Some characterizations involving uniform and powers of uniform random variables

Abstract

This paper deals with some problems of characterization involving uniform random variables. Twelve different cases are dealt with. It is shown that some cases have no solution, others lead to trivial solutions and finally, the rest lead to non-trivial solutions. The cases are also analyzed when the uniform distribution assumption is replaced by the power function or the Pareto assumptions.

Keywords:

• power function
• Pareto
• characterization
• maxima and minima
• positive Linnik distribution

Acknowledgements

We are grateful to an anonymous referee for suggestions that helped to improve the presentation of these results.