PDF下载链接 PMF If the random variable $X$ follows the binomial distribution with parameters $n$ and $p$, we write $X \sim B(n, p)$. The probability of getting exactly $x$ successes in $n$ trials is given by the probability mass function: $$f(x; n, p) =…

1. 定义 假设一串独立的伯努利实验(0-1,成功失败,伯努利实验),每次实验(trial)成功和失败的概率分别是 p 和 1−p.实验将会一直重复下去,直到实验失败了 r 次.定义全部实验中成功的次数为随机变量 X,则: X∼NB(r;p) 2. PMF(概率质量函数) f(k;r,p)≡Pr(X=k)=(r+k−1k)pk(1−p)r 最后一次显然为失败,前 r+k−1 中发生 k 次成功: 之所以称其为 negative binomial distribution(负二项式分布),在于:…

1.Normal distribution In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and…

PDF version PMF Suppose that a sample of size $n$ is to be chosen randomly (without replacement) from an urn containing $N$ balls, of which $m$ are white and $N-m$ are black. If we let $X$ denote the number of white balls selected, then $$f(x; N, m,…

We start with the fuzzy binomial. Then we discuss the fuzzy Poisson probability mass function. Fuzzy Binomial Let $E$ be a non-empty, proper subset of $X=\{x_1,x_2,x_3,...,x_n\}$. Let $P(E)=p$ so that $P(E^{'})=1-p$ where $p\in (0,1)$. Suppose we hav…

title: [概率论]5-5:负二项分布(The Negative Binomial Distribution) categories: - Mathematic - Probability keywords: - The Negative Binomial Distribution - The Geometric Distribution toc: true date: 2018-03-29 08:57:12 Abstract: 本文介绍负二项分布,几何分布的基础知识 Keywords: T…

The zero-inflated negative binomial – Crack distribution: some properties and parameter estimation Zero-inflated models and estimation in zero-inflated Poisson distribution Count data and GLMs: choosing among Poisson, negative binomial, and zero-infl…

PDF version PMF Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called "success" and "failure". In each trial the probability of success is $p$ and of failure is $(1-p)$. We are obs…

PDF version PMF A discrete random variable $X$ is said to have a Poisson distribution with parameter $\lambda > 0$, if the probability mass function of $X$ is given by $$f(x; \lambda) = \Pr(X=x) = e^{-\lambda}{\lambda^x\over x!}$$ for $x=0, 1, 2, \cd…

PDF version PDF & CDF The probability density function is $$f(x; \mu, \sigma) = {1\over\sqrt{2\pi}\sigma}e^{-{1\over2}{(x-\mu)^2\over\sigma^2}}$$ The cumulative distribution function is defined by $$F(x; \mu, \sigma) = \Phi\left({x-\mu\over\sigma}\ri…