Journal of Iranian Statistical Society
Volume:8 Issue: 1, 2009

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences ofthe residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the Frechet distributions are characterized through maximizing Shannon entropies of these statistics under some constraint.

When an ordering among parameters is known in advance, the problem of estimating the smallest or the largest parameters arises in various practical problems. Suppose independent random samples of size ni drawn from two gamma distributions withknown arbitrary shape parameter i > 0 and unknown scale parameter i > 0, i = 1, 2. We consider the class of mixed estimators of 1 and 2 under the restriction 0 < 1  2. It has been shown that a subclass of mixed estimators of i, beats the usual estimatorsXi/i, i = 1, 2, and a class of admissible estimators in the class of mixed estimators are derived under scale-invariant squared error loss function. Also it has been shown that the mixed estimator of (1, 2), 0 < 1  2, beats the usual estimator􀀀 X1/1,X2/2
simultaneously, and a class of admissible estimators in the class ofmixed estimators of (1, 2) are derived. Finally the results are extended to some subclass of exponential family

In this paper􀀀 the well
known proportional hazards model which includes several well
known lifetime distributions such as ex
ponential􀀀 Pareto􀀀 Lomax􀀀 Burr type XII􀀀 and so on is considered With both Bayesian and non
Bayesian approaches 􀀀 we consider the estimation of parameters of interest based on progressively Type
IIright censored samples The Bayes estimates are obtained based on symmetric and asymmetric loss functions We also provide Bayes and empirical Bayes prediction intervals for the times to failure of units censored in multiple stages in a progressively censored sample Finally􀀀 two numerical examples are given to illustrate the results

For the power of two-sided hypothesis testing about the mean of a normal population, we derive a 100(1 −)% confidence interval. Then by using a numerical method we will find a shortest confidence interval and consider some special cases.

The ratio of independent random variables arises in man 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 theanalysis 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 ratioof independent Rayleigh random variables.