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Stochastic orders using quantile-based reliability functions
B. Vineshkumar,N. Unnikrishnan Nair,P. G. Sankaran 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.2
The concept of stochastic orders plays a major role in the theory and practice of statistics. It generally refers to a set of relations that may hold between a pair of distributions of random variables. In reliability theory, stochastic orders are employed to compare lifetime of two systems. In the present work, we develop new stochastic orders using the quantilebased reliability measures like the hazard quantile function and the mean residual quantile function. We also establish relationships among the proposed orders and certain existing orders. Various properties of the orders are also studied.
Reversed percentile residual life and related concepts
N. Unnikrishnan Nair,,B. Vineshkumar 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1
In this work we discuss the properties of the reversed percentile residual life function and its relationship with the reversed hazard function. Some models with simple functional forms for both reversed hazard rate and reversed percentile residual life function are proposed. A method of distinguishing decreasing (increasing) reversed hazard rates (reversed percentile lives) is also presented.