Characterizations of the distribution of the Demmel condition number of real Wishart matrices

The Demmel condition number is an indicator of the matrix condition, and its properties have recently found applications in many practical problems, such as in MIMO communication systems, in the analytical prediction of level-crossing and fade duration statistics of Rayleigh channels, and in spectrum sensing for cognitive radio systems, among others. As the characterizations of a probability distribution play an important role in probability and statistics, in this paper we study the characterizations of the distribution of the Demmel condition number of real Wishart matrices by truncated first moment. Since the truncated distributions arise in practical statistics where the ability of record observations is limited to a given threshold or within a specified range, we hope that these characterizations will be quite useful for practitioners and researchers in the fields of probability, statistics, and other applied sciences, such as actuarial science, linear algebra, multivariate statistics, physics, wireless communications, among others.