Stability for the Arnold-Ghosh characterization of the geometric distribution (Q1918235)

We are interested in the characterization of the geometric law given by \textit{B. C. Arnold} and \textit{M. Ghosh} [Scand. Actuarial J. 1976; 232-234 (1976; Zbl 0342.62007)]. It is a result making use of identical distribution of the spacing \(\max \{X,Y\} - \min \{X,Y\}\) and \(X\), where \(X,Y\) are i.i.d. natural valued r.v.'s. At first we give a short proof of the original result in Section 2. In Section 3, stability of the characterization is studied.