# 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.

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### Expected value of a (kind of) continous negative binomial distribution

Let a random variable $X$ be the number of independent Bernoulli trials needed to reach $k$ successes and $r$ failures when the probability of success is $p$. We therefore stop trials when we have $k$ ...
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### Advice on what model for this data - count data with exposure/offset plus truncated 0s

This is a question about how well a disease testing program is doing. The testing is assessed by an indicator called coverage. It's measured by the number being tested out of the number eligible for ...
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### GLM negative binomial - what to do when one category has only zeros?

I have camera trap data for four different management types (A,B,C,D). I want to know whether there is an effect of these management types on the abundance of different mammalian herbivore species. ...
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### Estimate MLE of discrete distribution with two parameters in R [closed]

I want to estimate the MLE of a discrete distribution in R using a numeric method. My data looks like this: data1<-c(5,2,2,3,0,2,1 2,4,4,1) If we assume it ...
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### Zero-inflated Gaussian for weights below zero recorded as 0?

I'm aware of the general idea behind zero-inflated model, and have used the zero-inflated Poisson and negative binomial. However, the data I currently have has a little different format that makes me ...
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### Comparing quasi-Poisson and negative binomial fit on panel data

I am using the R package fixest to model over-dispersed count data with fixed effects. While I have read that quasi-poisson and negative binomial regressions ...
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### Comparing output of Pearson's chi-squared to output of R function qchisq

I have a dataset which contains count data. I am pretty sure the dataset is well suited to a negative binomial distribution, since the variance is greater than the mean, but I wanted to check this. I ...
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### How does PSCL fit zero-inflated negative binomial models?

I've been using the PSCL zero-inflated negative binomial model to simply fit count data. I'm not specifying any complex formula, essentially I just provide the count data and try to find the ...
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### Help in understanding zero inflated neg binomial model summary

I'm writing this topic because I would need to get some more information about model conversion in brms (zero-inflated_negbinomial) model. Let's say I have this model result : Where I want to model ...
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### Comparing fixed effects quasi-Poisson and negative binomial fix

I am using the R package [fixest] to model over-dispersed count data with fixed effects. While I have read that quasi-poisson and negative binomial distributions typically return similar results, ...
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### Independent / joint / multivariate negative binomial distribution

I'm not sure what variation of the negative binomial distribution is most suited to use. Say I have a bag of balls of m different colours, I draw n balls from the bag and want to model x_1, ... , x_m ...
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### zeroinfl doesn't seem to work (R)?

I´vd tried to fit a zero-inflated negative binomial model with zeroinfl (package pscl): ...
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### Proper regression for my dataset - Zero-inflated beta regression?

I'm a bit stumped on the regression that I should be using for my dataset. There seems to be a general trend that as distance to a location decreases, the percentage of red material increases (as a ...
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### Evaluation metrics for out-of-fold predictions obtained through negative binomial regression

I'm formulating count data out-of-fold predictions using a negative binomial regression and i am a bit confused as to which evaluation metrics apply best. My dependent variable has a long tail ...
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### How to interpret incidence rate ratio for an interaction term in a negative binomial regression in R?

I am trying to interpret the output of a brm() zero_inflated_negbinomial model in R. I would ...
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### Have I correctly specified my GAMM model?

I am new to GAMM models and I would like to ask you whether I designed the model correctly. I aim to evaluate the relationship of a blood protein (independent variable) with the disease scoring system ...
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### Interpretation of coefficients in multilevel mixed effects negative binomial regression analysis

I am wondering how to correctly interpret and describe the coefficients (betas) in a multilevel mixed effects negative binomial regression analysis. I conducted this analysis in Stata with the menbreg ...
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### Decompound a Compound Probability Distribution

I am trying to figure out how to deconvolve or decompound a compound probability density function - knowing one of the distributions and having samples from the compound distribution. Assume I only ...
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### Simulating draws from a negative binomial

I am looking for a way to simulate draws from a negative binomial distribution for a computational experiment on biological sequencing data. I am using a high performance package which only has ...
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### How to check linearity in count data with many 0's for negative binomial regression

I want to fit my data to a negative binomial regression model. The dependent variable Y is count data with many 0's and the independent variable X is continuous. For this, I want to check if the ...
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### Combining imputations of generalized linear model regression coefficients - same as linear multiple regression?

I'm doing some imputation with the MICE package. The outcome variables I am using are zero-inflated, and in the absence of imputation, I would analyze them with a zero-inflated negative binomial ...
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### Using time series observations to fit a distribution

I want to build a model that predicts the probability of an event during the time remaining. For example, say I'm taking observations of cars that pass through an intersection during an hour. (Say ...
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### Data count regression with a truncated distribution

Imagine that we are conducting an experiment to test the effectiveness of a treatment, where the «level of illness» is measured by a count that is distributed as a negative binomial (NB). The plan is ...
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### Goodness of fit that smooths/tolerates artificial bumps

Say we are conducting a social science experiment involving people answering questions such as how many times have you done this or that over the last 6 months. As they probably don't remember an ...
I am working with the negative multinomial and I have a doubt about a parameter. The probability mass of a $d$ dimensional count vector $y = (y_1, . . . , y_d)'$ under a NegMN distribution with ...