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This paper concerns with a new lifetime model named the inverted generalized linear exponential distribution (IGLED). Statistical properties like moments, quantile and modes are introduced. The classification of the behavior of IGLED based on reliability analysis like mean residual life (MRL) time, the mean waiting time (MWT), the hazard rate (HR) function and the reversed hazard rate (RHR) function are discussed. Bonferroni curve (Bc), Lorentz curve, the scaled total time on test (TTT) transform curve and the measures of income inequality are also studied. The heavy-weight property is proved for IGLED under the shape parameter ξ . The explanation of the other two shape parameter in the sense of economic is shown. Furthermore, maximum likelihood estimation is used to estimate the parameters of the new model. Four applications are used to show whether the IGLED is better than other well-known distribution in modeling lifetime data.

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