Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. Such data appear in several real-life situations like blind signal separation problems, modeling of loss data in finance and insurance, sales of consumer goods, daily precipitation data, to name a few. In this paper, we present a novel algorithm to estimate the density function for semi-continuous data using the principle of maximum entropy. Unlike existing methods in the literature, our algorithm provides a consistent estimate of the true maximum entropy distribution and considers both the discrete and continuous parts of the semi-continuous distribution simultaneously. Using simulations, we show that the estimate of the entropy produced by our algorithm has significantly less bias compared to existing methods. An application to the daily rainfall data is provided.

半连续数据来自一个分布，该分布是零点质量和在正实线上支持的连续分布的混合。此类数据出现在几种现实生活中，例如盲信号分离问题、金融保险损失数据建模、消费品销售、每日降水数据等。在本文中，我们提出了一种使用最大熵原理来估计半连续数据密度函数的新算法。与文献中的现有方法不同，我们的算法提供了对真实最大熵分布的一致估计，并同时考虑了半连续分布的离散和连续部分。使用模拟，我们表明，与现有方法相比，我们的算法产生的熵估计的偏差要小得多。提供了对每日降雨量数据的应用。