Thurstone scaling is widely used for presenting the priorities among the compared items. The mean values of the quantiles corresponding to frequencies of each stimilus’ preference over the other stimuli define the items’ locations on the psychological continuum of the Thurstone scale. This paper considers an extension of the scale levels to the aggregates of the independent covariates. In a sen...

Preprocessing an image is an important element of image processing. When images are corrupted with fixed-value impulse noise or random-value impulse noise, it is essential to restore the quality of the degraded image using linear or non-linear filters, in order to make them suitable for subsequent processing. It has been proved that non-linear filters are effective in suppressing or eliminating...

1 Asymptotics of Percentile Order Statistics Let Xi (i = 1, . . . , N) be independently identically distributed (IID) continuous random variables with CDF, P (x) = P(Xi ≤ x), and PDF, p(x) = dP . Let Y (α) be the 100αth percentile, which is dx N uniquely defined by ordering the outcomes, X(1) ≤ X(2) ≤ . . . ≤ X(N) (using the standard notation of order statistics) and setting YN (α) = X([αN ]) (...

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...

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...