2015/01/31 by Jacek Wesołowski, Wesolowski, Jacek
Mathematics · #60E05 #60E10 #62E10 #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1502.00140
openalex publication_date 2015/01/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions. This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). Since we work with differential equations for the Laplace transforms, no density assumptions are needed.