Subhash C. Kochar

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.

The signature of a coherent system and its application to comparisons among systems

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

Aspects of positive ageing

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.

Some new results on stochastic comparisons of parallel systems

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

Partial orderings of distributions based on right-spread functions

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.

Convergence of Probability Measures

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

Risk Management: 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.