Characterization of bivariate mean residual-life function

Kulkarni, H. V.; Rattihalli, R. N.

doi:10.1109/24.510810

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…That is, it is not clear that there exists a survival function S * n for which (1.4) holds with e 1 (x, y), e 2 (x, y) replaced by e * n1 (x, y), e * n2 (x, y). Nair and Nair [10] and Kulkarni and Rattihalli [6] provided necessary and sufficient conditions for a nonnegative functioñ m(x, y) to be a proper mrl function. The latter authors note that Nair and Nair's results are incomplete as their conditions are not necessary and sufficient.…”

Section: The One-sample Problemmentioning

confidence: 99%

Estimation of two ordered bivariate mean residual life functions

Rojo

Ghebremichael

2006

Journal of Multivariate Analysis

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Situations occur frequently in which the mean residual life (mrl) functions of two populations must be ordered. For example, if a mechanical device is improved, the mrl function for the improved device should not be less than that of the original device. Also, mrl functions for medical patients should often be ordered depending on the status of concomitant variables. This paper proposes nonparametric estimators of the bivariate mrl function under a mrl ordering. The estimators are shown to be asymptotically unbiased, strongly uniformly consistent and weakly convergent to a bivariate Gaussian process. The estimators are shown to be the projections, in a sense to be made precise, of the empirical mrl function onto an appropriate convex set of mrl functions. In the one-sample problem, the new estimators dominate the empirical mrl function in terms of risk with respect to a wide class of loss functions.

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Section: The One-sample Problemmentioning

confidence: 99%

Estimation of two ordered bivariate mean residual life functions

Rojo

Ghebremichael

2006

Journal of Multivariate Analysis

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“…For the last one decade, researchers have shown much interest in studying the remaining lifetime of a unit given it has survived a particular point of time t. For more on bivariate mean residual life based on distribution functions, one can refer to Nair and Nair (1989) and Kulkarni and Rattihalli (1996).…”

Section: Quantile Curves Based Bivariate Reliability Conceptsmentioning

confidence: 99%

“…Remark 3. The quantile curve based bivariate hazard rate obtained after interchanging X and Y given in (8) uniquely determines the underlying quantile curve through…”

Section: Properties and Characterizationsmentioning

confidence: 99%

A note on Quantile curves based bivariate reliability concepts

Sreelakshmi¹

2017

Preprint

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We extend the univariate quantile based reliability concepts to the bivariate case using quantile curves. We propose quantile curves based bivariate hazard rate and bivariate mean residual life function and establish a relationship between them. We study the uniqueness properties of these concepts to determine the underlying quantile curve. We also study the quantile curves based reliability concepts in reverse time.

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Bivariate Teissier Distributions

Kolev

Ngoc

2017

Analytical and Computational Methods in Probability Theory

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Characterization of bivariate mean residual-life function

Cited by 4 publications

References 10 publications

Estimation of two ordered bivariate mean residual life functions

Estimation of two ordered bivariate mean residual life functions

A note on Quantile curves based bivariate reliability concepts

Bivariate Teissier Distributions

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