In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution.

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall–Olkin extended family as a random variable. The closure of this model under...

The mean residual life function plays an important role in reliability theory and other branches of statistics. In this paper, we study some ageing properties of the residual life of , the nth upper k-records, given that , where n[greater-or-equal, slanted]m. Some stochastic comparison results...

Makino [Makino, T., 1984. Mean hazard rate and its applications to the normal approximation of the Weibull distribution. Naval Research Logistics Quarterly 31, 1-8] proves that, for any random variable X with finite mean [mu], E(1/r(X)][greater-or-equal, slanted]1/[mu], where r([dot operator])...

The reversed (backward) hazard rate ordering is an ordering for random variables which compares lifetimes with respect to their reversed hazard rate functions. In this paper, we have given some sufficient conditions under which the ordering between the components with respect to the reversed...

Recently, the concept of aging intensity (AI) function has been introduced in the literature for evaluating the aging property of a unit (that may be a system or a living organism) quantitatively. In this paper, we discuss the properties of AI function and study its nature for various...

We show that the order statistics, in a sample from a distribution that has a logconcave density function, are ordered in the up shifted likelihood ratio order. We also show that the order statistics from two different collections of random variables are ordered in the up shifted likelihood...

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the...

Any repairable system improves (deteriorates) with time if the interarrival times of failure tend to get larger (smaller) in some sense. In this paper we consider two such repairable systems, and their performance in terms of several partial orderings of their respective interarrival times of...

The characterization of distributions is well known in the field of Statistics and Reliability. This paper characterizes a few distributions with the help of failure rate, mean residual, log-odds rate, and aging intensity functions.