Journal of Mathematical Extension
Volume:3 Issue: 1, Winter 2008

For (n×m matrices) X, Y ∈ Mnm(R)(= Mnm), we say X is chain majorized by Y and write X ≺≺ Y if X = RY where R is a product of finitely many T-transforms. A linear operator T : Mnm → Mnm is said to be a linear preserver of the relation ≺≺ on Mnm if X ≺≺ Y implies that T X ≺≺ T Y . Also, it is said to be strong linear preserver if X ≺≺ Y is equivalent to T X ≺≺ T Y . In this paper we characterize linear and strong linear preservers of ≺≺.

Let S be matrix of residual sum of square in linear model Y = Aβ + e where matrix e is distributed as elliptically contoured with unknown scale matrix Σ. In present work, we consider the problem of estimating Σ with respect to squared loss function, L(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2 . It is shown that improvement of the estimators were obtained by James, Stein [7], Dey and Srivasan [1] under the normality assumption remains robust under an elliptically contoured distribution respect to squared loss function.

This paper introduces a two-parameter family of distributions which includes the ordinary exponential distribution as a special case. This distribution exhibits monotone hazard rate and may be a competitor to the families of two parameter gamma and Weibull distributions. Various statistical and reliability aspects of this model is explored. Several numerical examples based on real data show the flexibility of the new distribution for modeling proposes.

In this paper, we derived the exact form of the entropy for Exponentiated Pareto Distribution (EPD). Some properties of the entropy and mutual information are presented for order statistics of EPD. Also, the bounds are computed for the entropies of the sample minimum and maximum for EPD.

There are many situations in which experiments are not available or data are recorded from the population proportion to a nonnegative function called weight function. In a such situations the classical methods for inferencing about unknown parameters are not useful. In this study the problem of statistical hypothesis testing is considered for weighted distributions to obtain (uniformly) most powerful tests.

. In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given.

Let X be a Banach space of functions analytic on a plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that X contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.

Let M and P be right R−modules. A submodule K of an R−module M is called P−dense if for each m ∈ M,(K : m) is a P−faithful right ideal of R. PR is nonsingular if and only if, for each R−module M, every essential submodule of M is a P−dense submodule. For any R−module M, we obtain P−rational extention of M and equivalent condition in order that M is equal with its P−rational extention is found. An R−module P is called right Kasch if every simple R−module can be embedded in P. Finally, we given some equivalent conditions for an R−module P to be right Kasch.