Journal of Iranian Statistical Society
Volume:5 Issue: 1, 2006

This article presents a test based on quadratic form using Type-2 with replacement-censored sample for testing exponentiality against weibull IFR/DFR alternative. The percentile points and powers are simulated. The proposed test is compared with that of Bain and Engelhardt (1986) test. An example based on Type-2 censoring is also discussed.

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher informationof their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi distance is the same as that induced by Fisher information.

Recently Habibi et al. (2006) defined a pre-experimental criterion for the potential strength of evidence provided by an experiment, based on Kullback-Leibler distance. In this paper, we investigate the potential statistical evidence in an experiment in termsof Renyi distance and compare the potential statistical evidence in lower (upper) record values with that in the same number of iid observations from the same parent distribution.

Let {Xn, n ≥1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1)based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the sequence {Xn, n≥ 1}. Then, we derive uniform strong convergence rates for two-dimensional distribution function of (X1,Xk+1) without any condition on the covariance structure of the variables. Finally,assuming a convenient decrease rate of the covariances Cov(X1,Xn+1), n ≥ 1,we introduce uniform strong convergence rate for covariance function of the limit empirical process.

In this paper, we obtain some Rosenthal’s type inequalities for negatively orthant dependent (NOD) random variables. Inequalities of this kind are very important since they reduce (for n sufficiently large) the behaviors of E|Sn|p to those of (V arSn)p/2.Their main interest is that they give the right bound for integrated moments in non parametric estimation (cf. Doukhan [2] for more