Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

This work establishes exact formulae for the persistence probabilities pk(θ)=P[Y1⩾0,…,Yk⩾0] of an AR(1) sequence Yn=θYn−1+Xn, n=1,2,… with parameter θ∈R﹨(12,2) and symmetric uniform innovations Xn. The are in terms certain polynomials, most notably a family that arises case −1<θ<12 was introduced by Mallows Riordan very different context counting finite labeled trees when ordered inversions. co...

in this paper we study the relation between module amenability of θ - lau product a×θb and that of banach algebras a, b. we also discuss module biprojectivity of a×θb. as a consequent we will see that for an inverse semigroup s, l 1 (s) ×θ l 1 (s) is module amenable if and only if s is amenable.