Let X1:3<=X2:3<=X3:3 be the order statistics from independent and identically distributed random variables X1,X2 and X3. We use the regression relation E[(X2:3-X1:3)2X2:3=x]=E[(X3:3-X2:3)2X2:3=x] to characterize the Student's t3 distribution on three degrees of freedom.

The Fisher information contained in records, weak records and numbers of records are discussed in this paper. In the case when the initial distribution belongs to the exponential family, the Fisher information contained in record values as well as in record values and record times are found...

Let X1,n[less-than-or-equals, slant]X2,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n be the order statistics obtained from a sample from a continuous distribution and Zi,j,n=Xj,n/Xi,n be the ratio of order statistics. In this paper, asymptotic properties of Zi,j,n are...

Let be independent and identically distributed random vectors with continuous distribution. Let Kn(a,b1,b2) be the number of sample elements that belong to the open rectangle -- numbers of near-maxima in the bivariate case. In the present paper, we discuss asymptotic properties of Kn(a,b1,b2)...

Let X1,X2,... be independent identically distributed (iid) random variables (rvs) with support on positive integers and (Wn,n[greater-or-equal, slanted]1) denote the corresponding sequence of weak record values. In the present paper we derive weak and strong limit theorems for the ratio of weak...

Let X1,...,Xn be a sequence of i.i.d. random variables from some continuous distribution function F. Let Zn(a) be the number of observations of the sample that appeared after the maximum Mn was already registered and belong to the random interval (Mn-a,Mn] (a0). In this note, we prove a strong...

A new concept of runs was proposed in the work of Eryilmaz and Stepanov (2008). A sequence of spacings forms a run if the lengths of these spacings do not exceed [epsilon]0. In that paper, asymptotic properties of such spacings were investigated and statistical criteria proposed. In our present...