An Extension of the Law of the Iterated Logarithm to Variables without Variance

On the Law of the Iterated Logarithm for L-statistics without Variance

Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables with distribution function F (x). For each positive integer n, let X1:n ≤ X2:n ≤ · · · ≤ Xn:n be the order statistics of X1, X2, · · · , Xn. Let H(·) be a real Borel-measurable function defined on R such that E|H(X)| < ∞ and let J(·) be a Lipschitz function of order one defined on [0, 1]. Write μ = μ(F, J,H) = E(J(U)H(F←(U))) and Ln(F, ...

On the law of the iterated logarithm.

The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...

surveying the relevance of proportions to the content of quran verses

چکیده : قرآن چشمه سار زلال هدایتی است که از سوی خداوند حکیم نازل شده تا بشر را به سر منزل کمال برساند. و در این راستا از شیوه های گوناگون بیانی خطابی و بلاغی استفاده کرده تا با فطرت زیبا طلب انسان درآمیزد و اورا مقهور خویش ساخته، به سوی کمالات سوق دهد.ازجمله جنبه های بارز اعجاز بیانی قرآن وجود فواصل در پایان آیات است که کار برد سجع و قافیه در کلام بشر شبیه آن است. برخی ازعلمای سلف تفاوت هایی ب...

An Analogue of the Law of the Iterated Logarithm

from linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar

chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...