In the absolutely continuous case, order statistics, record values and several other models of ORDERED RANDOM VARIABLES can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither records nor weak records are submodels of discrete generalized order statistics. Next, we show that progressively Type-II right censored order statistics from an arbitrary distribution can be embedded in the model of generalized order statistics and then use this fact to establish some distributional properties of progressively Type-II right censored order statistics. Finally, we present some characterizations of the geometric distribution based on progressively Type-II right censored order statistics.

STOCHASTICALLY ORDERED RANDOM VARIABLES with given marginal distributions are combined into a joint distribution preserving the ordering and the marginals using a maximum entropy principle. A closed-form of the maximum entropy density function is obtained. Next we have compared the entropies of maximum entropy distributions, under two constraints The constraints are either prescription of marginal distributions and the marginals and covariance matrix.

This paper extends the sign test to the case where data are observations of fuzzy RANDOM VARIABLES, and the hypotheses are imprecise rather than crisp. In this approach,  rst a new notion of fuzzy RANDOM VARIABLES is introduced. Then, the -level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are de ned. We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis. A numerical example is provided to clarify the discussions made in this paper.

In a celebrated work by Shao [13] several inequalities for negatively associated RANDOM VARIABLES were proved. In this paper we obtain some maximal inequalities for associated RANDOM VARIABLES. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].

In this paper, the properties of fuzzy RANDOM VARIABLES with new meter and some extended results of monotone convergence theorem and dominated convergence theorem for fuzzy RANDOM VARIABLES are discussed. The main result is given by usingDp, q -distance defined on the set of fuzzy numbers.

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all VARIABLES simultaneously. Results willbe evaluated by a relatively extensive simulation studies on Bivariate normal distribution and two real case studies on commercial and medicinal use of flowers, and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in some regions of the southwest of Germany.

The ratio of independent RANDOM VARIABLES arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice RANDOM VARIABLES.Ratios of such RANDOM variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) and the existing moments have been derived in terms of several special functions. The delta method is used to approximate moments.As a special case, we have obtained the PDF and CDF of the ratio of independent Rayleigh RANDOM VARIABLES.