On relations for generalized Rayleigh distributions based on lower generalized order statistics and its characterization

In this paper, we derive the explicit expressions and some recurrence relations for single
and product moments of lower generalized order statistics from generalized Rayleigh distribution.
The results include as particular cases the above relations for moments of order
statistics and lower records. Further, using a recurrence relation for single moments we
obtain characterization of generalized Rayleigh distribution.