Author

# Subhash C. Kochar

Other affiliations: Northern Illinois University, Panjab University, Chandigarh, Indian Statistical Institute ...read more

Bio: Subhash C. Kochar is an academic researcher from Portland State University. The author has contributed to research in topics: Order statistic & Independent and identically distributed random variables. The author has an hindex of 35, co-authored 124 publications receiving 3603 citations. Previous affiliations of Subhash C. Kochar include Northern Illinois University & Panjab University, Chandigarh.

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##### Papers

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TL;DR: Theoretical results for comparing coherent systems are derived for comparing systems of a given order when components are assumed to have independent and identically distributed lifetimes as mentioned in this paper, and sufficient conditions are provided for the lifetime of one system to be larger than that of another system in three different senses: stochastic ordering, hazard rate ordering, and likelihood ratio ordering.

Abstract: Various methods and criteria for comparing coherent systems are discussed. Theoretical results are derived for comparing systems of a given order when components are assumed to have independent and identically distributed lifetimes. All comparisons rely on the representation of a system's lifetime distribution as a function of the system's “signature,” that is, as a function of the vector p= (p1, … , pn), where pi is the probability that the system fails upon the occurrence of the ith component failure. Sufficient conditions are provided for the lifetime of one system to be larger than that of another system in three different senses: stochastic ordering, hazard rate ordering, and likelihood ratio ordering. Further, a new preservation theorem for hazard rate ordering is established. In the final section, the notion of system signature is used to examine a recently published conjecture regarding componentwise and systemwise redundancy. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 507–523, 1999

268 citations

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TL;DR: The concept of positive ageing describes the adverse effects of age on the lifetime of units and various aspects of this concept are described in terms of conditional probability distributions of residual lifetimes, failure rates, equilibrium distributions, etc as mentioned in this paper.

Abstract: The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distributions of residual lifetimes, failure rates, equilibrium distributions, etc. In this paper we further analyse this concept and relate it to stochastic dominance of first and higher orders. In the process we gain many insights and are able to define several new kinds of ageing criteria which supplement those existing in the literature.

177 citations

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TL;DR: In this paper, it was shown that the reverse hazard rate of Xn:n is Schur convex in λ, which is the same as the Schur-convexity of the survival function.

157 citations

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TL;DR: In this article, it was shown that the hazard rate of a random sample of size n from an exponential distribution with common hazard rate λ ˜ = ( ni = 1 λ i ) 1 /n, the geometric mean of the λ I s s is greater than that of an independent exponential random variable X n : n.

Abstract: Let X 1 ,...,X n be independent exponential random variables with X i having hazardrate λ i ,i = 1 ,...,n . Let Y 1 ,...,Y n be a random sample of size n from an exponentialdistribution with common hazard rate λ ˜ = ( ni =1 λ i ) 1 /n , the geometric mean of the λ i s.Let X n : n = max{ X 1 ,...,X n }. It is shown that X n : n is greater than Y n : n according todispersive as well as hazard rate orderings. These results lead to a lower bound for thevariance of X n : n and an upper bound on the hazard rate function of X n : n in terms of λ ˜. These bounds are sharper than those obtained by Dykstra et al. ((1997), J. Statist.Plann. Inference 65, 203–211), which are in terms of the arithmetic mean of the λ i s.Furthermore, let X ∗1 ,...,X ∗ n beanothersetofindependentexponentialrandomvariableswith X ∗ i having hazard rate λ ∗ i ,i = 1 ...,n . It is proved that if ( log λ 1 , ··· , log λ n ) weakly majorizes ( log λ ∗1 , ··· , log λ ∗n ) , then X n : n is stochastically greater than

133 citations

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TL;DR: In this article, a quantile dispersion measure is proposed to characterize different classes of ageing distributions. But it is weaker than the well known dispersive ordering and it retains most of its interesting properties.

Abstract: In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

114 citations

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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

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698 citations

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TL;DR: In this article, a generalized order statistics (GOS) model is proposed to explain the similarities and analogies in the two models and to generalize related results, and sufficient conditions for the existence of moments are given for the moments of GOS.

670 citations

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TL;DR: In this paper, the authors present a risk management approach for value at risk and beyond in the context of risk management, which is based on the concept of Value at Risk and Beyond.

Abstract: (2003). Risk Management: Value at Risk and Beyond. Journal of the American Statistical Association: Vol. 98, No. 462, pp. 494-494.

612 citations