This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations...

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 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 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,...

A procedure for clustering and classifying images determined by three classification variables is presented. A measure of global variability based on the singular value decomposition of the image matrices, and two average measures of local variability based on spatial correlation and spatial...

Functional data are becoming increasingly available and tractable because of the last technological advances. We enlarge the number of functional depths by defining two new depth functions for curves. Both depths are based on a spatial approach: the functional spatial depth (FSD), that shows an...

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 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...

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 comparisons of allocation policies of components in two-parallel-series systems with two types of components are provided with respect to both, the hazard rate and the reversed hazard rate orders. The main results indicate that the life of this kind of system is stochastically...