This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time from a set of LFR distributed variables. We define the model, derive certain statistical properties such as the mean residual life, the mean inactivity time, moments, quantile, order statistics and also discuss the results on stochastic orders of the proposed distribution. The proposed model has increasing, bathtub shaped and inverse bathtub shaped hazard rate function. We use the method of maximum likelihood estimation to estimate the unknown parameters. We conduct simulation studies to examine the behavior of the estimators. We also use three real datasets to evaluate the model, which turns out superior compared to classical alternatives.

翻译：本文提出了一种线性失效率（LFR）模型的新扩展，以更好地捕捉现实世界中的寿命数据。该模型引入了一个额外的形状参数以增强灵活性，有助于对一组LFR分布变量的最小生存时间进行建模。我们定义了该模型，推导了若干统计性质，如平均剩余寿命、平均不活动时间、矩、分位数、顺序统计量，并讨论了所提分布在随机序方面的结果。所提模型具有递增型、浴盆型和反浴盆型的风险率函数。我们采用最大似然估计方法来估计未知参数，并通过模拟研究检验估计量的性质。此外，我们使用三个真实数据集对模型进行评估，结果表明其性能优于经典替代模型。