On the Conditions for Convergence of the Quasi-Ranges and Random Quasi-Ranges to the Same Distribution

ABSTRACT

In the present paper we study the following question: when do the quasi-range and quasi-half-range have the same asymptotic distribution as the random quasi-range and random quasi-half-range?. We have established some theorems answering the above question. Finally, we give an example to illustrate the main results.

Key Words and Phrases:

• Quasi-ranges
• Random quasi-ranges
• Convergence
• Asymptotic distribution
• Order statistics
• Random indices