Showing papers by "Palaniappan Vellaisamy published in 2008"
TL;DR: In this article, the authors considered the problem of estimating θ ( 1 ) and θ( m + 1 ) under the loss L k ( t, θ ) = ( t − θ 2 / θ k, for k ≥ 0, an integer.
11 citations
TL;DR: In this article, the authors discuss model collapsibility and collapsibility with respect to regression coefficients for linear regression models and give simple and different proofs of some of the known results and obtain also certain new results.
10 citations
TL;DR: In this paper, the authors consider a parallel system with n independent components and derive an optimal reliability test plans which ensure the usual probability requirements on system reliability, and solve the associated nonlinear integer programming problem by a simple enumeration of integers over the feasible range.
5 citations
TL;DR: In this paper, the authors developed classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain with Dirichlet boundary conditions, and established a correspondence with the case of a half-derivative in time.
Abstract: Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain $D\subset\mathbb{R}^d$ with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded domain are then solved by establishing a correspondence with the case of a half-derivative in time.