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Multivariate Lomax distribution: properties and usefulness in reliability theory

  • Tapan Kumar Nayak (a1)

Abstract

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

Copyright

COPYRIGHT: © Applied Probability Trust 1987 

Corresponding author

∗ Postal address: Department of Statistics, Computer and Information Systems, The George Washington University, Washington, DC 20052, USA.

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Research sponsored by Grant DAAG 29–84–K–0160, U.S. Army Research Office.

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References

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[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
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[5] Harris, C. M. (1968) The Pareto distribution as a queue service discipline. Operat. Res. 16, 307–313.
[6] Hutchison, T. P. (1979) Four applications of a bivariate distribution. Biom. J. 21, 553–563.
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[11] Mardia, K. V. (1962) Multivariate Pareto distributions. Ann. Math. Statist. 33, 1008–1015.
[12] Mardia, K. V. (1964) Some results on the order statistics of the multivariate normal and Pareto type 1 populations. Ann. Math. Statist. 35, 1815–1818.
[13] Renyi, A. (1953) On the theory of order statistics. Acta Math. Acad. Sci. Hungar. 4, 191–206.
[14] Satterthwaite, S. P. and Hutchison, T. P. (1978). A generalization of Gumbel's bivariate logistic distribution. Metrika 25, 163–170.
[15] Shaked, M. (1977) A concept of positive dependence for exchangeable random variables. Ann. Statist. 5, 505–515.
[16] Thompson, W. A. Jr. and Brindley, E. C. Jr. (1972) Dependence and aging aspects of multivariate survival. J. Amer. Statist. Assoc. 67, 822–830.
[17] Winterbottom, A. (1984) The interval estimation of system reliability from component test data. Operat. Res. 32, 628–640.

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  • Cited by 59

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Multivariate Lomax distribution: properties and usefulness in reliability theory

  • Tapan Kumar Nayak (a1)

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