The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.

中文翻译：

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多重删失数据下逆 Lomax 分布的熵估计

逆 Lomax 分布已广泛应用于可靠性、地球物理学、经济学和工程科学等许多应用领域。在本文中，研究了一个涉及逆 Lomax 分布的未探索的实际问题：当观察到多个删失数据时其熵的估计。为了达到这个目标，熵是通过 Rényi 和 q-entropies 定义的，我们通过结合最大似然和插件方法来估计它们。然后，通过确定均方误差、两侧近似置信区间和相应的平均长度，提供数值结果以显示不同样本大小的估计行为。我们的数值研究表明，当样本量增加时，均方误差和平均长度的值会减小。还，当审查水平降低时，Rényi 和 q-entropies 估计的考虑接近真实值。所得结果验证了该方法的有效性和有效性。给出了对两个现实生活数据集的应用。