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…

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…

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…

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:…

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) =…

Random Variable \(\underline{cdf:}\)cumulative distribution function \(F(x)=P(X \leq x)\) \(\underline{pmf:}\)probability mass function(for discrete probability distribution ) (1)\(p(x) \geq0,x \in X\) (2)\(\sum\limits_{x \in X}P(x)=1\) \(\underline{…

Basis(基础): SSE(Sum of Squared Error, 平方误差和) SAE(Sum of Absolute Error, 绝对误差和) SRE(Sum of Relative Error, 相对误差和) MSE(Mean Squared Error, 均方误差) RMSE(Root Mean Squared Error, 均方根误差) RRSE(Root Relative Squared Error, 相对平方根误差) MAE(Mean Absolute Error, 平均绝…

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Conjugate prior relationships The following diagram summarizes conjugate prior relationships for a number of common sampling distributions. Arrows point from a sampling distribution to its conjugate prior distribution. The symbol near the arrow indic…