Abstract
In this paper, we derive hitherto unknown expressions for the generalized Sibuya distribution Kozubowski and Podgorski (Ann Inst Stat Math 70(4):855-887, 2018), which include shape properties, order statistic properties, distribution of sample range, conditional distributions of extreme order statistics, stress strength probability, sum of random variables, Shannon entropy, maximum likelihood estimation and censored maximum likelihood estimation. Finally, two data illustrations are provided.