The study describes the general concept of the XLindley distribution. Forms of density and hazard rate functions are investigated. Moreover, precise formulations for several numerical properties of distributions are derived. Extreme order statistics are established using stochastic ordering, the...

In winner-take-all tournaments, agents' performance is determined jointly by effort and luck, and the top performer is rewarded. We study the impact of the ''shape of luck'' -- the details of the distribution of performance shocks -- on incentives in such settings. We are concerned with the...