Multivariate Life Distributions Induced by Gamma Process Environments,

Singpurwalla, Nozer D.; Youngren, Mark A.

doi:10.21236/ada293918

Cited by 12 publications

(18 citation statements)

References 9 publications

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“…Such distributions are often considered in reliability literature when dependence between units is assumed (see, e.g., Lindley and Singpurwalla [13], Singpurwalla and Youngren [23]). …”

Section: Consider a Random Vectormentioning

confidence: 99%

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Improving series and parallel systems through mixtures of duplicated dependent components

Crescenzo

Pellerey

2011

Naval Research Logistics

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We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components’ lifetimes. We also characterize the classes of bivariate distributions where this phenomenon arises through a new weak dependence notion

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“…Such distributions are often considered in reliability literature when dependence between units is assumed (see, e.g., Lindley and Singpurwalla [13], Singpurwalla and Youngren [23]). …”

Section: Consider a Random Vectormentioning

confidence: 99%

“…satisfy conditions (23 It is now interesting to consider a case when a pair of bivariate random vectors X and Y satisfy simultaneously (9) and …”

Section: Parallel Systemsmentioning

confidence: 99%

Improving series and parallel systems through mixtures of duplicated dependent components

Crescenzo

Pellerey

2011

Naval Research Logistics

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“…In [32] (rediscovered recently in [23]), a multivariate credit model can be defined by assuming the integrated hazard function of every name (say i) is given by…”

Section: Theorem 13 Under the Clayton Copula Model Assume (I) (Q') mentioning

confidence: 99%

On Break-Even Correlation: The Way to Price Structured Credit Derivatives by Replication

Vigneron

Fermanian

2009

SSRN Journal

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We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.

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“…Of course, this is by no means the only way to generate multivariate distributions. For the purpose of illustration, we limit attention to the bivariate case and consider as seeds the bivariate exponentials of Marshall and Olkin (1967), Gumbel (1960), and Singpurwalla and Youngren (1993;henceforth S-Y), and a bivariate exponential induced by the copula of a bivariate Pareto distribution.…”

Section: Generating New Families Of Dependent Lifetimesmentioning

confidence: 99%

The Hazard Potential

Singpurwalla

2006

Journal of the American Statistical Association

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The author thanks Hakon Gjessing for his help regarding the distribution of killing times of an integrated geometric Brownian motion process. The detailed comments by two referees are gratefully acknowledged. This is an expository article directed at reliability theorists, survival analysts, and others interested in looking at life history and event data. Here we introduce the notion of a hazard potential as an unknown resource that an item is endowed with at inception. The item fails when this resource becomes depleted. The cumulative hazard is a proxy for the amount of resource consumed, and the hazard function is a proxy for the rate at which this resource is consumed. With this conceptualization of the failure process, we are able to characterize accelerated, decelerated, and normal tests and are also able to provide a perspective on the cause of interdependent lifetimes. Specifically, we show that dependent life lengths are the result of dependent hazard potentials. Consequently, we are able to generate new families of multivariate life distributions using dependent hazard potentials as a seed. For an item that operates in a dynamic environment, we argue that its lifetime is the killing time of a continuously increasing stochastic process by a random barrier, and this barrier is the item's hazard potential. The killing time perspective enables us to see competing risks from a process standpoint and to propose a framework for the joint modeling of degradation or cumulative damage and its markers. The notion of the hazard potential generalizes to the multivariate case. This generalization enables us to replace a collection of dependent random variables by a collection of independent exponentially distributed random variables, each having a different time scale.

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Multivariate Life Distributions Induced by Gamma Process Environments,

Cited by 12 publications

References 9 publications

Improving series and parallel systems through mixtures of duplicated dependent components

Improving series and parallel systems through mixtures of duplicated dependent components

On Break-Even Correlation: The Way to Price Structured Credit Derivatives by Replication

The Hazard Potential

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