Some new stochastic orders based on quantile function

ABSTRACT

Recently, in the literature, the use of quantile functions in the place of distribution functions has provided new models, alternative methodology and easier algebraic manipulations. In this paper, we introduce new orders among the random variables in terms of their quantile functions like the reversed hazard quantile function, the reversed mean residual quantile function and the reversed variance residual quantile function orders. The relationships among the proposed orders and some existing orders are also discussed.

KEYWORDS:

• Quantile function
• Reversed hazard quantile function
• Reversed mean residual quantile function
• Reversed variance residual quantile function
• Stochastic order.

Acknowledgments

The authors are grateful to the editor and anonymous referees for their valuable comments and suggestions which improved the presentation of the paper.