Journal of Statistical Research of Iran
Volume:8 Issue: 2, 2012

In this paper, we introduce new tests for exponentiality based on estimators of Renyi entropy of a continuous random variable. We first consider two transformations of the observations which turn the test of exponentiality into one of uniformity and use a corresponding test based on Renyi entropy. Critical values of the test statistics are computed by Monte Carlo simulations. Then, we compare powers of the tests for various alternatives and sample sizes with exponentiality tests based on Kullback-Leibler information proposed by Ebrahimi {et al.} (1992) and Choi {et al.} (2004). Our simulation results show that the proposed tests have higher powers than the competitor tests.

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, occur when the recorded data have the probability proportional to an increasing function of absolute value of deviations. In this paper a new family of distributions called double normal family of distribution is introduced and characterized. This symmetric family is a subclass of the univariate Kotz type distributions. The normal distribution is a special case of this family. Estimation of location and scale parameters by moment and maximum likelihood methods are given. Some pivotal quantity are introduced. Confidence intervals for some parameters by numerical methods are given.

Fitting a suitable covariance function for the correlation structure of spatial-temporal data requires de-trending the data. In this article, some potential models for spatial-temporal trend are presented. Eventually the best model will be announced for de-trending tropospheric ozone concentration data for the city of Tehran (Capital city of Iran). By using the selected trend model, some features of the covariance function of de-trended data will be specified.

This paper focuses on a Bayes inference model for a simple step-stress life test using Type-I censored sample in a discrete set-up. Assuming the failure times at each stress level are geometrically distributed, the Bayes estimation problem of the parameters of interest is investigated in the both of point and interval approaches. To derive the Bayesian point estimators, some various balanced loss functions are used. Furthermore, a simulation study and sensitivity analysis is performed to carry out the performance of the results of the paper. An example is also presented to illustrate the proposed procedure. Finally, some conclusions are stated.

The unified hybrid censoring is a mixture of generalized Type-I and Type-II hybrid censoring schemes. This article presents the statistical inferences on Generalized Exponential Distribution parameters when the data are obtained from the unified hybrid censoring scheme. It is observed that the maximum likelihood estimators can not be derived in closed form. The EM algorithm for computing the maximum likelihood estimators is proposed. We calculated the observed Fisher information matrix using the missing information principle which is useful for constructing the asymptotic confidence intervals. Simulations studies are performed to compare the performances of the estimators obtained under different schemes. Finally, a real data set has been analyzed for illustrative purposes.

Census counts are subject to different types of nonsampling errors. One of these main errors is coverage error. Undercount and overcount are two types of coverage error. Undercount usually occurs more than the other, thus net undercount estimation is important. There are various methods for estimating the coverage error in censuses. One of these methods is dual system (DS) that usually uses data from the census and a post-enumeration survey (PES). In this paper, the coverage error and necessity of its evaluation, PES design and DS method are explained. Then PES associated approaches and their effects on DS estimation are illustrated and these approaches are compared. Finally, we explain the Statistical Center of Iran method of estimating net undercount in Iran 2006 population and dwelling census and a suggestion will be given for improving net undercount estimation in population and dwelling censuses of Iran.