• Title/Summary/Keyword: Gaussian Distribution

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Shrinkage Estimator of Dispersion of an Inverse Gaussian Distribution

  • Lee, In-Suk;Park, Young-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.805-809
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    • 2006
  • In this paper a shrinkage estimator for the measure of dispersion of the inverse Gaussian distribution with known mean is proposed. Also we compare the relative bias and relative efficiency of the proposed estimator with respect to minimum variance unbiased estimator.

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A Test of Fit for Inverse Gaussian Distribution Based on the Probability Integration Transformation (확률적분변환에 기초한 역가우스분포에 대한 적합도 검정)

  • Choi, Byungjin
    • The Korean Journal of Applied Statistics
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    • v.26 no.4
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    • pp.611-622
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    • 2013
  • Mudholkar and Tian (2002) proposed an entropy-based test of fit for the inverse Gaussian distribution; however, the test can be applied to only the composite hypothesis of the inverse Gaussian distribution with an unknown location parameter. In this paper, we propose an entropy-based goodness-of-fit test for an inverse Gaussian distribution that can be applied to the composite hypothesis of the inverse Gaussian distribution as well as the simple hypothesis of the inverse Gaussian distribution with a specified location parameter. The proposed test is based on the probability integration transformation. The critical values of the test statistic estimated by simulations are presented in a tabular form. A simulation study is performed to compare the proposed test under some selected alternatives with Mudholkar and Tian (2002)'s test in terms of power. The results show that the proposed test has better power than the previous entropy-based test.

Kullback-Leibler Information-Based Tests of Fit for Inverse Gaussian Distribution (역가우스분포에 대한 쿨백-라이블러 정보 기반 적합도 검정)

  • Choi, Byung-Jin
    • The Korean Journal of Applied Statistics
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    • v.24 no.6
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    • pp.1271-1284
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    • 2011
  • The entropy-based test of fit for the inverse Gaussian distribution presented by Mudholkar and Tian(2002) can only be applied to the composite hypothesis that a sample is drawn from an inverse Gaussian distribution with both the location and scale parameters unknown. In application, however, a researcher may want a test of fit either for an inverse Gaussian distribution with one parameter known or for an inverse Gaussian distribution with both the two partameters known. In this paper, we introduce tests of fit for the inverse Gaussian distribution based on the Kullback-Leibler information as an extension of the entropy-based test. A window size should be chosen to implement the proposed tests. By means of Monte Carlo simulations, window sizes are determined for a wide range of sample sizes and the corresponding critical values of the test statistics are estimated. The results of power analysis for various alternatives report that the Kullback-Leibler information-based goodness-of-fit tests have good power.

A Modi ed Entropy-Based Goodness-of-Fit Tes for Inverse Gaussian Distribution (역가우스분포에 대한 변형된 엔트로피 기반 적합도 검정)

  • Choi, Byung-Jin
    • The Korean Journal of Applied Statistics
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    • v.24 no.2
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    • pp.383-391
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    • 2011
  • This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.

Comparison of parameter estimation methods for normal inverse Gaussian distribution

  • Yoon, Jeongyoen;Kim, Jiyeon;Song, Seongjoo
    • Communications for Statistical Applications and Methods
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    • v.27 no.1
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    • pp.97-108
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    • 2020
  • This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

Power Investigation of the Entropy-Based Test of Fit for Inverse Gaussian Distribution by the Information Discrimination Index

  • Choi, Byungjin
    • Communications for Statistical Applications and Methods
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    • v.19 no.6
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    • pp.837-847
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    • 2012
  • Inverse Gaussian distribution is widely used in applications to analyze and model right-skewed data. To assess the appropriateness of the distribution prior to data analysis, Mudholkar and Tian (2002) proposed an entropy-based test of fit. The test is based on the entropy power fraction(EPF) index suggested by Gokhale (1983). The simulation results report that the power of the entropy-based test is superior compared to other goodness-of-fit tests; however, this observation is based on the small-scale simulation results on the standard exponential, Weibull W(1; 2) and lognormal LN(0:5; 1) distributions. A large-scale simulation should be performed against various alternative distributions to evaluate the power of the entropy-based test; however, the use of a theoretical method is more effective to investigate the powers. In this paper, utilizing the information discrimination(ID) index defined by Ehsan et al. (1995) as a mathematical tool, we scrutinize the power of the entropy-based test. The selected alternative distributions are the gamma, Weibull and lognormal distributions, which are widely used in data analysis as an alternative to inverse Gaussian distribution. The study results are provided and an illustrative example is analyzed.

Signal Subspace-based Voice Activity Detection Using Generalized Gaussian Distribution (일반화된 가우시안 분포를 이용한 신호 준공간 기반의 음성검출기법)

  • Um, Yong-Sub;Chang, Joon-Hyuk;Kim, Dong Kook
    • The Journal of the Acoustical Society of Korea
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    • v.32 no.2
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    • pp.131-137
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    • 2013
  • In this paper we propose an improved voice activity detection (VAD) algorithm using statistical models in the signal subspace domain. A uncorrelated signal subspace is generated using embedded prewhitening technique and the statistical characteristics of the noisy speech and noise are investigated in this domain. According to the characteristics of the signals in the signal subspace, a new statistical VAD method using GGD (Generalized Gaussian Distribution) is proposed. Experimental results show that the proposed GGD-based approach outperforms the Gaussian-based signal subspace method at 0-15 dB SNR simulation conditions.

Study on Energy Distribution of the 6 MeV Electron Beam using Gaussian Approximation (가우시안 근사를 이용한 6 MeV 전자선의 에너지분포에 관한 연구)

  • Lee, Jeong-Ok;Kim, Seung-Kon
    • Journal of radiological science and technology
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    • v.22 no.2
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    • pp.53-56
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    • 1999
  • A Gaussian distribution was parametrized for the initial distribution of the electron beam emitted from a 6MeV medical linear accelerator. A percent depth dose was measured in a water phantom and the corresponding Monte Carlo calculations were performed starting from a Gaussian distribution for a range of standard deviations, ${\sigma}=0.1$, 0.15, 0.2, 0.25, and 0.3 with being the mean value for the Incident beam energy. When measurement and calculation were compared, the calculation with the Gaussian distribution for ${\sigma}=0.25$ turned out to agree best with the measurement. The results from the present work can be utilized as input energy data in planning an electron beam therapy with a Monte Carlo calculation.

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Bayesian One-Sided Hypothesis Testing for Shape Parameter in Inverse Gaussian Distribution

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.3
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    • pp.995-1006
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    • 2008
  • This article deals with the one-sided hypothesis testing problem in inverse Gaussian distribution. We propose Bayesian hypothesis testing procedures for the one-sided hypotheses of the shape parameter under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

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