In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.

中文翻译：

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新的改良Kies族：属性，在完整和II型删失样本下的估计以及工程应用

在本文中，我们介绍了一个新的连续分布族，称为修正的Kies分布族。推导了新族的主要数学性质。已经详细考虑了新家庭的特殊情况。即，这两个参数修改了浴缸形状的Kies指数分布，降低和增加了失效率函数。新分布的重要性在于它能够对带有两个以上参数的一些广义分布进行正负偏斜的真实数据建模。讨论了危险率的形状行为和修正的Kies指数分布的平均剩余寿命函数。我们使用最大似然法来基于完整的和II类删失样本估计分布参数。在这两种方案下，也可以获得近似的置信区间。进行了仿真研究，并分析了来自工程领域的两个真实数据集，以显示新分布在建模真实生活数据中的灵活性。