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The truncated distributions have been widely studied, mainly in life-testing and reliability analysis. In this paper, we introduce a new right truncated generator related to power Lomax distribution, referred to right truncated power Lomax--G family. The proposed family is a generalization of recently [0, 1] truncated Lomax-G family. Statistical properties like; moments, moment generating function, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are derived. Five new sub-models from the truncated family are presented. Maximum likelihood estimation is investigated and simulation issues are discussed for truncated power Lomax Weibull model as particular case from the family. The flexibility of the truncated power Lomax Weibull is assessed by applying it to a real data set. The application indicates that the truncated power Lomax Weibull distribution model can give better fits than other well-known lifetime distributions.
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