Author

# Nuria Torrado

Other affiliations: Charles III University of Madrid, University of Zaragoza, University of Coimbra ...read more

Bio: Nuria Torrado is an academic researcher from Autonomous University of Madrid. The author has contributed to research in topics: Order statistic & Random variable. The author has an hindex of 12, co-authored 26 publications receiving 308 citations. Previous affiliations of Nuria Torrado include Charles III University of Madrid & University of Zaragoza.

##### Papers

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TL;DR: In this article, the effect of changes in the scale parameters (λ 1, λ 2, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings was investigated.

Abstract: Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

58 citations

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TL;DR: Stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different are discussed.

Abstract: In this work, we discuss stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different. That is, if Xn:n(p,q) is the largest order statistic among X1,…,Xp,Xp+1,…,Xn and Xn∗:n∗(p∗,q∗) is the largest order statistic among X1,…,Xp∗,Xp∗+1,…,Xn∗, where q=n−p and q∗=n∗−p∗, we discuss whether Xn:n(p,q) and Xn∗:n∗(p∗,q∗) are ordered in some stochastic sense.

29 citations

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TL;DR: Stochastic orders are focused on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other.

Abstract: In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by Dykstra et al. (1997) and Joo and Mi (2010) from exponential to Weibull distributions. Also, we present some results for parallel systems from multiple-outlier Weibull models.

28 citations

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TL;DR: In this article, it was shown that under some conditions, one largest order statistic Xλn: n is smaller than another one Xθn : n according to likelihood ratio ordering.

Abstract: Let be independent non negative random variables with , i = 1, …, n, where λi > 0, i = 1, …, n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic Xλn: n is smaller than another one Xθn: n according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.

27 citations

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TL;DR: In this article, the hazard rate order of the smallest order statistics from lower-truncated Weibull distributions is studied. But, in general, Weibell random variables are not ordered according to this ordering in the shape parameter.

Abstract: Weibull distribution is a very flexible family of distributions which has been applied in a vast number of disciplines. In this work, we investigate stochastic properties of the smallest order statistics from two independent heterogeneous Weibull random variables with different scale and shape parameters. Furthermore, we study the hazard rate order of the smallest order statistics from lower-truncated Weibull distributions due to, in general, Weibull random variables are not ordered according to this ordering in the shape parameter.

24 citations

##### Cited by

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01 Jan 2013

TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.

Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

1,957 citations

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671 citations

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TL;DR: In this paper, the Mathematical Theory of Reliability (MTR) is used to describe the relationship between reliability and operational reliability in the context of the ORS problem, and it is shown that it can be achieved.

Abstract: (1966). Mathematical Theory of Reliability. Journal of the Operational Research Society: Vol. 17, No. 2, pp. 213-215.

578 citations

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376 citations