Jorge Navarro - Academia.edu (original) (raw)

Papers by Jorge Navarro

Research paper thumbnail of Connecting copula properties with reliability properties of coherent systems

Applied Stochastic Models in Business and Industry

Research paper thumbnail of Inactivity times of coherent systems with dependent components under periodical inspections

Applied Stochastic Models in Business and Industry

Research paper thumbnail of Signature Representation and Preservation Results for Engineered Systems and Applications to Statistical Inference

Springer Series in Reliability Engineering, 2011

ABSTRACT The aim of this article is to provide an overview of some of the recent developments rel... more ABSTRACT The aim of this article is to provide an overview of some of the recent developments relating to the theory of signatures and their role in the study of dynamic reliability, systems with shared components and nonparametric inference for a component lifetime distribution. Some new results and interpretations are also presented in the process. KeywordsCoherent system-Mixed system-Signature- k-out-of-n system-Exchangeability-Order statistics-Stochastic ordering-Hazard rate ordering-Likelihood ratio ordering-Dynamic reliability-Dynamic signature-Systems with shared components-Burned-in systems- D-spectrum-Nonparametric inference-Parametric inference-Best linear unbiased estimator-Proportional hazard rate model

Research paper thumbnail of Stochastic comparisons of generalized mixtures and coherent systems

TEST, 2015

ABSTRACT A distribution function \(F\) is a generalized mixture of the distribution functions \(F... more ABSTRACT A distribution function \(F\) is a generalized mixture of the distribution functions \(F_1,\ldots ,F_k\) if \(F=w_1 F_1+\ldots +w_k F_k\) , where \(w_1,\ldots ,w_k\) are some real numbers (weights) which should satisfy \(w_1+\ldots +w_k=1\) . If all the weights are positive, then we have a classical finite mixture. If some weights are negative, then we have a negative mixture. Negative mixtures appear in different applied probability models (order statistics, estimators, coherent systems, etc.). The conditions to obtain stochastic comparisons of classical (positive) mixtures are well known in the literature. However, for negative mixtures, there are only results for the usual stochastic order. In this paper, conditions for hazard rate and likelihood ratio comparisons of generalized mixtures are obtained. These theoretical results are applied in this paper to study distribution-free comparisons of coherent systems using their representations as generalized mixtures. They can also be applied to other probability models in which the generalized mixtures appear.

Research paper thumbnail of New Stochastic Orders Based on Double Truncation

Probability in the Engineering and Informational Sciences, 1997

The purpose of this paper is to study definitions and characterizations of orders based on reliab... more The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

Research paper thumbnail of Negative Mixtures Order Statistics and Systems

Advances in Mathematical and Statistical Modeling, 2008

... Jorge Navarro1 and Pedro J. Hernández2 ... ( j − 1 n − k ) Rj:j(t) (7.6) (see David and Nagar... more ... Jorge Navarro1 and Pedro J. Hernández2 ... ( j − 1 n − k ) Rj:j(t) (7.6) (see David and Nagaraja (2003), p. 46). ... The minimal and maximal signatures of all the coherent systems with three or four components can be seen in Navarro and Shaked (2006) and Navarro et al. (2007). ...

Research paper thumbnail of Characterization of discrete distributions using expected values

Statistical Papers, 1995

ABSTRACT

Research paper thumbnail of Distorted Lorenz curves: models and comparisons

Social Choice and Welfare, 2014

ABSTRACT The economic literature contains many parametric models for the Lorenz curve. A number o... more ABSTRACT The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve LLL L by a function hhh h , giving rise to a distorted Lorenz curve widetildeL=hcircL{\widetilde{L}}=h\circ LwidetildeL=hcircL L ~ = h ∘ L . In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve LLL L affect the transformed curve widetildeL{\widetilde{L}}widetildeL L ~ . Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.

Research paper thumbnail of Dynamic signatures and their use in comparing the reliability of new and used systems

Naval Research Logistics, 2009

Research paper thumbnail of Some new results on the cumulative residual entropy

Journal of Statistical Planning and Inference, 2010

... The main measure of the uncertainty contained in random variable X is the Shannon entropy Vie... more ... The main measure of the uncertainty contained in random variable X is the Shannon entropy View the MathML source , where f X is the probability density function of X. Ebrahimi (1996) considered the entropy of the residual lifetime X t =[X-t|X>t] as a dynamic measure of ...

Research paper thumbnail of Dynamic signatures of coherent systems based on sequential order statistics

Journal of Applied Probability, 2013

Sequential order statistics can be used to describe the ordered lifetimes of components in a syst... more Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

Research paper thumbnail of Linear inference for Type-II censored lifetime data of reliability systems with known signatures

… , IEEE Transactions on, 2011

... Narayanaswamy Balakrishnan, Hon Keung Tony Ng, Senior Member, IEEE, and Jorge Navarro ... N. ... more ... Narayanaswamy Balakrishnan, Hon Keung Tony Ng, Senior Member, IEEE, and Jorge Navarro ... N. Balakrishnan is with the Department of Mathematics and Statis-tics, McMaster University, Hamilton, ON L8S 4K1 Canada (e-mail: bala@mcmail.cis.mcmaster.ca). ...

Research paper thumbnail of Kernel density estimation using weighted data ∗

Communications in Statistics - Theory and Methods, 1998

In this paper we compare the kernel density estimators proposed by Bhattacharyya et al. (1988) an... more In this paper we compare the kernel density estimators proposed by Bhattacharyya et al. (1988) and Jones (1991) for length biased data, showing the asymptotic normality of the estimators. A method to construct a new estimator is proposed. Moreover, we extend these results to weighted data and we study an estimator for the weight function.

Research paper thumbnail of ‘Understanding the shape of the mixture failure rate’ by Maxim Finkelstein: Discussion 2

Applied Stochastic Models in Business and Industry, 2000

Research paper thumbnail of Mixture representations of residual lifetimes of used systems

Journal of Applied …, 2008

The representation of the reliability function of the lifetime of a coherent system as a mixture ... more The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. ...

Research paper thumbnail of On the application and extension of system signatures in engineering reliability

Research paper thumbnail of Are the order statistics ordered? A survey of recent results

The distributions of coherent systems with components with exchangeable lifetimes can be represen... more The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985). This ...

Research paper thumbnail of Tail hazard rate ordering properties of order statistics and coherent systems

Naval Research Logistics (NRL), 2007

Abstract: We study tail hazard rate ordering properties of coherent systems using the representat... more Abstract: We study tail hazard rate ordering properties of coherent systems using the representation of the distribution of a coherent system as a mixture of the distributions of the series systems obtained from its path sets. Also some ordering properties are obtained for order statistics ...

Research paper thumbnail of Comparisons and bounds for expected lifetimes of reliability systems

Research paper thumbnail of Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components

Advances in Applied Probability, 2013

The signature of a system is defined as the vector whose ith element is the probability that the ... more The signature of a system is defined as the vector whose ith element is the probability that the system fails concurrently with the ith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the ‘joint bivariate signature’, of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.

Research paper thumbnail of Connecting copula properties with reliability properties of coherent systems

Applied Stochastic Models in Business and Industry

Research paper thumbnail of Inactivity times of coherent systems with dependent components under periodical inspections

Applied Stochastic Models in Business and Industry

Research paper thumbnail of Signature Representation and Preservation Results for Engineered Systems and Applications to Statistical Inference

Springer Series in Reliability Engineering, 2011

ABSTRACT The aim of this article is to provide an overview of some of the recent developments rel... more ABSTRACT The aim of this article is to provide an overview of some of the recent developments relating to the theory of signatures and their role in the study of dynamic reliability, systems with shared components and nonparametric inference for a component lifetime distribution. Some new results and interpretations are also presented in the process. KeywordsCoherent system-Mixed system-Signature- k-out-of-n system-Exchangeability-Order statistics-Stochastic ordering-Hazard rate ordering-Likelihood ratio ordering-Dynamic reliability-Dynamic signature-Systems with shared components-Burned-in systems- D-spectrum-Nonparametric inference-Parametric inference-Best linear unbiased estimator-Proportional hazard rate model

Research paper thumbnail of Stochastic comparisons of generalized mixtures and coherent systems

TEST, 2015

ABSTRACT A distribution function \(F\) is a generalized mixture of the distribution functions \(F... more ABSTRACT A distribution function \(F\) is a generalized mixture of the distribution functions \(F_1,\ldots ,F_k\) if \(F=w_1 F_1+\ldots +w_k F_k\) , where \(w_1,\ldots ,w_k\) are some real numbers (weights) which should satisfy \(w_1+\ldots +w_k=1\) . If all the weights are positive, then we have a classical finite mixture. If some weights are negative, then we have a negative mixture. Negative mixtures appear in different applied probability models (order statistics, estimators, coherent systems, etc.). The conditions to obtain stochastic comparisons of classical (positive) mixtures are well known in the literature. However, for negative mixtures, there are only results for the usual stochastic order. In this paper, conditions for hazard rate and likelihood ratio comparisons of generalized mixtures are obtained. These theoretical results are applied in this paper to study distribution-free comparisons of coherent systems using their representations as generalized mixtures. They can also be applied to other probability models in which the generalized mixtures appear.

