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Questions tagged [negative-binomial-distribution]

A discrete, univariate distribution modelling the number of ${\rm Bernoulli}(p)$ trial successes until a specified number of failures occur.

Overview

The negative binomial is a discrete, univariate distribution modelling the number of ${\rm Bernoulli}(p)$ trials until a specified number of failures occur. It is parametrized by $r$, the number of failures in $k$ ${\rm Bernoulli}(p)$ trial successes.

A discrete random variable $X$ has a negative binomial distribution, indexed by parameters $p \in (0,1)$ and $r \in \mathbb{Z}$ if its probability mass function is

$$ \Pr(X = k) = {k+r-1 \choose k} (1-p)^r p^k $$

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Can I use negative binomial regression for non-count data?

I have a set of data and I want to model a response variable which is "amount of money paid by the participants". I have data of about 600 people, who chose to pay between 0 and 100 (only integers). These data do not follow a normal distribution,…
ClaudiaRR
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negative binomial regression link function

Does anybody know apart from the log link, what other common link functions negative binomial regression use? And what's the criteria to choose these link functions? Thanks so much!
tomtomxu
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Requirements for negative binomial regression

In my study, I experiment with fixed and mixed effects negative binomial regression to my data (in R) as the response variable is a count variable. Normally I should use Poisson regression but (and here I have doubts whether I have done it right) I…
dysko
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How do I solve for $x$ in $x =\Biggl(\frac{px}{1-(1-p)x}\Biggr)^n$

I have an equation for the probability generating function of a negative binomial $(n,p)$ distribution: $$G(x)= \Biggl(\frac{px}{1-(1-p)x}\Biggr)^n$$ I'd like to solve for $x$ in the following equation: $$x =\Biggl(\frac{px}{1-(1-p)x}\Biggr)^n$$ But…
user255658
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How can I interpolate within a negative binomial distribution?

I have information about a negative binomial distribution at the 10%, 50%, and 90% quantiles. I want to be able to interpolate to know what the probability of a certain count is within this distribution. For example, I know that the value for the…
mdrishan
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Need code for sampling negative binomial with non-integer $r$

I'm trying to write code (in C) to sample from a negative binomial distribution parameterized by $r,p$, where $r$ is not necessarily integer (also called Polya distribution). I've found a number of explanations, and it looks like I could sample $y$…
Mike Dunlavey
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What is theta in negative binomial distribution?

https://www.rdocumentation.org/packages/MASS/versions/7.3-51.5/topics/theta.md The above page says this. Given the estimated mean vector, estimate theta of the Negative Binomial Distribution. But it is not clear what the definition of theta is as…
user1424739
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Truncated negative binomial

I am trying to understand if I should use truncated negative binomial for my research. 50 percent of my dependent variable is zero. I already used negative binomial but I would like to use another model as well. So, I was wondering if someone could…
Susan mohammad.k
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Negative Binomial to Normal

I want to use normalisation technique that has assumption of residuals' normality (GLMs), but my data is $\sim$Negative Binomial. Can I map values from NB distributed distribution to Normal distribution, using probabilities and cumulative…
German Demidov
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What is the relationship between theta and size in negative binomial distribution?

In negative binomial regression glm.nb(y~x), I got a parameter theta and two coefficients? And then I want to use dnbinom(x, size, prob, mu, log = FALSE) to calculate the predicted probability. can anyone show me what is the relationship between…
user22062
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Laplace Transformation for the Negative Binomial Distribution

I am trying to do this using the Poisson-Gamma mixture parameterization. I think the derivation is related to the derivation of the expected value. But I have only seen how to derive the mean using conditioning, not from summation. Could someone…
Ka Lee
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Sum of correlated negative binomials

Suppose $X, Y$ are non-independent random variables with $X\sim NB(r,p)$ and $Y\sim NB(s,p)$; correlation between $X$ and $Y$ is $<$ 1. Is sum $X + Y$ distributed as negative binomial? Or not?
den2042
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Distribution of Theta parameter in negative binomial model

I'm trying to simulate outcomes in a zero-inflated negative binomial model. My model gives an estimate of the dispersion parameter theta, as well as a standard error for log (theta). My question is, what is the uncertainty distribution around…
EdSeab
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Commonality analysis in negative binomial regression?

I am new to negative binomial regression and am using Generalized Linear Models in SPSS to analyze some highly skewed count data (it is not zero inflated and the variance is much higher than the mean so I'm not using Poisson regression). I'm…
madison
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Negative binomial regression: Different results between the glm y x, (nbinomial 1) link(log) and glm y x, (nbinomial ml) link(log) Stata command?

I'm running a negative binomial regression. I found big differences in the results* if I compute with the glm y x, (nbinomial 1) link(log) and glm y x, (nbinomial ml) link(log) (for Stata) command. What is the difference between computing with ML**…
Walter
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