Abstract
         In this paper, we  propose the truncated version of the power Lindley distribution which is more flexible than many well-known distributions.  Mathematical and statistical properties of truncated power Lindley distribution are given only for upper truncated version of power Lindley distribution. The statistical proprieties such as moments, quantile function and order statistics are also discussed. The maximum likelihood estimators are constructed for estimating the unknown parameters of the upper, lower and double truncated power Lindley distributions. A set of real data containing the strengths of the glass of aircraft window, is considered to show the applicability of the truncated power Lindley distributions. The real data set is considered to illustrate the utility and potential of the proposed model.