7 papers
Second-order stochastic comparisons of order statistics
Tommaso Lando, Idir Arab, Paulo Eduardo Oliveira
We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationsh…
Convex transform order of Beta distributions with some consequences
Idir Arab, Paulo Eduardo Oliveira, Tilo Wiklund
The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisa…
Non-comparability with respect to the convex transform order with applications
Idir Arab, Milto Hadjikyriakou, Paulo Eduardo Oliveira
In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results…
On a conjecture about the comparability of parallel systems with respect to convex transform order
Idir Arab, Milto Hadjikyriakou, Paulo Eduardo Oliveira
In this paper we prove that two heterogeneous parallel systems with independent exponentially distributed components are comparable via the star transform order while the compariso…
On the limit behavior of iterated equilibrium distributions for the Gamma and Weibull families
Idir Arab, Milto Hadjikyriakou, Paulo Eduardo Oliveira
In this paper, we study the evolution of iterated equilibrium distributions for the Gamma and Weibull families of distributions as the iteration step increases. We characterize the…
Iterated failure rate monotonicity and ordering relations within Gamma and Weibull distributions
Idir Arab, Paulo Eduardo Oliveira
Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings…