Jorge Navarro - Profile on Academia.edu (original) (raw)
Papers by Jorge Navarro
Connecting copula properties with reliability properties of coherent systems
Applied Stochastic Models in Business and Industry
Inactivity times of coherent systems with dependent components under periodical inspections
Applied Stochastic Models in Business and Industry
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
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.
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.
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). ...
Characterization of discrete distributions using expected values
Statistical Papers, 1995
ABSTRACT
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.
Naval Research Logistics, 2009
The signature of a system with independent and identically distributed (i.i.d.) component lifetim... more The signature of a system with independent and identically distributed (i.i.d.) component lifetimes is a vector whose ith element is the probability that the ith component failure is fatal to the system. System signatures have been found to be quite useful tools in the study and comparison of engineered systems. In this article, the theory of system signatures is extended to versions of signatures applicable in dynamic reliability settings. It is shown that, when a working used system is inspected at time t and it is noted that precisely k failures have occurred, the vector s ∈ [0, 1] n−k whose j th element is the probability that the (k + j)th component failure is fatal to the system, for j = 1, 2,. .. , n − k, is a distribution-free measure of the design of the residual system. Next, known representation and preservation theorems for system signatures are generalized to dynamic versions. Two additional applications of dynamic signatures are studied in detail. The well-known "new better than used" (NBU) property of aging systems is extended to a uniform (UNBU) version, which compares systems when new and when used, conditional on the known number of failures. Sufficient conditions are given for a system to have the UNBU property. The application of dynamic signatures to the engineering practice of "burn-in" is also treated. Specifically, we consider the comparison of new systems with working used systems burned-in to a given ordered component failure time. In a reliability economics framework, we illustrate how one might compare a new system to one successfully burned-in to the kth component failure, and we identify circumstances in which burn-in is inferior (or is superior) to the fielding of a new system.
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 ...
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.
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). ...
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.
Applied Stochastic Models in Business and Industry, 2000
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. ...
Naval Research …, 2008
Following a review of the basic ideas in structural reliability, including signature-based repres... more Following a review of the basic ideas in structural reliability, including signature-based representation and preservation theorems for systems whose components have independent and identically distributed (i.i.d.) lifetimes, extensions that apply to the comparison of coherent systems of different sizes, and stochastic mixtures of them, are obtained. It is then shown that these results may be extended to vectors of exchangeable random lifetimes. In particular, for arbitrary systems of sizes m < n with exchangeable component lifetimes, it is shown that the distribution of an m-component system's lifetime can be written as a mixture of the distributions of k-out-of-n systems. When the system has n components, the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R-34 (1985) 69-72. These mixture representations are then used to obtain new stochastic ordering properties for coherent or mixed systems of different sizes.
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 ...
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 ...
Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with... more Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non-identically distributed lifetimes are expressed in terms of expected lifetimes of components. Similar evaluations are concluded for the respective mean residual lifetimes. In the IID case, improved inequalities dependent on a concentration parameter connected to the Gini dispersion index are obtained. The results can be used to compare systems with component lifetimes ordered in the convex ordering. In the INID case, some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes, and the expected lifetime of single unit for the equivalent systems with IID components. The latter can be further simplified in the case of weak Schur-concavity and Schur-convexity of the system generalized domination polynomial.
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.
Connecting copula properties with reliability properties of coherent systems
Applied Stochastic Models in Business and Industry
Inactivity times of coherent systems with dependent components under periodical inspections
Applied Stochastic Models in Business and Industry
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
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.
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.
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). ...
Characterization of discrete distributions using expected values
Statistical Papers, 1995
ABSTRACT
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.
Naval Research Logistics, 2009
The signature of a system with independent and identically distributed (i.i.d.) component lifetim... more The signature of a system with independent and identically distributed (i.i.d.) component lifetimes is a vector whose ith element is the probability that the ith component failure is fatal to the system. System signatures have been found to be quite useful tools in the study and comparison of engineered systems. In this article, the theory of system signatures is extended to versions of signatures applicable in dynamic reliability settings. It is shown that, when a working used system is inspected at time t and it is noted that precisely k failures have occurred, the vector s ∈ [0, 1] n−k whose j th element is the probability that the (k + j)th component failure is fatal to the system, for j = 1, 2,. .. , n − k, is a distribution-free measure of the design of the residual system. Next, known representation and preservation theorems for system signatures are generalized to dynamic versions. Two additional applications of dynamic signatures are studied in detail. The well-known "new better than used" (NBU) property of aging systems is extended to a uniform (UNBU) version, which compares systems when new and when used, conditional on the known number of failures. Sufficient conditions are given for a system to have the UNBU property. The application of dynamic signatures to the engineering practice of "burn-in" is also treated. Specifically, we consider the comparison of new systems with working used systems burned-in to a given ordered component failure time. In a reliability economics framework, we illustrate how one might compare a new system to one successfully burned-in to the kth component failure, and we identify circumstances in which burn-in is inferior (or is superior) to the fielding of a new system.
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 ...
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.
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). ...
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.
Applied Stochastic Models in Business and Industry, 2000
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. ...
Naval Research …, 2008
Following a review of the basic ideas in structural reliability, including signature-based repres... more Following a review of the basic ideas in structural reliability, including signature-based representation and preservation theorems for systems whose components have independent and identically distributed (i.i.d.) lifetimes, extensions that apply to the comparison of coherent systems of different sizes, and stochastic mixtures of them, are obtained. It is then shown that these results may be extended to vectors of exchangeable random lifetimes. In particular, for arbitrary systems of sizes m < n with exchangeable component lifetimes, it is shown that the distribution of an m-component system's lifetime can be written as a mixture of the distributions of k-out-of-n systems. When the system has n components, the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R-34 (1985) 69-72. These mixture representations are then used to obtain new stochastic ordering properties for coherent or mixed systems of different sizes.
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 ...
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 ...
Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with... more Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non-identically distributed lifetimes are expressed in terms of expected lifetimes of components. Similar evaluations are concluded for the respective mean residual lifetimes. In the IID case, improved inequalities dependent on a concentration parameter connected to the Gini dispersion index are obtained. The results can be used to compare systems with component lifetimes ordered in the convex ordering. In the INID case, some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes, and the expected lifetime of single unit for the equivalent systems with IID components. The latter can be further simplified in the case of weak Schur-concavity and Schur-convexity of the system generalized domination polynomial.
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.