Frechet Research Articles

Estimation of the Parameters of Mixed Frechet Distribution and Its Employment in Simple Linear Regression

Probability distribution is important to those who are interested in the subject of mathematical statistics, so in this research a probability function of the mixed distribution Frechet-Frechet was formed and its parameters were estimated using maximum likelihood and moment methods. These methods are applied on real data which represents the number of cancer cases in Iraq for the years (1991-2016).

An Extended Fr echet Distribution: Properties and Applications

In this paper, we introduce an extended four-parameter Fr´echet model called the exponentiated exponential Fr´echet distribution, which arises from the quantile function of the standard exponential distribution. Various of its mathematical properties are derived including the quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, generating function, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new distribution is illustrated by means of three real lifetime data sets. In fact, the new model provides a better fit to these data than the Marshall-Olkin Fr´echet, exponentiated-Fr´echet and Fr´echet models.

A Generalized Transmuted Fre ́chet Distribution

A Generalized Transmuted Fre ́chet Distribution

High resolution conductivity-depth transformation of TEM data

Conductivity depth transformation of TEM data remains an important tool for preliminary interpretation, despite the increasing speed of 1D inversion. Conductivity-depth imaging (CDI) is very fast, does not require a starting model, and is an effective means for data quality assessment. Moreover, CDI sections can serve as starting models for inversion. This paper describes a high resolution enhancement of an existing CDI algorithm for TEM data. Conductivitydepth transformation is accomplished in two steps. Measured voltages or B-field at a given delay time are first transformed to apparent conductivity. For dB/dt data, the assigned depth, z(t), at each time is the depth of the electric field or current maximum (Emax depth) in a half-space with conductivity equal to the apparent conductivity. For B-field data, the depth to the halfspace B-field maximum (Bmax depth) is employed. CDI sections based on apparent conductivity provide a vertically smoothed representation of the true conductivity profile. The apparent conductivity at any time can be represented as an inner product of the true conductivity with the Frechet kernel. The Frechet kernel at time t can be approximated as a linear function, decreasing from its maximum value at the surface to zero at a depth d(t). Therefore, given apparent conductivities from the CDI algorithm, a sharper estimate of the true conductivity can be generated via solution of a simple integral equation. We solve the integral equation for a ?minimum structure? model using linear programming. The implementation of this high resolution CDI algorithm is illustrated on selected examples of synthetic and real airborne TEM data.

Powers of countable Fréchet spaces

Powers of countable Fréchet spaces

Hypothesis testing for network data in functional neuroimaging

In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measure- ments, typically assumed to be reective of either functional or structural relationships between regions of interest in the brain. One of the most basic tasks of interest in the analysis of such data is the testing of hypotheses, in answer to questions such as \'Is there a dierence between the networks of these two groups of subjects? In the classical setting, where the unit of interest is a scalar or a vector, such questions are answered through the use of familiar two-sample testing strategies. Networks, however, are not Euclidean objects, and hence classical methods do not directly apply. We address this challenge by drawing on concepts and techniques from geom- etry, and high-dimensional statistical inference. Our work is based on a precise geometric characterization of the space of graph Laplacian matri- ces and a nonparametric notion of averaging due to Fr echet. We motivate and illustrate our resulting methodologies for testing in the context of net- works derived from functional neuroimaging data on human subjects from the 1000 Functional Connectomes Project. In particular, we show that this global test is more statistical powerful, than a mass-univariate approach. AMS 2000 subject classications: Fr echet mean, fMRI, Graph Lapla- cian, Hypothesis Testing, Matrix manifold, Network data, Neuroscience.

Spatiality of derivations of Fréchet GB$^{*}$-algebras

Spatiality of derivations of Fréchet GB$^{*}$-algebras

FUNCTIONS ON κ-NET CONVERGENCE STRUCTURES

Abstract. We investigate various properties of -net convergencestructures and de ne a -net-based continuous function on -netL + -convergence structures, and study relationships between conti-nuity and -net-based continuity on -net L + -convergence struc-tures. We also provide some characterizations of -net-based con-tinuity. 1. IntroductionThere is a classical axiomatization of convergence for sequences(Frechet’s L-space and L-space) as follows:De nition 1.1 ([2]). If Sis any set, a sequential convergence Con Sis a relation between sequences fs n g 1n=1 of members of Sand memberssof S, denoted s n ! C s, such that(1) if s n = sfor all n, s n ! C s; and(2) if s n ! C sand fr m gis any subsequence fs n m gof fs n g, thenr m ! C s.If Cis a sequential convergence such that(3) if s n ! C sand s n ! C t, then s= t,Cis called an L-convergence.De nition 1.2 ([2]). If Cis an L-convergence such that(4) if s n 9 C s(i.e., it is false that s n ! C s), then there is a subse-quence fr m gof fs

