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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 2 | Year 2017 | Article Id. IJMTT-V44P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P513

Closure of Some Bivariate Ageing Classes under Poisson Shock Models


U. Rizwan, Syed Tahir Hussainy, A. Sathiyaraj
Abstract

In this paper, we determine the closure properties of the bivariate ageing classes of life distributions under Poisson Shock models. AMS Subject Classification: 60K10

Keywords
Bivariate Ageing classes, BIFR, BIFRA, BNBU, BNBUE, BHNBUE, Survival probability, Preservation Properties.
References

1) A-Hameed, M.S., and Proschan, F., (1975), Shock Models with underlying Birth Process, Journal of Applied Probability, 12, pp
2) Barlow, R.E., and Proschan, F., (1981), Statistical Theory of Reliability and Life Testing. To Begin with. Silver Spring, MD.
3) Basu, A. P., (1971), Bivariate Failure Rate, J. Amer. Statist. Assoc. (Theory and Methods), 66, pp. 103 104.
4) Diab, L. S., (2013), A New Approach to Moment Inequalities for NRBU and RNBU classes with Hypothesis Testing Applications, International Journal of Basic and Applied Sciences, 13, pp. 7 13.
5) Esary J. D. and Marshall, A. W., (1973), Shock Models and Wear Processes, Annals of Probability, 1, pp
6) Klefsjö, B., (1981), HNBUE Survival under Some Shock Models, Scandinavian Journal of Statistics, 8 (1), pp
7) Freund, J. F., (1961), A Bivariate Extension of the Exponential Distribution, J. Amer. Statist. Assoc., 56, pp. 971 977.
8) Marshall, A. W. and Olkin, I., (1967), A Multivariate Exponential Distribution, J. Amer. Statist. Assoc., 62, pp. 30 44.
9) Suresh, R. P., (2001), A simple inequality of moments in some classes of bivariate ageing disrtibutions, J. Indian Statist. Assoc., 39,pp. 131 136.
10) Syed Tahir Hussainy, (2015), On Some Ageing Properties of Bivariate Life Distributions under Convolution, International Journal of Science and Humanities, 1(1), pp. 47 52.
11) Zohdy M. Nofal, (2013), A New Bivariate Class of Life Distributions, Applied Mathematical Sciences, 7,pp. 49 60.

Citation :

U. Rizwan, Syed Tahir Hussainy, A. Sathiyaraj, "Closure of Some Bivariate Ageing Classes under Poisson Shock Models," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 2, pp. 64-70, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P513

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