Some representation theorems in terms of mean residual lifetime and mean inactivity time of coherent systems

Abstract

In this paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes. We show that when the underlying distribution function F(t) is absolutely continuous, then it can be univocally determined by some particular mean residual lives or mean inactivity times of the system. It is then shown that these results may be extended to coherent (or mixed) systems.     

On the Characteristic Function for Asymmetric Exponential Power Distributions

The econometric literature has seen a surge of developments in the theory and applications of asymmetric exponential power distributions (AEPDs). Here, for the first time, we derive explicit closed form expressions for the characteristic function of AEPDs. The expressions involve the complex parameter Wright generalized hypergeometric function.     

Toward a Deep Insight into Employee Participation in Employer-Supported Volunteering in Iranian Organizations: A Grounded Theory

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - Antecedents and consequences of employer-supported volunteering (ESV) have been widely studied. Yet, in the literature,...     

Generalized inferential procedures for generalized Lorenz curves under the Pareto distribution

This paper considers problems of interval estimation and hypotheses testing for the generalized Lorenz curve under the Pareto distribution. Our approach is based on the concepts of generalized test variables and generalized pivotal quantities. The merits of the proposed procedures are numerically carried out and compared with asymptotic and bootstrap methods. Empirical evidence shows that the coverage accuracy of the proposed confidence intervals and the type I error control of the proposed exact tests are satisfactory. For illustration purposes, a real data set on median income of the 20 occupations in the United States Census of Population is analysed.     

A revised Cholesky decomposition to combat multicollinearity in multiple regression models

As known, the ordinary least-squares estimator (OLSE) is unbiased and also, has the minimum variance among all the linear unbiased estimators. However, under multicollinearity the estimator is generally unstable and poor in the sense that variance of the regression coefficients may be inflated and absolute values of the estimates may be too large. There are several classes of biased estimators in statistical literature to decrease the effect of multicollinearity in the design matrix. Here, based on the Cholesky decomposition, we propose such an estimator which makes the data to be slightly distorted. The exact risk expressions as well as the biases are derived for the proposed estimator. Also, some results demonstrating superiority of the suggested estimator over OLSE are obtained. Finally, a Monté-Carlo simulation study and a real data application related to acetylene data are presented to support our theoretical discussions.     

Feasible robust estimator in restricted semiparametric regression models based on the LTS approach

Under some nonstochastic linear restrictions based on either additional information or prior knowledge in a semiparametric regression model, a family of feasible generalized robust estimators for the regression parameter is proposed. The least trimmed squares (LTS) method proposed by Rousseeuw as a highly robust regression estimator is a statistical technique for fitting a regression model based on the subset of h observations (out of n) whose least-square fit possesses the smallest sum of squared residuals. The coverage h may be set between n/2 and n. The LTS estimator involves computing the hyperplane that minimizes the sum of the smallest h squared residuals. For practical purpose, it is assumed that the covariance matrix of the error term is unknown and thus feasible estimators are replaced. Then, we develop an algorithm for the LTS estimator based on feasible methods. Through the Monte Carlo simulation studies and a real data example, performance of the feasible type of robust estimators is compared with the classical ones in restricted semiparametric regression models.     

Estimation with the lognormal distribution on the basis of records

Record scheme is a method to reduce the total time on test of an experiment. In this scheme, items are sequentially observed and only values smaller than all previous ones are recorded. In some situations, when the experiments are time-consuming and sometimes the items are lost during the experiment, the record scheme dominates the usual random sample scheme [M. Doostparast and N. Balakrishnan, Optimal sample size for record data and associated cost analysis for exponential distribution, J. Statist. Comput. Simul. 80(12) (2010), pp. 1389–1401]. Estimation of the mean of an exponential distribution based on record data has been treated by Samaniego and Whitaker [On estimating population characteristics from record breaking observations I. Parametric results, Naval Res. Logist. Q. 33 (1986), pp. 531–543] and Doostparast [A note on estimation based on record data, Metrika 69 (2009), pp. 69–80]. The lognormal distribution is used in a wide range of applications when the multiplicative scale is appropriate and the log-transformation removes the skew and brings about symmetry of the data distribution [N.T. Longford, Inference with the lognormal distribution, J. Statist. Plann. Inference 139 (2009), pp. 2329–2340]. In this paper, point estimates as well as confidence intervals for the unknown parameters are obtained. This will also be addressed by the Bayesian point of view. To carry out the performance of the estimators obtained, a simulation study is conducted. For illustration proposes, a real data set, due to Lawless [Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley & Sons, New York, 2003], is analysed using the procedures obtained.     

Some results on conditional expectations of lower record values

In this paper, we propose a measure for obtaining the expectation of time between two lower k-records under the condition that the greater one is given. Several properties of the proposed measure are derived. Some characterization results and stochastic comparisons based on the new measure are also provided.