Differential stability of convex optimization problems under inclusion constraints

Motivated by the recent work of Mordukhovich et al. [Subgradients of marginal functions in parametric mathematical programming. Math. Program. Ser. B. 2009;116:369–396] on the optimal value function in parametric programming under inclusion constraints, this paper presents some new results on differential stability of convex optimization problems under inclusion constraints and functional constraints in Hausdorff locally convex topological vector spaces. By using the Moreau–Rockafellar theorem and appropriate regularity conditions, we obtain formulas for computing the subdifferential and the singular subdifferential of the optimal value function. By virtue of the convexity, several assumptions used in the above paper by Mordukhovich et al., like the nonemptyness of the Frechet upper subdiffential of the objective function, the existence of a local upper Lipschitzian selection of the solution map, as well as the -inner semicontinuity and the -inner semicompactness of the solution map, are no longer needed....

Basic bounds of Fréchet classes

Basic bounds of Fréchet classes

Mild solutions for perturbed evolution equations with infinite state-dependent delay

In this paper, we give sucient conditions to get the existence of mild solutions for two classes of rst order partial and neutral of perturbed evolution equations by using the nonlinear alternative of Avramescu for contractions operators in Fr echet spaces, combined with semigroup theory. The solution here is depending on an innite delay and is giving on the real half-line.

Quasinormability and diametral dimension

Two versions of diametral dimension are shown to coincide for quasinormable Fr echet spaces. The diametral

SDE solutions in the space of smooth random variables

In this paper we analyze properties of a dual pair (G;G ) of spaces of smooth and generalized random variables on a L evy white noise space. We show that G L 2 ( ) which shares properties with a Fr echet algebra contains a larger class of solutions of It^ o equations driven by pure jump L evy processes. Further a characterization of ( G;G ) in terms of the S-transform is given. We propose (G;G ) as an attractive alternative to the Meyer-Watanabe test function and distribution space (D1;D1 ) (W) to study strong solutions of SDE's.

Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators

Let ω, ω 0 be appropriate weight functions and ${\fancyscript{B}}$ be an invariant BF-space. We introduce the wave-front set ${{\rm WF}_{\mathcal{B}}(f)}$ with respect to the weighted Fourier Banac ...

CODERIVATIVE AND MONOTONICITY OF CONTINUOUS MAPPINGS

Sufficient conditions for a norm-to-weak$^*$ continuous mapping $f:X\rightarrow X^*$ being monotone or submonotone are established by its Fr e chet and normal coderivatives, where $X$ is an Asplund space with its dual space $X^*$. Under some additional assumptions, they are also necessary conditions. Among other things, we obtain a criterion for the monotonicity of continuous mappings which extends the following classical result: a differentiable mapping $F:\Bbb R^n\rightarrow\Bbb R^n$ is monotone if and only if for each $x\in\Bbb R^n$ the Jacobian matrix $\nabla F(x)$ is positive semi-definite; see [22, Proposition 12.3]. As a by-product, sufficient conditions for a function being convex or approximately convex are given.

On non-Archimedean Fréchet spaces with nuclear Köthe quotients

On non-Archimedean Fréchet spaces with nuclear Köthe quotients

MEAN ERGODIC THEOREMS FOR ALMOST PERIODIC SEMIGROUPS

We show mean ergodic theorems for vector-valued weakly almost periodic functions (in the sense of Eberlein) defined on a semigroup which take values in a locally convex topological vector space. Next, motivated by Fr´echet [10], we study the relationship between almost periodicity of semigroups of mappings and their equicontinuity, and also prove mean ergodic theorems for equicontinuous semigroups.

A class of weighted convolution Fréchet algebras

A class of weighted convolution Fréchet algebras

Une application du lemme de Mittag-Leffler dans la categorie des quotients d’espaces de Frechet

An application of Mittag-Leffler lemma in the category of quotients of Fréchet spaces. We use Mittag-Leffler Lemma to prove that for a nonempty interval $]a,b[\subset \mathbb{R}$, the restriction mapping $H^{\infty }(]a,b[+\mathrm{i}\mathbb{R}) \rightarrow C^{\infty }\left( ]a,b[\right)$ is surjective and we give a corollary.

Axioms for Sequential Convergence

Centro de Matematica da Universidade de Coimbra/FCT; Unidade de Investigacao e Desenvolvimento Matematica e Aplicacoes da Universidade de Aveiro/FCT