A note on the characterizations of the distributions of the condition numbers of real Gaussian matrices

• Main Authors: Shakil M., Ahsanullah M.
• Format: Article
• Language: English
• Published: De Gruyter 2018-07-01
• Series: Special Matrices
• Subjects: characterization; condition number; truncated first moment; gaussian matrices
• Online Access: https://doi.org/10.1515/spma-2018-0022

Many researchers and authors have studied the distributions of the condition numbers of real Gaussian matrices, which appear in many fields of pure and applied sciences, such as, probability, statistics, multivariate statistics, linear algebra, operator algebra theory, actuarial science, physics, wireless communications, and polarimetric synthetic aperture radar (PolSAR). Motivated by this, in this paper, we first present several new distributional properties of the distributions of the condition numbers of real Gaussian matrices. Since it is important to know the percentage points of a given distribution for any statistical application, we have also computed percentiles of the said distributions of the condition numbers. Before a particular probability distribution model is applied to fit the real world data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterizations. Also, the truncated distributions arise in practical statisticswhere the ability of record observations is limited to a given threshold or within a specified range. In view of these facts, some characterizations by truncated first moment are also presented. We hope that the findings of this paper will be quite useful to the researchers in various fields of pure and applied sciences as stated above.