• 정보처리학회논문지A
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• 제9A권2호
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• pp.267-270
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• 2002

비중심 $\chi^2$분포의 누적분포 함수의 계산은 $\chi^2$검정에서 검정력 계산에 요구된다. 본 논문서는 중심 $\chi^2$분포 함수를 통하여 비중심 $\chi^2$분포 함수의 계산을 구하는 알고리즘을 제시하고 있으며 기존의 접근 방법에 의한 계산 결과와 비교하였다.

• Journal of the Korean Data and Information Science Society
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• 제15권2호
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• pp.423-430
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• 2004

We provide the exact form of a Rao-Robson version of the chi-squared test of multivariate normality suggested by Park(2001). This test is easy to apply in practice since it is easily computed and has a limiting chi-squared distribution under multivariate normality. A self-contained formal argument is provided that it has the limiting chi-squared distribution. A simulation study is provided to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study in a nonnormal distribution is conducted in order to compare the power of our test with those of other popular normality tests.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.429-440
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• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

• Journal of the Korean Data and Information Science Society
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• 제16권2호
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• pp.227-236
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• 2005

A chi-squared test of spherical symmetry is suggested. This test is easy to apply in practice since it is easy to compute and has a limiting chi-squared distribution under spherical symmetry. The result of Park(1998) can be used to show that it has the limiting chi-squared distribution. A simulation study is conducted to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study that compares the power of our test with those of other tests of spherical symmetry is performed.

• 대한수학회보
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• 제45권3호
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• pp.509-522
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• 2008

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.197-203
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• 1998

To test the hypothesis of complete or total independence for a multi-way contingency table, the Pearson chi-squared test statistic is usually employed under Poisson or multinomial models. It is well known that, under the hypothesis, this statistic follows an asymptotic chi-squared distribution. We consider the case where all marginal sums of the contingency table are fixed. Using conditional limit theorems, we show that the chi-squared test statistic has the same limiting distribution for this case.

• International Journal of Reliability and Applications
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• 제4권3호
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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.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.447-456
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• 2007

On the basis of marginal likelihood of the residual vector which is free of nuisance mean parameters, we propose new Lagrange Multiplier seasonal unit root tests in seasonal autoregressive process. The limiting null distribution of the tests is the standardized ${\chi}^2-distribution$. A Monte-Carlo simulation shows the new tests are more powerful than the tests based on the ordinary least squares (OLS) estimator, especially for large number of seasons and short time spans.

• Journal of the korean society of oceanography
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• 제34권2호
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• pp.95-112
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• 1999

To investigate a phytoplankton community structure and its biomass distribution in the Korea Strait, phytoplankton pigments were quantitatively measured by HPLC method, with hydro-graphic conditions in August and October, 1996. The measured chi. a concentrations were in the range of 7.1-1,280.7 ng/1. Horizontal distribution pattern of chi. a in summer (August) was very different from that of autumn (October). High concentration of chi. a occurred near the coast with relatively low salinity (< 33%). Vertically, the highest concentrations of pigments at most of the stations were found near the surface and above the thermocline. The maximum concentration of chi. a in October was four times higher than in August. It was notable to measure relatively high concentration of chi. b up to 190.8 ng/1 in the study area, since chi. bcontaining green algae and prochlophytes have been ignored because of their minute size and sensitivity to common preservatives. Major carotenoids detected were fucoxanthin, zeaxanthin, 19'-hexanoyloxyfucoxanthin, and prasinoxanthin. Diatoms were the dominant group with secondary important groups as pryrnnesiophytes and cyanobacteria for the biomass of phytoplankton for both cruises. The dominant species of diatoms in summer were Thalassiosira sp. and Chaetoceros peruvianus. As minor groups, prasinophytes, crysophytes, and cryptophytes were confirmed by their marker pigments and dinoflgellates by microscopical observation. Degradation products of chi. a was minor. Interestingly, at 200 m depth of St A4, the deepest station in the western channel of the Korea Strait, substantial amounts of chi. a including fucoxanthin, 19'-hexanoyloxyfucoxanthin, chi. b, and degradation products of chi. a was measured from both cruises. Higher concentration (2-3 times) of those pigments were detected from samples in summer than in autumn. Small decrease in concentration of phosphate at this depth of St. A4 was also observed. It suggested that this bottom cold water was transported from the subsurface water with biomass of active phytoplankton, which was sunk and flowed southward.