论文标题
三峰分布的一般类别：属性和推理
A General Class of Trimodal Distributions: Properties and Inference
论文作者
论文摘要
这种方式是建模的重要主题。使用参数模型是一种有效的方法，当真实数据集显示三示示。在本文中，我们提出了一类新的三示概率分布，即具有多达三种模式的概率分布。通过将适当的转换应用于某些连续概率分布的密度函数来实现三连电本身。首先，我们获得了仲裁密度函数$ g（x）$的初步结果，接下来，我们将重点放在高斯案例上，更深入地研究三峰高斯模型。高斯分布用于产生高斯的三峰形式，称为正态分布。正态分布的分析表达的障碍性和三峰正态分布的性能是我们选择正态分布的重要原因。此外，应改进现有的分布，以便在数据集中存在三峰形式时能够有效地建模。提出了新的密度函数后，估计其参数很重要。由于Mathematica 12.0软件具有优化工具和重要的建模技术，因此使用此软件执行计算步骤。实际数据集的自举形式用于显示所提出的分布的建模能力时，当真实数据集显示三示射性时。
The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions that have up to three modes. Trimodality itself is achieved by applying a proper transformation to density function of certain continuous probability distributions. At first, we obtain preliminary results for an arbitratry density function $g(x)$ and, next, we focus on the Gaussian case, studying trimodal Gaussian model more deeply. The Gaussian distribution is applied to produce the trimodal form of Gaussian known as normal distribution. The tractability of analytical expression of normal distribution, and properties of the trimodal normal distribution are important reasons why we choose normal distribution. Furthermore, the existing distributions should be improved to be capable of modelling efficiently when there exists a trimodal form in a data set. After new density function is proposed, estimating its parameters is important. Since Mathematica 12.0 software has optimization tools and important modelling techniques, computational steps are performed by using this software. The bootstrapped form of real data sets are applied to show the modelling ability of the proposed distribution when real data sets show trimodality.
