteristics of inductively coupled plasma were investigated by using electrostatic probe and fluid simulation. The Inductively Coupled Plasma source driven by 13.56 Mhz was prepared. The signal attenuation ratios of the electrostatic probe at first and second harmonic frequency was tuned in 13.56Mhz and 27.12Mhz respectively. Electron temperature, electron density, plasma potential, electron energy distribution function and electron energy probability function were investigated by using the electrostatic probe. Experiment results were compared with the fluid simulation results. Ar plasma fluid simulations including Navier-Stokes equations were calculated under the same experiment conditions, and the dependencies of plasma parameters on process parameters were well agreed with simulation results. Because of the reason that the more collision happens in high pressure condition, plasma potential and electron temperature got lower as the pressure was higher and the input power was higher, but Electron density was higher under the same condition. Due to the same reason, the electron energy distribution was widening as the pressure was lower. And the electron density was higher, as close to the gas inlet place. It was found that gas flow field significantly affect to spatial distribution of electron density and temperature.

On Simulation for Normalization of Game Satisfaction Density Function (게임만족도 분포의 정규화에 관한 시뮬레이션)

  • Ham, Hyung-Bum
    • Journal of Korea Multimedia Society
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    • v.10 no.9
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    • pp.1185-1196
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    • 2007
  • To enhance competitiveness of game industry and added value, it needs scientific research and bases that suggest satisfaction standard which quantitatively evaluates satisfaction to develop games which have high satisfaction for demanders. Specially, scoring of satisfaction factors and estimation of population distribution are important task. This allows which a game have high or low satisfaction compared to other games. Also we predict improvable factors and technical aspects to promote satisfaction. For it, in this paper we discuss ways to normalization of score distribution for satisfaction factors and estimate its density function using parametric density estimation by simulation.

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A Comparison on the Differential Entropy

  • Kim, Dae-Hak
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.3
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    • pp.705-712
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    • 2005
  • Entropy is the basic concept of information theory. It is well defined for random varibles with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations. In this paper, we consider a kernel based approximation and compare it to the cumulant approximation method for several distributions. Monte carlo simulation for various sample size is conducted.

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Monte Carlo Estimation of Multivariate Normal Probabilities

  • Oh, Man-Suk;Kim, Seung-Whan
    • Journal of the Korean Statistical Society
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    • v.28 no.4
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    • pp.443-455
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    • 1999
  • A simulation-based approach to estimating the probability of an arbitrary region under a multivariate normal distribution is developed. In specific, the probability is expressed as the ratio of the unrestricted and the restricted multivariate normal density functions, where the restriction is given by the region whose probability is of interest. The density function of the restricted distribution is then estimated by using a sample generated from the Gibbs sampling algorithm.

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The Nonparametric Deconvolution Problem with Gaussian Error Distribution

  • Cho, Wan-Hyun;Park, Jeong-Soo
    • Journal of the Korean Statistical Society
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    • v.25 no.2
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    • pp.265-276
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    • 1996
  • The nonparametric deconvolution problems are studied to recover an unknown density when the data are contaminated with Gaussian error. We propose the estimator which is a linear combination of kernel type estimates of derivertives of the observed density function. We show that this estimator is consistent and also consider the properties of estimator at small sample by simulation.

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GLOBAL MINIMA OF LEAST SQUARES CROSS VALIDATION FOR A SYMMETRIC POLYNOMIAL KEREL WITH FINITE SUPPORT

  • Jung, Kang-Mo;Kim, Byung-Chun
    • Journal of applied mathematics & informatics
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    • v.3 no.2
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    • pp.183-192
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    • 1996
  • The least squares cross validated bandwidth is the mini-mizer of the corss validation function for choosing the smooth parame-ter of a kernel density estimator. It is a completely automatic method but it requires inordinate amounts of computational time. We present a convenient formula for calculation of the cross validation function when the kernel function is a symmetric polynomial with finite sup-port. Also we suggest an algorithm for finding global minima of the crass validation function.

Notes on the Ratio and the Right-Tail Probability in a Log-Laplace Distribution

  • Woo, Jung-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.4
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    • pp.1171-1177
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    • 2007
  • We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

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NEW EXPRESSIONS FOR REPEATED LOWER TAIL INTEGRALS OF THE NORMAL DISTRIBUTION

  • Withers, Christopher S.;Nadarajah, Saralees
    • Journal of the Korean Statistical Society
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    • v.36 no.3
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    • pp.411-421
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    • 2007
  • The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

ℓ-RANKS OF CLASS GROUPS OF FUNCTION FIELDS

  • Bae, Sung-Han;Jung, Hwan-Yup
    • Journal of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.49-67
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    • 2012
  • In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.