الفهرس 
Introduction and a Review of Relevant ResultsOnly 14 pages are availabe for public view
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Abstract
TL-moments, as one of the methods of estimation, is introduced by Elamir and Seheult (2003) as natural generalization of the L-moments method which introduced by Hosking (1990). TL-moments, as L-moments, are linear combinations of order statistics (or quantile function for the continuous distributions). But, TL-moments depend on trimming some observations from both tails of the distribution by assigning these extreme values zero weights. Thus, it is an important method, since it gives more robust estimators than the L-moments in the presence of outliers. Also, a population TL-moment exists when the corresponding population L-moment or the conventional moment does not exist. In other words, they are defined for heavy tailed distributions where they do not involve some values at the extreme ends of the distribution. As interest in statistical modeling using heavy-tailed distributions is increasing, so is the important of the potential by the L-moment and TL-moment approaches.
The importance of the density quantile function in statistical data modeling was realized by parzen (1979). Therefore, the estimation of population density quantile is of great interest when a parametric form for the underlying distribution is not available. In addition, the density quantile function could be used as an alternative of the density function. < So, throughout this dissertation we have used TL-moments in introduce a new nonparametric method of estimation of the density quantile function.
The thing that distinguishes this method is that it depends on the quantile function. Thus, the estimate of the density quantile function implies estimating the quantile function. So, this method has the ability to capture more information about the arbitrary distribution that generated the data. In addition, this method may have a wide applicability range to include most distributions.In addition, althogh the mean, variance and the coefficient of variation of residual life which are based on the usual moments of the residual life distribution are extensively used in reliability analysis. It has been established in various theoretical and empirical studies that the L-moments have some advantages over the usual moments in many situations. Recently, Nair and Vineshkumar (2010) investigated the properties of the L-moments of residual life.