An exponentiated geometric distribution

•Proposes a discrete version of the exponentiated exponential distribution.•Mathematical properties and procedures for estimation are derived for the proposed distribution.•Proposed distribution provides better and more accurate fits than Gómez-Déniz et al.’s [14] distribution for at least two data sets.

The exponentiated exponential distribution is one of the most seminal distributions of the 20th century. Here, we propose a discrete exponentiated exponential distribution. We derive its mathematical properties and procedures for estimation by common methods. The estimation procedures are assessed by simulation. Finally, the proposed distribution is compared with one of the most recent discrete distributions using two real data sets on insurance.