The capability of modeling non-exponentially distributed and dependent inter-arrival times as well as correlated batches makes the Batch Markovian Arrival Processes (BMAP) suitable in different real-life settings as teletraffic, queueing theory or actuarial contexts. An issue to be taken into...

In this paper, we solve for some cases a conjecture by Kochar and Korwar (1996) in relation with the normalized spacings of the order statistics related to a sample of independent exponential random variables with different scale parameter. In the case of a sample of size n=3, they proved the...

A great number of articles have dealt with stochastic comparisons of ordered random variables in the last decades. In particular, distributional and stochastic properties of ordinary order statistics have been studied extensively in the literature. Sequential order statistics are proposed as an...

In reliability theory and survival analysis, many set of data are generated by distributions with bathtub shaped hazard rate functions. Launer (1993) established several relations between the behaviour of the hazard rate function and the percentile residual life function. In particular,...

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

In this paper we consider the problem of identifiability of the two-state Markovian Arrival process (MAP2). In particular, we show that the MAP2 is not identifiable and conditions are given under which two different sets of parameters, induce identical stationary laws for the observable process.

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0 ? 1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of nonparametric statistical estimation of...

In the context of functional data analysis, we propose a new method to test the homogeneity of families of functions. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two families. A simulation study is performed to check...

In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate...