Journal of Iranian Statistical Society
Volume:14 Issue: 1, 2015

Ranked Set Sampling (RSS) is a statistical method for data collection that leads to more efficient estimators than competitors based on Simple Random Sampling (SRS). We consider testing the correlation coefficient of bivariate normal distribution based on Bivariate RSS (BVRSS). Under one-sided and two-sided alternatives, we show that the new tests based on BVRSS are more powerful than the usual uniformly most powerful tests based on bivariate SRS. Furthermore, the proposed tests for repeated and unrepeated samples are compared.

In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglected for semiparametric regression models. The main focus of this paper is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression model, making use of differencing methodology. In this respect, some new estimators for shrinkage parameter are also proposed. It is shown that one of these estimators which is constructed based on well-known harmonic mean, performs better for large values of signal to noise ratio. For our proposal, the Monte Carlo simulation studies and a real application related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on minimum risk criteria.

We consider a (n-k+1)-out-of-n system with exchangeablelifetimes of the components. The paper investigates the stochastic ordering properties of the residual lifetime of the system under condition that, at time t, at least (n-r+1) components are alive. Some results are then extended to the case where the system has a coherent structure with exchangeable components.

We introduce in this paper a new four-parameter generalized version of the linear failure rate distribution which is called Beta-linear failure rate distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, A closed form expressions for the probability density, cumulative distribution and hazard rate functions of this new distribution is given. Also, the rth order moment of this distribution is derived. We discuss the maximum likelihood estimation of the unknown parameters of the new model for complete data and obtain an expression for the Fisher information matrix. In the end, to show the flexibility of the new distribution and illustrative purposes, an application using a real data set is presented.

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

This paper considers an extension of probability space based on interval random variables. In this approach, first, a notion of interval random variable is introduced. Then, based on a family of continuous distribution functions with interval parameters, a concept of probability space of an interval random variable is proposed. Then, the mean and variance of an interval random variable are introduced. The presented theoretical results will be illustrated with some lemmas. Some numerical examples will be used to show the performance of the proposed method.