• Title/Summary/Keyword: Normal Distribution

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A NOTE ON THE GEOMETRICAL PROPERTIES OF THE NORMAL DISTRIBUTION

  • Cho, Bong-Sik
    • Honam Mathematical Journal
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    • v.29 no.1
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    • pp.75-81
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    • 2007
  • The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the normal distribution using its Fisher's matrix is defined. The Riemannian curvature and J-divergence to parameter space are calculated.

On the Support Vector Machine with the kernel of the q-normal distribution

  • Joguchi, Hirofumi;Tanaka, Masaru
    • Proceedings of the IEEK Conference
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    • 2002.07b
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    • pp.983-986
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    • 2002
  • Support Vector Machine (SVM) is one of the methods of pattern recognition that separate input data using hyperplane. This method has high capability of pattern recognition by using the technique, which says kernel trick, and the Radial basis function (RBF) kernel is usually used as a kernel function in kernel trick. In this paper we propose using the q-normal distribution to the kernel function, instead of conventional RBF, and compare two types of the kernel function.

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Sign IV Cointegration Tests

  • Oh, Yu-Jin
    • Communications for Statistical Applications and Methods
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    • v.16 no.4
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    • pp.707-711
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    • 2009
  • We propose new cointegration tests using signs of the regressors as instrumental variable. Our tests have the asymptotic standard normal distribution and are free from the dimension of regressors under the null hypothesis of no cointegration. A Monte-Carlo simulation shows that the proposed tests have a stable size and an improved power. Particulary, the tests have better power for small numbers of observations.

Estimation of the Mean and Variance for Normal Distributions whose Both Sides are Truncated

  • Hong, Chong-Sun;Choi, Yun-Young
    • Communications for Statistical Applications and Methods
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    • v.9 no.1
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    • pp.249-259
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    • 2002
  • In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

On Estimating the Variance of a Normal Distribution With Known Coefficient of Variation

  • Ray, S.K.;Sahai, A.
    • Journal of the Korean Statistical Society
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    • v.7 no.2
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    • pp.95-98
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    • 1978
  • This note deals with the estimations of the variance of a normal distribution $N(\theta,c\theta^2)$ where c, the square of coefficient of variation is assumed to be known. This amounts to the estimation of $\theta^2$. The minimum variance estimator among all unbiased estimators linear in $\bar{x}^2$ and $s^2$ where $\bar{x}$ and $s^2$ are the sample mean and variance, respectively, and the minimum risk estimator in the class of all estimators linear in $\bar{x}^2$ and $s^2$ are obtained. It is shown that the suggested estimators are BAN.

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Disturbance due to internal heat source in thermoelastic solid using dual phase lag model

  • Ailawalia, Praveen;Singla, Amit
    • Structural Engineering and Mechanics
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    • v.56 no.3
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    • pp.341-354
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    • 2015
  • The dual-phase lag heat transfer model is employed to study the problem of isotropic generalized thermoelastic medium with internal heat source. The normal mode analysis is used to obtain the exact expressions for displacement components, force stress and temperature distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. The results are discussed and depicted graphically.

An Improved Quantize-Quantize Plot for Normality Test

  • Lee, Jea-Young;Rhee, Seong-Won
    • Communications for Statistical Applications and Methods
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    • v.5 no.1
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    • pp.67-75
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    • 1998
  • A new graphical method, named transformed quantize-quantile (TQQ), of a quantize-quantile (Q-Q) Plot is developed for the detection of deviations from the normal distribution. It will be shown that TQQ is helpful for detecting patterns of how points depart from normality. TQQ characteristics of the various kinds of representations are illustrated by a generated sample from a composite of a normal distribution and a clinical example for TQQ is constructed and explained.

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Air-water two-phase distribution in an aluminum parallel flow heat exchanger header having different inlet orientations (유입 방향에 따른 알루미늄 평행류 열교환기 헤더내 공기-물 2 상류 분지 실험)

  • Kim, Nae-Hyun;Ham, Jung-Ho;Park, Tae-Kyun;Kim, Do-Young
    • Proceedings of the KSME Conference
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    • 2007.05b
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    • pp.2108-2112
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    • 2007
  • The air and water flow distribution are experimentally studied for a round header-ten microchannel tube configuration. Three different inlet orientations (parallel, side, normal) were investigated. Tests were conducted with downward flow configuration for the mass flux from 70 to 130 kg/$m^2s$, quality from 0.2 to 0.6, non-dimensional protrusion depth (h/D) from 0.0 to 0.5. It is shown that, for almost all the test conditions, normal inlet yielded the best flow distribution, followed by side and parallel inlet. Possible reasoning is provided using flow visualization results.

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How to Improve Classical Estimators via Linear Bayes Method?

  • Wang, Lichun
    • Communications for Statistical Applications and Methods
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    • v.22 no.6
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    • pp.531-542
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    • 2015
  • In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks.

BAYESIAN ROBUST ANALYSIS FOR NON-NORMAL DATA BASED ON A PERTURBED-t MODEL

  • Kim, Hea-Jung
    • Journal of the Korean Statistical Society
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    • v.35 no.4
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    • pp.419-439
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    • 2006
  • The article develops a new class of distributions by introducing a nonnegative perturbing function to $t_\nu$ distribution having location and scale parameters. The class is obtained by using transformations and conditioning. The class strictly includes $t_\nu$ and $skew-t_\nu$ distributions. It provides yet other models useful for selection modeling and robustness analysis. Analytic forms of the densities are obtained and distributional properties are studied. These developments are followed by an easy method for estimating the distribution by using Markov chain Monte Carlo. It is shown that the method is straightforward to specify distribution ally and to implement computationally, with output readily adopted for constructing required criterion. The method is illustrated by using a simulation study.