Studia Scientiarum Mathematicarum Hungarica
We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the nth order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some of these distributions are infinitely divisible via Bondesson’s 1979 classifications.
Hamedani, Gholamhossein G., "On Characterizations and Infinite Divisibility of Recently Introduced Distributions" (2016). Mathematics, Statistics and Computer Science Faculty Research and Publications. 491.
ADA Accessible Version
Accepted version. Studia Scientiarum Mathematicarum Hungarica, Vol. 53, No. 4 (November 2016): 467-511. DOI. © 2016 Akadémiai Kiadó, Budapest. Used with permission.