The mean Stieltjes integral representation of a bounded linear transformation

Estimating a Bounded Normal Mean Under the LINEX Loss Function

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...

Properties of the linear canonical integral transformation.

We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems for these transformations, such as shift, scaling, derivation, etc., together with the canonical integral transforms of selected functions, are derived.

On the Distributional Stieltjes Transformation

This paper is concerned with some general theorems on the distributional Stieltjes transformation. Some Abelian theorems are proved. Throughout the paper, r will denote a positive continuous function on an interval (X,=), X > 0, such that the limit lim r(pt) r(t) exists for' every p > 0. Such functions are called regularly varying fu.Lc-tions (r.v.f.) at infinity and it is well known ([ 7] that...

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral

on the effect of linear & non-linear texts on students comprehension and recalling

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