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...

Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than...

In this paper, we consider a multivariate hypergeometric population with k-category [pi] = [pi](N, M, s1,...,sk), where si, I = 1,...,k, is the number of units in category [pi]i, with [Sigma]i-1k si = M, the total number of units in population [pi], and N is the number of units selected from...

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.

Linear functions on spacings--instead of linear functions on order statistics--are considered, in order to simplify the form of best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the scale parameter in the classical location-scale family. Also, a sufficient...

In this paper, we consider n independent observations from a multivariate normal distribution and discuss the multivariate order statistics induced by ordering linear combinations of the components observed. Specifically, we derive means, variances and covariances of the induced multivariate...

We derive exact distributions of weak record values in lattice as well as non-lattice cases. We obtain the Fisher information contained in the first m weak records and the first m (strong) records from a discrete distribution. We give geometric and Poisson examples.

Often, in industrial stress testing, meteorological data analysis, athletic events, and other similar situations, measurements may be made sequentially and only values larger or smaller than all previous ones are observed. When the number of records is fixed in advance, the data are referred to...

Suppose upper records were observed from a X-sequence of iid continuous random variables, and that another independent Y-sequence of iid variables from the same distribution is to be observed. In this paper, we then derive various exact distribution-free prediction intervals for records from the...

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...