Complete convergence for arrays of minimal order statistics

نویسنده

  • André Adler
چکیده

For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first moment of our order statistics is infinite.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Complete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables

Let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

متن کامل

On convergence of sample and population Hilbertian functional principal components

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

متن کامل

Synthesis of Antenna Arrays of Maximum Directivity for a Specified Sidelobe Level

Linear and planar antenna arrays are synthesized to have maximum directivity for a specified sidelobe level. The directivity is maximized subject to a given SLL. The beamwidth and the zeros of array factor are studied as well as the directivity. Maximum directivity-arrays are compared through some examples with super-directive, uniform, Dolph-Chebyshev and Riblet-Chebychev arrays to find a comp...

متن کامل

Statistical Convergence and Strong $p-$Ces`{a}ro Summability of Order $beta$ in Sequences of Fuzzy Numbers

In this study we introduce the concepts of statistical convergence of order$beta$ and strong $p-$Ces`{a}ro summability of order $beta$ for sequencesof fuzzy numbers. Also, we give some relations between the statisticalconvergence of order $beta$ and strong $p-$Ces`{a}ro summability of order$beta$ and construct some interesting examples.

متن کامل

The convergence space of minimal usco mappings

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence struct...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Int. J. Math. Mathematical Sciences

دوره 2004  شماره 

صفحات  -

تاریخ انتشار 2004