On proportional reversed failure rate class

Motivated by the recent use of the proportional reversed failure rate in economics (rates of increase and elasticity, see Veres-Ferrer and Pavia (Stat Pap 55:275–284, 2014) and in reliability (stochastic comparisons among systems, see Khaledi et al. (J Stat Plan Inference 141:276–286, 2011), in this work, we investigate characterizations and closure properties of the decreasing proportional reversed failure rate (DPRFR) classes for continuous, nonnegative random variables. Among others, we prove that DPRFR distributions are closed under convolutions. In addition, we relate this class of distributions with the class of monotone failure rate, proportional failure rate and likelihood ratio distributions.