We study d–records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d–record occurs, when one computes the d–largest values, and the variable maintaining it changes its value while the sequence is scanned from left to right. This is done for the “strict model,” but a “weak model” is a...

Run statistics about a sequence of independent geometrically distributed random variables has attracted some attention recently in many areas such as applied probability, reliability, statistical process control, and computer science. In this paper, we first study the mean and variance of the number of alternating runs in a sequence of independent geometrically distributed random variables. The...

Let X1;X2;...;Xn have a jointly multivariate exchangeable normal distribution. In this work we investigate another proof of the independence of X and S2 using order statistics. We also assume that (Xi ; Yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party’s output than what its own output reveals. To aid in this, they have available a set up — correlated ran...