Limit Laws for Norms of IID Samples with Weibull Tails

Limit Laws for Norms of IID Samples with Weibull Tails

We are concerned with the limit distribution of lt-norms RN (t) = ‖XN‖t (of order t) of samples XN = (X1, . . . , XN ) of i.i.d. positive random variables, as N → ∞, t → ∞. The problem was first considered by Schlather(10), but the case where {Xi} belong to the domain of attraction of Gumbel’s double exponential law (in the sense of extreme value theory) has largely remained open (even for an e...

A Test for Weibull IFR/DFR Alternatives Based on Type-2 with Replacement Censored Samples

This article presents a test based on quadratic form using Type-2 with replacement-censored sample for testing exponentiality against weibull IFR/DFR alternative. The percentile points and powers are simulated. The proposed test is compared with that of Bain and Engelhardt (1986) test. An example based on Type-2 censoring is also discussed.

Reliability Measures of a Series System with Weibull Failure Laws

The Weibull distribution is widely used in reliability and life data analysis due to its versatility. And, this distribution has been considered as a popular life time distribution which describes modeling phenomena with monotonic failure rates of components. Depending on the values of the parameters it can be used to model a variety of life behaviors. In this paper, reliability measures such a...

Limit Laws for Random Exponentials

We study the limiting distribution of the sum SN (t) = ∑N i=1 e tXi as t→∞, N →∞, where (Xi) are i.i.d. random variables. Attention to such exponential sums has been motivated by various problems in the theory of random media. Examples include the quenched mean population size of branching random processes with random branching rates and the partition function of Derrida’s Random Energy Model. ...

Limit Laws for Basic Parameters of Lattice Paths with . . .