In a sequence of independent and identically distributed (iid) random variables, the kth largest (smallest) observation in a partial sample is well-known as the upper (lower) k-record value, when its value is greater (smaller) than the corresponding observation in the previous partial sample. In...

We discuss here a new class of skew-Cauchy distributions, which is related to Azzalini's [1985. A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178] skew-normal distribution denoted by Z[lambda]~SN([lambda]). A random variable W[lambda] is said to have a...

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...

Let N have a Poisson distribution with parameter [lambda]0, and let U1,U2,... be a sequence of independent standard uniform variables, independent of N. Then the random sum , where IA is an indicator of the set A, is a Poisson process on [0,1]. Replacing N by its weighted version Nw, we obtain...

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...

A simple method is presented for improving Hartley-David-Gumbel's universal bound for the mean of extreme order statistics.

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.

We discuss a two-parameter generalization of the skew-normal distribution, denoted by GSN([lambda]1,[lambda]2). We then establish some simple and useful properties of this distribution and derive the moment generating function. Finally, we use a numerical example to illustrate the practical...