A Brief Overview and Survey of the Scientific Work by Feng Qi

Abstract

In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.

Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions

“…The sharpness of the two-sided inequality ( 7) on (0, ∞) is concluded from the second limit in (3) and the limits in (4). The proof of Theorem 1 is complete.…”

“…In the electronic arXiv preprints [1,2] and their formally published version [3], the authors investigated the geometry induced by the Fisher-Rao metric on the parameter space of the Dirichlet distributions in statistics theory, showed that the parameter space is a Hadamard manifold (that is, the manifold is geodesically complete and has negative sectional curvature everywhere), and demonstrated that the Fréchet mean of a set of the Dirichlet distributions is uniquely defined in the geometry. The papers [1][2][3] have been cited in [4][5][6][7][8][9][10][11][12][13][14][15][16]. This means that the papers [1][2][3] have attracted great interest from more and more mathematicians in a short time.…”