• Communications for Statistical Applications and Methods
• /
• 제19권6호
• /
• pp.837-847
• /
• 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.

• Composites Research
• /
• 제29권5호
• /
• pp.299-305
• /
• 2016

본 연구는 이변량 Gaussian 분포함수를 적용하여 CFRP 적층판의 섬유물성 변화를 추정하는 방법을 제안하였다. 섬유의 손상 분포를 규명하기 위하여 수정된 이변량 Gaussian 분포함수를 적용하여 5개의 미지 변수가 고려되었다. 조합된 컴퓨터 기법을 적용하여 역문제를 해결하기 위하여 본 연구에서는 몇 개의 고유진동수와 모드 정보를 입력데이터로 활용하였다. 수치해석 예제는 제안된 기법이 적층배열 변화에 따른 CFRP 판의 섬유 손상 분포 및 위치를 규명할 수 있는 적합하고 실용적은 방법임을 보여준다.

• Journal of the Korean Data and Information Science Society
• /
• 제16권3호
• /
• pp.539-547
• /
• 2005

We propose the Bayesian testing for the equality of two independent Inverse Gaussian population means using the fractional Bayesian factors suggested by O' Hagan(1995). As prior distribution for the parameters, we assumed the noninformative priors. In order to investigate the usefulness of the proposed Bayesian testing procedures, the behaviors of the proposed results are examined via real data analysis.

• Journal of the Korean Statistical Society
• /
• 제30권1호
• /
• pp.99-113
• /
• 2001

This paper deals with the problem of estimating the means in two inverse Gaussian populations with equal but unknown coefficient of variation. The maximum likelihood estimators are derived by solving a cubic equation and their asymptotic variances are presented for comparative purpose. Monte-Carlo simulation is conducted to investigate the efficiency of the estimators relative to the sample means over a wide range of values for the sample size and the coefficient of variation. The effect on this efficiency under the departure from the assumption of common coefficient of variation is also studied.

• Communications for Statistical Applications and Methods
• /
• 제15권5호
• /
• pp.655-666
• /
• 2008

Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

• Journal of the Korean Data and Information Science Society
• /
• 제19권3호
• /
• pp.995-1006
• /
• 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.

• 한국데이터정보과학회:학술대회논문집
• /
• 한국데이터정보과학회 2005년도 추계학술대회
• /
• pp.85-93
• /
• 2005

Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model procedures, we compare with the classical tests.

• Journal of the Korean Data and Information Science Society
• /
• 제16권4호
• /
• pp.1167-1176
• /
• 2005

Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model selection procedures, we compare with the classical tests.

• Journal of the Korean Data and Information Science Society
• /
• 제26권1호
• /
• pp.243-253
• /
• 2015

In this paper, we develop the noninformative priors for the common shape parameter of several inverse Gaussian distributions. Specially, we want to develop noninformative priors which satisfy certain objective criterion. The probability matching priors and reference priors of the common shape parameter will be developed. It turns out that the second order matching prior does not exist. The reference priors satisfy the first order matching criterion, but Jeffrey's prior is not the first order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• Journal of the Korean Data and Information Science Society
• /
• 제26권3호
• /
• pp.739-748
• /
• 2015

This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.