Journal of Iranian Statistical Society
Volume:10 Issue: 1, 2011

In this article, we use a measure of expected true evidence for determine the required sample size in type-II censored experiments for obtaining statistical evidence in favor of one hypothesis about the exponential mean against another.

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any restriction on the parameters of the model of dual GOS.

‎Independent random‎ ‎variables $Y_{1},ldots‎, ‎Y_{n}$ belongs to the‎ ‎proportional reversed hazard rate (PRHR) model with‎ ‎proportionality parameters $lambda_1,...,lambda_n$‎, ‎if‎ ‎$Y_{k}sim G^{lambda _{k}}(x)$‎, ‎for $k=1,...,n$‎, ‎where $G$ is an‎ ‎absolutely continuous distribution function‎. ‎In this paper we compare‎ ‎the smallest order‎ ‎statistics‎, ‎the sample ranges and the ratios of the smallest and‎ ‎largest order statistics of two sets of independent random‎ ‎variables belonging to PRHR model‎, ‎in the sense of (reversed) hazard‎ ‎rate order‎, ‎likelihood ratio order and dispersive order‎, ‎when the‎ ‎variables in one set have proportionality parameters‎ ‎$lambda_1,...,lambda_n$ and the variables in the other set are‎ ‎independent and identically distributed with common parameter‎ ‎$overline{lambda}=sum_{k=1}^{n}lambda_k/n$‎. ‎We also compare‎ ‎the relative degree of dependence between the smallest and the largest‎ ‎order statistics of these samples whit respect to the monotone‎ ‎regression dependence order‎.

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for the integrated square error of the kernel density estimators in the left-truncation model. It is assumed that the lifetime observations form a stationary strong mixing sequence. A central limit theorem (CLT) for the ISE of the kernel hazard rate estimators is also presented.

Prediction on the basis of censored data is very important topic in many fields including medical and engineering sciences. In this paper, based on progressive Type-II right censoring scheme, we will discuss Bayesian two-sample prediction. A general form for lifetime model including some well known and useful models such asWeibull and Pareto is considered for obtaining prediction bounds as well as Bayes predictive estimations under squared error loss function for the sth order statistic in a future random sample drawn from the parent population, independently and with an arbitrary progressive censoring scheme. As an illustration, we will present two numerical examples as well as a simulation study to carry out the performance of the procedures obtained.