Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples
In the present communication, stochastic comparison
of a series (parallel) system having heterogeneous components with
random lifetimes and series (parallel) system having homogeneous
exponential components with random lifetimes has been studied.
Further, conditions under which such a comparison is possible has
been established.
[1] N. Balakrishnan and C.R. Rao, Handbook of Statistics 16 - Order
Statistics: Theory and Methods, Elsevier, New York, 1998a.
[2] N. Balakrishnan and C.R. Rao Handbook of Statistics 17 - Order
Statistics: Applications, Elsevier, New York, 1998b.
[3] P. Pledger and F. Proschan, Comparison of Order Statistics and of spacings
from Heterogenous distributions, in : J.S. Rustagi (Ed.), Optimizing
Methods in Statistics, Academic Press, New York, 1971.
[4] S.C. Kochar and J. Rojo, Some new results on stochastic comparisons
of spacings from heterogeneous exponential distributions, Journal of
Multivariate Analysis 57, 69-83, 1996.
[5] S.C. Kochar and M. Xu, Stochastic comparisons of parallel systems
when components have proportional hazard rates, Probability in the
Engineering and Informational Sciences 21, 597-609, 2007.
[6] B. Khaledi and S.C. Kochar, Sample range some stochastic comparisons
results, Calcutta Statistical Association Bulletin 50, 283-291, 2000.
[7] C. Genest, S.C. Kochar and M. Xu, On the range of heterogeneous
samples, Journal of Multivariate Analysis, 100, 1587-1592, 2009.
[8] P. Zhao and X. Li Stochastic order of sample range from heterogeneous
exponential random variables, Probability in the Engineering and Informational
Sciences 23, 17-29, 2009.
[9] T. Mao and T. Hu, Equivalent characterizations on orderings of order
statistics and sample ranges, Probability in the Engineering and Informational
Sciences, 24, 245-262, 2010.
[10] M. Xu and N. Balakrishnan, On the convolution of heterogeneous
Bernoulli random variables, Journal of Applied Probability, 48 (3), 877-
884, 2011.
[11] S.C. Kochar and M. Xu, Stochastic comparisons of spacings from
heterogeneous samples, In: Advances in Directional and Linear Statistics
(Eds., M. Wells and A. Sengupta), 113-129, Springer, New York, 2011a.
[12] S.C. Kochar and M. Xu, Some unified results on comparing linear
combinations of independent gamma random variables, Technical Report,
Illinois State University, Normal, Illinois, 2011b.
[13] R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life
Testing, To Begin With, Silver Spring, Maryland, 1981.
[14] M. Shaked and J.G. Shanthikumar, Stochastic Orders and Their Applications,
Springer, New York, 2007.
[15] A. M¨uller and D. Stoyan, Comparison Methods for Stochastic Models
and Risks, Wiley Series in Probability and Statistics. John Wiley & Sons
Ltd., Chichester, 2002.
[1] N. Balakrishnan and C.R. Rao, Handbook of Statistics 16 - Order
Statistics: Theory and Methods, Elsevier, New York, 1998a.
[2] N. Balakrishnan and C.R. Rao Handbook of Statistics 17 - Order
Statistics: Applications, Elsevier, New York, 1998b.
[3] P. Pledger and F. Proschan, Comparison of Order Statistics and of spacings
from Heterogenous distributions, in : J.S. Rustagi (Ed.), Optimizing
Methods in Statistics, Academic Press, New York, 1971.
[4] S.C. Kochar and J. Rojo, Some new results on stochastic comparisons
of spacings from heterogeneous exponential distributions, Journal of
Multivariate Analysis 57, 69-83, 1996.
[5] S.C. Kochar and M. Xu, Stochastic comparisons of parallel systems
when components have proportional hazard rates, Probability in the
Engineering and Informational Sciences 21, 597-609, 2007.
[6] B. Khaledi and S.C. Kochar, Sample range some stochastic comparisons
results, Calcutta Statistical Association Bulletin 50, 283-291, 2000.
[7] C. Genest, S.C. Kochar and M. Xu, On the range of heterogeneous
samples, Journal of Multivariate Analysis, 100, 1587-1592, 2009.
[8] P. Zhao and X. Li Stochastic order of sample range from heterogeneous
exponential random variables, Probability in the Engineering and Informational
Sciences 23, 17-29, 2009.
[9] T. Mao and T. Hu, Equivalent characterizations on orderings of order
statistics and sample ranges, Probability in the Engineering and Informational
Sciences, 24, 245-262, 2010.
[10] M. Xu and N. Balakrishnan, On the convolution of heterogeneous
Bernoulli random variables, Journal of Applied Probability, 48 (3), 877-
884, 2011.
[11] S.C. Kochar and M. Xu, Stochastic comparisons of spacings from
heterogeneous samples, In: Advances in Directional and Linear Statistics
(Eds., M. Wells and A. Sengupta), 113-129, Springer, New York, 2011a.
[12] S.C. Kochar and M. Xu, Some unified results on comparing linear
combinations of independent gamma random variables, Technical Report,
Illinois State University, Normal, Illinois, 2011b.
[13] R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life
Testing, To Begin With, Silver Spring, Maryland, 1981.
[14] M. Shaked and J.G. Shanthikumar, Stochastic Orders and Their Applications,
Springer, New York, 2007.
[15] A. M¨uller and D. Stoyan, Comparison Methods for Stochastic Models
and Risks, Wiley Series in Probability and Statistics. John Wiley & Sons
Ltd., Chichester, 2002.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57344", author = "Nitin Gupta and Rakesh Kumar Bajaj", title = "Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples", abstract = "In the present communication, stochastic comparison
of a series (parallel) system having heterogeneous components with
random lifetimes and series (parallel) system having homogeneous
exponential components with random lifetimes has been studied.
Further, conditions under which such a comparison is possible has
been established.", keywords = "Exponential distribution, Order statistics, Star ordering,
Stochastic ordering.", volume = "6", number = "8", pages = "1024-3", }
