It is shown by a simple argument that all recurrence relations and identities satisfied by distribution functions of order statistics arising from exchangeable random variables also hold good for averages of such distribution functions for arbitrary random variables.

Starting from any univariate density function f(x) and an associated orthogonal function g(x), we present in this note a method of constructing multivariate distributions of all dimensions. It is shown that these multivariate distributions, in addition to being closed under marginal and...

Let X1:2, X2:2 be the order statistics of a sample of size two from an absolutely continuous distribution F with finite variance. In this note, we show that the upper bound for Cov(X1:2, X2:2) (and the associated characterization of the uniform distribution) established recently by Papathanasiou...

The waiting time problems introduced by Ebneshahrashoob and Sobel (1990) for independent trials are generalized to Markov correlated Bernoulli trials. A new waiting time problem arising due to mixed quotas is also discussed. A learning model is used as illustration.

Sen [1970. A note on order statistics for heterogeneous distributions. Ann. Math. Statist. 41, 2137-2139] derived some inequalities for distributions of order statistics from independent and non-identically distributed (INID) random variables. For this purpose, he used Hoeffding's [1956. On the...

An indicator method is used to derive a recurrence relation satisfied by the distribution of order statistics from n random variables having an arbitrary joint distribution.

For a collection of n arbitrary events, we derive a sufficient condition for the log-concavity property of the sequence of probabilities of occurrence of exactly r events. For the special case of independent events, this sufficient condition is shown to be satisfied. Further, some dependence...