Research paper thumbnail of New Stochastic Orders Based on Double Truncation

Probability in the Engineering and Informational Sciences, 1997

The purpose of this paper is to study definitions and characterizations of orders based on reliab... more The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

Research paper thumbnail of Negative Mixtures Order Statistics and Systems

Advances in Mathematical and Statistical Modeling, 2008

... Jorge Navarro1 and Pedro J. Hernández2 ... ( j − 1 n − k ) Rj:j(t) (7.6) (see David and Nagar... more ... Jorge Navarro1 and Pedro J. Hernández2 ... ( j − 1 n − k ) Rj:j(t) (7.6) (see David and Nagaraja (2003), p. 46). ... The minimal and maximal signatures of all the coherent systems with three or four components can be seen in Navarro and Shaked (2006) and Navarro et al. (2007). ...

Research paper thumbnail of Characterization of discrete distributions using expected values

Statistical Papers, 1995

ABSTRACT

Research paper thumbnail of Distorted Lorenz curves: models and comparisons

Social Choice and Welfare, 2014

ABSTRACT The economic literature contains many parametric models for the Lorenz curve. A number o... more ABSTRACT The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve LLL L by a function hhh h , giving rise to a distorted Lorenz curve widetildeL=hcircL{\widetilde{L}}=h\circ LwidetildeL=hcircL L ~ = h ∘ L . In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve LLL L affect the transformed curve widetildeL{\widetilde{L}}widetildeL L ~ . Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.

Research paper thumbnail of Dynamic signatures and their use in comparing the reliability of new and used systems

Naval Research Logistics, 2009

Research paper thumbnail of Some new results on the cumulative residual entropy

Journal of Statistical Planning and Inference, 2010

... The main measure of the uncertainty contained in random variable X is the Shannon entropy Vie... more ... The main measure of the uncertainty contained in random variable X is the Shannon entropy View the MathML source , where f X is the probability density function of X. Ebrahimi (1996) considered the entropy of the residual lifetime X t =[X-t|X>t] as a dynamic measure of ...

Research paper thumbnail of Dynamic signatures of coherent systems based on sequential order statistics

Journal of Applied Probability, 2013

Sequential order statistics can be used to describe the ordered lifetimes of components in a syst... more Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

Research paper thumbnail of Linear inference for Type-II censored lifetime data of reliability systems with known signatures

… , IEEE Transactions on, 2011

... Narayanaswamy Balakrishnan, Hon Keung Tony Ng, Senior Member, IEEE, and Jorge Navarro ... N. ... more ... Narayanaswamy Balakrishnan, Hon Keung Tony Ng, Senior Member, IEEE, and Jorge Navarro ... N. Balakrishnan is with the Department of Mathematics and Statis-tics, McMaster University, Hamilton, ON L8S 4K1 Canada (e-mail: bala@mcmail.cis.mcmaster.ca). ...

Research paper thumbnail of Kernel density estimation using weighted data ∗

Communications in Statistics - Theory and Methods, 1998

In this paper we compare the kernel density estimators proposed by Bhattacharyya et al. (1988) an... more In this paper we compare the kernel density estimators proposed by Bhattacharyya et al. (1988) and Jones (1991) for length biased data, showing the asymptotic normality of the estimators. A method to construct a new estimator is proposed. Moreover, we extend these results to weighted data and we study an estimator for the weight function.

Research paper thumbnail of ‘Understanding the shape of the mixture failure rate’ by Maxim Finkelstein: Discussion 2

Applied Stochastic Models in Business and Industry, 2000

Research paper thumbnail of Mixture representations of residual lifetimes of used systems

Journal of Applied …, 2008

The representation of the reliability function of the lifetime of a coherent system as a mixture ... more The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. ...

Research paper thumbnail of On the application and extension of system signatures in engineering reliability

Research paper thumbnail of Are the order statistics ordered? A survey of recent results

The distributions of coherent systems with components with exchangeable lifetimes can be represen... more The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985). This ...

Research paper thumbnail of Tail hazard rate ordering properties of order statistics and coherent systems

Naval Research Logistics (NRL), 2007

Abstract: We study tail hazard rate ordering properties of coherent systems using the representat... more Abstract: We study tail hazard rate ordering properties of coherent systems using the representation of the distribution of a coherent system as a mixture of the distributions of the series systems obtained from its path sets. Also some ordering properties are obtained for order statistics ...

Research paper thumbnail of Comparisons and bounds for expected lifetimes of reliability systems

Research paper thumbnail of Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components

Advances in Applied Probability, 2013

The signature of a system is defined as the vector whose ith element is the probability that the ... more The signature of a system is defined as the vector whose ith element is the probability that the system fails concurrently with the ith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the ‘joint bivariate signature’, of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.