Fix a base B > 1 and let ζ have the standard exponential distribution; the distribution of digits of ζ base B is known to be very close to Benford’s law. If there exists a C such that the distribution of digits of C times the elements of some set is the same as that of ζ, we say that set exhibits shifted exponential behavior base B. Let X1, . . . , XN be i.i.d.r.v. If the Xi’s are Unif, then as...

there are several theorical results about order statistics and copulas in the literature that have  been mentioned also by nelsen cite{p20}. the present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. the study concentrates on two well known archimedean gumbel and frank families in the case tha...

Correntropy has recently been introduced as a generalized correlation function between two stochastic processes, which contains both high-order statistics and temporal structure of the stochastic processes in one functional form. Based on this blend of high-order statistics and temporal structure in a single functional form, we propose a unified criterion for instantaneous blind source separati...

Three different problems in order statistics are considered in this dissertation. The first problem deals with the recurrence relations between moments and other functions of order statistics. It is shown that recurrence relations valid for independent and identically distributed random variables continue to hold for exchangeable variables. In the second problem a method, based upon orthogonal ...

in this paper, we derive rst some results on the shannon entropyin order statistics and their concomitants arising from a sequence of f(xi; yi): i = 1; 2; :::g independent and identically distributed (iid) random variablesfrom the bivariate normal distribution and extend our results to a collectionc(x; y ) = f(xr1:n; y[r1:n]); (xr2:n; y[r2:n]); :::; (xrk:n; y[rk:n])g of order sta-tistics and t...