Characterizations of Truncated Univariate Continuous Distributions Introduced by Lorenzo Zaninetti, I-XV - Hamedani, G. G.; Roshani, Amin (Statistics, Optimization & Information Computing, 2026)
This paper deals with various characterizations of 15 truncated univariate continuous distributions proposed by Lorenzo Zaninetti from 2019-2025, all published in the "International Journal of Astronomy and Astrophysics". Zaninetti masterfully and with a lot of super complicated derivations presents the cdfs and pdfs for these distributions. The present work may be considered as a supplement to Zaninetti’s excellent works. These characterizations are based on: ( i) a simple relationship between two truncated moments and ( ii) the reverse hazard function and. It should be mentioned that for the characterization ( i) the cumulative distribution function need not to have a closed form and depends on the solution of a first order differential equation, which provides a bridge between probability and differential equation.