论文标题
广义的Bernoulli过程和分数分布
Generalized Bernoulli Process and Fractional Binomial Distribution
论文作者
论文摘要
最近，开发了广义的Bernoulli过程（GBP）作为固定的二进制序列，其协方差函数遵守权力定律。在本文中，我们进一步开发了广义的Bernoulli过程，揭示其渐近行为并找到应用。我们表明，GBP可以具有与分数泊松过程相同的缩放限制。考虑到泊松过程在某些条件下近似于伯努利的过程，我们在GBP和分数泊松过程之间发现的联系被认为是在远程依赖性下的对应物。当应用于指示数据时，GBP在存在远程依赖性的情况下优于马尔可夫链。分数二项式模型被定义为GBPS中的总和，并且表明，当应用于多余零的数据计数时，分数二项式模型的表现优于零膨胀的模型，这些模型被广泛用于当前文献中的此类数据。
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors, and find applications. We show that a GBP can have the same scaling limit as the fractional Poisson process. Considering that the Poisson process approximates the Bernoulli process under certain conditions, the connection we found between GBP and the fractional Poisson process is thought of as its counterpart under long-range dependence. When applied to indicator data, a GBP outperforms a Markov chain in the presence of long-range dependence. Fractional binomial models are defined as the sum in GBPs, and it is shown that when applied to count data with excess zeros, a fractional binomial model outperforms zero-inflated models that are used extensively for such data in current literature.
