Modeling fractional data in various real life scenarios is a challenging task. This paper consider situations where fractional data is observed on the interval [0,1]. The unit-Lindley distribution has been discussed in the literature where its support lies between 0 and 1. In this paper, we focus on an inflated variant of the unit-Lindley distribution, where the inflation occurs at both 0 and 1. Various properties of the inflated unit-Lindley distribution are discussed and examined, including point estimation based on the maximum likelihood method and interval estimation. Finally, extensive Monte Carlo simulation and real-data analyses are carried out to compare the fit of our proposed distribution along with some of the existing ones such as the inflated beta and the inflated Kumaraswamy distributions.

翻译：在各种现实生活中模拟分数数据是一项具有挑战性的任务。本文件考虑了在[0,1]间隔期间观察到分数数据的情况。单位-Lindley分布在文献中讨论过,其支持范围在0与1.之间。在本文件中,我们侧重于单位-Lindley分布的膨胀变式,其中通货膨胀发生在0与1. 讨论和审查膨胀单位-Lindley分布的各种特性,包括基于最大可能性方法和间隔估计的点数估计。最后,进行了广泛的蒙特卡洛模拟和真实数据分析,以比较我们拟议分布的合适性,以及某些现有分布,如膨胀的贝塔和膨胀的库马拉斯瓦米分布。