In this communication, we introduce a new statistical model and study its various mathematical properties. The expressions for hazard rate, reversed hazard rate, and odd functions are provided. We explore the asymptotic behaviors of the density and hazard functions of the newly proposed model. Further, moments, median, quantile, and mode are obtained. The cumulative distribution and density functions of the general $k$th order statistic are provided. Sufficient conditions, under which the likelihood ratio order between two inverse generalized linear failure rate (IGLFR) distributed random variables holds, are derived. In addition to these results, we introduce several estimates for the parameters of IGLFR distribution. The maximum likelihood and maximum product spacings estimates are proposed. Bayes estimates are calculated with respect to the squared error loss function. Further, asymptotic confidence and Bayesian credible intervals are obtained. To observe the performance of the proposed estimates, we carry out a Monte Carlo simulation using $R$ software. Finally, two real-life data sets are considered for the purpose of illustration.

翻译：本文提出了一种新的统计模型，并研究了其多种数学性质。给出了危险率、逆危险率和奇函数的表达式。探讨了新提出模型的密度函数和危险函数的渐近行为。进一步，得到了矩、中位数、分位数和众数。给出了一般$k$阶次序统计量的累积分布函数和密度函数。推导了使两个逆广义线性失效率（IGLFR）分布随机变量之间满足似然比排序的充分条件。除这些结果外，我们还引入了IGLFR分布参数的几种估计方法。提出了极大似然估计和最大乘积间距估计。在平方误差损失函数下计算了贝叶斯估计。此外，得到了渐近置信区间和贝叶斯可信区间。为观察所提出估计量的性能，我们使用$R$软件进行了蒙特卡罗模拟。最后，为说明目的考虑了两个真实数据集。