The theory and practice of finance draws heavily on probability theory. All MBA programs prepare finance majors for their career in the profession by requiring one generalist course in probability theory and statistics attended by all business majors. While several probability distributions are covered in the course, the primary focus is on the normal or Gaussian distribution. Students find it easy to understand and apply the normal distribution: Give them the expected value and standard deviation and probability statements about outcomes can be easily made. Moreover, even if a random variable of interest is not normally distribution, students are told that a theorem in statistics called the Central Limit Theorem proves that under certain conditions the sum of independent random variables will be asymptotically normally distributed. Loosely speaking, this means that as the number of random variables are summed, the sum will approach a normal distribution. Armed with this rudimentary knowledge of probability theory, finance students march into their elective courses in finance that introduce them to the quantitative measures of risk (the standard deviation) and the quantitative inputs needed to implement modern portfolio theory (the expected value or mean and the standard deviation). In listing assumptions for most theories of finance, the first assumption on the list is often: “Assume asset returns are normally distributed.” The problem, however, is that empirical evidence does not support the assumption that many important variables in finance follow a normal distribution. The application of the Central Limit Theorem to such instances is often inappropriate because the conditions necessary for its application are not satisfied. And this brings us to the purpose of this book. Our purpose is fourfold. First, we explain alternative probability distributions to the normal distributions for describing asset returns as well as defaults. We focus on the stable Paretian (or alpha stable) distribution because of the strong support for that distribution that dates back four decades to the seminal work of Benoit Mandelbrot. Second, we explain how to estimate distributions. Third, we present empirical evidence rejecting the hypothesis that returns for stocks and bonds are normally distributed T and instead show that they exhibit fat tails and skewness. Finally, we explain the implications of fat tails and skewness to portfolio selection, risk management, and option pricing. We must admit that our intent at the outset was to provide a “nontechnical” treatment of the topic. However, we could not do so. Rather, we believe that we have provided a less technical treatment than is provided in the many excellent books and scholarly articles that deal with probability and statistics applied to finance and risk management. The book is not simple reading. It must be studied to appreciate the pitfalls that result from the application of the normal distribution to real-world financial problems.

Filtering Distributions of Normals for Shading Antialiasing

Probability Distributions Involving Gaussian Random Variables.pdf

资源来自pypi官网。 资源全名：done_distributions-0.1.tar.gz

这项工作首先证明了基于电子束蒸发二氧化f（HfO2）的无杂质空位扩散（IFVD）诱导的量子阱混合（QWI）。 红光二极管激光晶片具有两个6纳米厚的GaInP量子阱和三个8纳米厚的AlGaInP量子势垒的有源区。 在200℃下在二极管激光晶片的表面上蒸发出135nm厚的HfO 2膜。 QWI过程是通过在不同温度下快速热退火（RTA）20 s引起的。 发现活性区域发射波长的强度和半峰全宽（FWHM）分别随着退火温度的升高而增加和降低。 当样品在1000°C退火时，HfO2 IFVD诱导的QWI发现蓝移为18 nm。 此外，基于活性区域中的浓度分布来计算扩散长度和扩散系数，并且扩散系数值高于Zn杂质扩散诱导的QWI中的结果。

matlab泊松分布验证代码概率分布比较 该项目是B.Tech三年级概率和随机过程课程的一部分，在该课程中，我试图验证以下近似值并绘制不同概率分布的概率分布函数/概率质量函数以进行比较。 二项分布趋于正态分布 二项分布趋于泊松分布 泊松分布趋于正态分布 趋于二项式分布的超几何分布 该项目是使用MATLAB 2020a完成的。 存储库内容：- binomial_and_normal.m-用于验证二项分布趋于正态分布的近似值的MATLAB代码 binomial_and_poisson.m-用于验证二项分布趋于泊松分布的近似值的MATLAB代码 poisson_and_normal.m-用于验证Poisson分布趋于正态分布的近似值的MATLAB代码 hypergeometric_and_binomial.m-用于验证超几何分布趋于二项分布的近似值的MATLAB代码 binomial_vs_normal.pdf-包含用于验证案例的代码和图的PDF文件 binomial_vs_poisson.pdf-包含用于验证案例的代码和图的PDF文件 poisson_vs_normal.pdf-包含用于验

两个高斯分布之间的 Kullback-Leibler 散度

Continuous Univariate Distributions, Vol.

js-pert 计划评审技术 给定一系列具有悲观，乐观，可能的时间和依赖性的活动，这些活动将提供： 每次活动的expected time 每项活动的variance 具有predecessors和successors节点[AON]网络图上活动的描述 每个节点的最早开始[ES]次 每个节点最早完成[EF]次 每个节点的最晚开始[LS]次 每个节点的最新完成[LF]次 每个节点都slack critical path描述 使用pert的描述还将提供一个函数，以计算x天完成项目的概率。 安装 npm install js-pert --save 例 请看。 文献资料 jsPERT 默认的导

Continuous Univariate Distributions, Vol. 2