• Communications for Statistical Applications and Methods
• /
• v.5 no.2
• /
• pp.531-538
• /
• 1998

This paper first examines the skewness of Wishart distribution, using Tracy and Sultan(1993)'s results. Second, it investigates the variance-covariance matrix of random matrix $S_Y=YY'$ which has a non-central Wishart distribution. Third, it proposes the exact form of the third moment of the random matrix with non-central Wishart distribution.

• Journal of the Korean Statistical Society
• /
• v.25 no.3
• /
• pp.393-406
• /
• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.323-334
• /
• 2003

We review the developmental history of the moment matrix of matrix quadratic form. This paper also investigates, the moment matrix of (non-central) Wishart distribution, which is multi-version of X$^2$ distribution.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.31-50
• /
• 1999

We revisit the problems of testing three-factor classifica-tion models with a single observation per cell. A common approach in analyzing such nonreplicated data is to omit the highest order in-teraction and regard it as error. This paper discusses the use of a multiplicative model(See and Smith 1996 and 1998) which is applied on residuals in order to separate the variablility due to three-factor interaction from what is counted as random error. in particualr to test the significance of the interaction term we derived an approxi-mated distribution of the likelihood ratio test statistic based on the quadrilinear model known as Tucher's three-mode principal compo-nent model. The derivation utilizes the distribution of the eignevalues of the Wishart matrix.

• Korean Journal of Remote Sensing
• /
• v.25 no.6
• /
• pp.531-546
• /
• 2009

The main objective of this study is to analyse the polarimetric characteristics of the various terrain targets by ground-based polarimetric SAR system and to confirm the compatible and effective polarimetric analysis method to reveal the polarization properties of different terrain targets by the GB-SAR. The fully polarimetric GB-SAR data with HH, HV, VH, and VV components were focused using the Deramp-FFT (DF) algorithm. The focused GB-SAR images were processed by the H/A/$\alpha$ polarimetric decomposition and the combined H/$\alpha$ or H/A/$\alpha$ and Wishart classification method. The segmented image and distribution graphs in H/$\alpha$ plane using Cloude and Pottier's method showed a reliable result that this quad-polarization GB-SAR data could be useful to classified corresponding scattering mechanism. The H/$\alpha$-Wishart and H/A/$\alpha$-Wishart classification results showed that a natural media and an artificial target were discriminated by the combined classification, in particular, after applying multi-looking and the Lee refined speckle filter.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.5
• /
• pp.1107-1116
• /
• 2014

In this paper, we review recent developments in network analysis using the graph theory, and introduce ongoing research area with relevant theoretical results. In specific, we introduce basic notations in graph, and conditional and marginal approach in constructing the adjacency matrix. Also, we introduce the Marcenko-Pastur law, the Tracy-Widom law, the white Wishart distribution, and the spiked distribution. Finally, we mention the relationship between degrees and eigenvalues for the detection of hubs in a network.