Distributions and Function Spaces

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Asymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...

A new class of function spaces on domains of R^d and its relations to classical function spaces

Comparsion Between Several Distributions of Exponential Family and Offering Their Features and Applications

‎In this paper‎, ‎first‎, ‎we investigate probability density function and the failure rate function of some families of exponential distributions‎. ‎Then we present their features such as expectation‎, ‎variance‎, ‎moments and maximum likelihood estimation and we identify the most flexible distributions according to the figure of probability density function and the failure rate function and f...

Totally probabilistic Lp spaces

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.

Strongly $[V_{2}, lambda_{2}, M, p]-$ summable double sequence spaces defined by orlicz function

In this paper we introduce strongly $left[  V_{2},lambda_{2},M,pright]-$summable double vsequence spaces via Orlicz function and examine someproperties of the resulting these spaces. Also we give natural relationshipbetween these spaces and $S_{lambda_{2}}-$statistical convergence.