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Multivariate Lomax distribution: properties and usefulness in reliability theory

Published online by Cambridge University Press:  14 July 2016

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

Keywords

MIXTURE OF DISTRIBUTIONSMULTIVARIATE PARETOORDER STATISTICSSURVIVAL FUNCTIONREGRESSION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 170 - 177
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

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

References

[1]Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2]Cook, R. E. and Johnson, M. E. (1981) A family of distributions for modelling non-elliptically symmetric multivariate data. J. R. Statist. Soc. B 43, 210–218.Google Scholar
[3]Cramér, H. (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton.Google Scholar
[4]Everitt, B. S. and Hand, D. J. (1981) Finite Mixture Distributions. Chapman and Hall, New York.10.1007/978-94-009-5897-5Google Scholar
[5]Harris, C. M. (1968) The Pareto distribution as a queue service discipline. Operat. Res. 16, 307–313.Google Scholar
[6]Hutchison, T. P. (1979) Four applications of a bivariate distribution. Biom. J. 21, 553–563.Google Scholar
[7]Johnson, N. L. and Kotz, S. (1970) Continuous Univariate Distributions, I: Distributions in Statistics. Houghton Mifflin, New York.Google Scholar
[8]Johnson, N. L. and Kotz, S. (1972) Distributions in Statistics, Continuous Multivariate Distributions. Wiley, New York.Google Scholar
[9]Lindley, D. V. and Singpurwalla, N. D. (1986) Multivariate distributions for the life lengths of a system sharing a common environment. J. Appl. Prob. 23, 418–431.Google Scholar
[10]Malik, H. J. and Abraham, B. (1973) Multivariate logistic distributions. Ann. Statist. 3, 588–590.Google Scholar
[11]Mardia, K. V. (1962) Multivariate Pareto distributions. Ann. Math. Statist. 33, 1008–1015.Google Scholar
[12]Mardia, K. V. (1964) Some results on the order statistics of the multivariate normal and Pareto type 1 populations. Ann. Math. Statist. 35, 1815–1818.10.1214/aoms/1177700405Google Scholar
[13]Renyi, A. (1953) On the theory of order statistics. Acta Math. Acad. Sci. Hungar. 4, 191–206.Google Scholar
[14]Satterthwaite, S. P. and Hutchison, T. P. (1978). A generalization of Gumbel's bivariate logistic distribution. Metrika 25, 163–170.Google Scholar
[15]Shaked, M. (1977) A concept of positive dependence for exchangeable random variables. Ann. Statist. 5, 505–515.Google Scholar
[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.Google Scholar
[17]Winterbottom, A. (1984) The interval estimation of system reliability from component test data. Operat. Res. 32, 628–640.Google Scholar