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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58 views

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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1answer
461 views

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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1answer
47 views

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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11 views

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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38 views

Comparing fixed effects quasi-Poisson and negative binomial fix

I am using the R package [fixest][1] 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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10 views

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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1answer
49 views

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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10 views

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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1answer
37 views

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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1answer
67 views

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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3answers
113 views

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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1answer
56 views

Estimate dispersion parameters in negative binomial distribution

A popular parameterization of the negative binomial distribution is by $\mu$ and $r$, which represent mean and dispersion, respectively. The probability mass function states: $$ \text{P(x = k)} = \...
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How to do negative binomial regression with the rms package in R? [closed]

How can I use the rms package in R to execute a negative binomial regression? With the MASS package, I use the ...
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10 views

Which statistical test should be used to compare the frequency of categorical variables across a period of time?

hope everyone is having a good day. I'm developing an study that evaluates the number of deaths of COVID across a period of time and the risk factor associated with it; Figure 1(example) illustrates ...
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1answer
73 views

Expected value of balls left, drawing colored balls with 0.5 probability

In an urn, there are m red balls and n green balls. Every minute, you toss a coin and decide which color to draw, then remove one ball of that color from the urn. (e.g. remove one green ball if it is ...
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1answer
80 views

Interpretation of Positive Count Coefficients in Hurdle Model

What is the proper interpretation of the coefficients for the positive count part of a hurdle model (truncated Poisson or Negative Binomial)? I have read that the interpretation of the coefficients ...
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29 views

exp(b) negative binomial regression

I am currently running a negative binomial regression, the log of expected counts is not as easy to understand, interpret. So I am wondering if I can, just like in logistic regression take the exp(b), ...
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1answer
47 views

How to interpret Scipy's negative binomial distribution

In Python Scipy I obtain the follow result and am not sure how to interpret it >>> scipy.stats.nbinom(n=2, p=0.5).pmf(1) 0.25 As far as I understood the ...
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How to handle big count data with huge orders of magnitude in GLMMs: center & scaling but than negative values are introduced?

I'm relatively new to GLMMs and so far only handled relative data. Now I'm trying to model if the abundance of a taxon is affected in the disease state (condition) when considering random effects like ...
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AIC difference after adding offset in negative binomial in R

I'm quite confused about how R calculate likelihood/AIC in glm.nb after adding the offset. In this example, the regression coefficients are the same but the AICs ...
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1answer
23 views

For overdispered data, should the correlation matrix exclude zero?

I have 4 species and their distributions are overdispersed in space (i.e. lots of zeros). I calculated a Pearson correlation matrix and there is a lot of cluster around the 0s and 1s. Should I ...
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Assessing fit of count regression models

I'm new to modelling count outcomes and was hoping an expert could take a look at the rootogram and Q-Q plot of deviance residual below and let me know how important the misfit is as regards ...
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Predictor variable with opposite relationship than expected

I have run a GLM (negative binomial family) to test the effect of environmental factors on the longevity/duration (days) of turtle tracks left on beaches. Looking at the "Estimate" values in ...
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2answers
109 views

Negative binomial distribution mean and variance

The equation below indicates expected value of negative binomial distribution. I need a derivation for this formula. I have searched a lot but can't find any solution. Thanks for helping :) $ E(X)=\...
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1answer
40 views

The formula of zero-inflated count regression in "pscl" package of R?

Currently, I'm trying to learn the zero-inflated count model. So, I read about the model in the "pscl" package of R. It said that: "The formula can be used to specify both components of ...
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Calculating Reorder Point with Negative Binomial distribution

I'm an intern working on a project that requires calculating minimum stock levels for skus with low demand and high volatility. I found from research that a negative binomial distribution is best ...
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1answer
32 views

Is my choice between quasi-Poisson and Negative Binomial well-justified?

I know that quasi-Poisson gives more weight to large values, whereas Negative Binomial gives more weight to small values (see source). Small values are more frequent in my dependent variable, so it ...
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Modelling overdispersed rate data using a negative-binomial distribution

A quick overview of the analysis I'm wanting to do: I am wanting to analyze the relationship between habitat factors and the capture of my research species over a network of traps, in order to be able ...
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2answers
62 views

How to correct pattern in residuals when using a negative binomial distribution? Is it due to overdispersion?

I have a large dataset with the count data and I computed the following full model (covariates are all scaled) : ...
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1answer
38 views

How to prove stochastic dominance of negative binomial random variable

Let $X\sim NegBin(n_1,p)$ and $Y\sim NegBin(n_2,p)$ with $n_1>n_2$. How do I show that $X$ stochastically dominates $Y$ (i.e. $F_X(x)\le F_Y(x)\quad\forall\:x\in\Bbb R$)? My try Since a Negative ...
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Negative Binomial as Gamma-Poisson Mixture or Compound Logarithmic Poisson: can this correspondence be generalized to other distributions?

Preamble A random variable $X$ with a negative binomial distribution can be characterized in three ways: [Negative Binomial] $X\sim\operatorname{NegBin}(r,p)$ for some $r$ and $p$; [Gamma-Poisson ...
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What model should I use for a Gamma distribution with some non positive values in the response?

I'm working on a research about mapping the QLQ-C30 to EQ5D score. The response has a non normal distribution with some negative values. I've read some articles transforming the utility score into ...
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How do I describe this negative binomial regression with offsets in math and words?

I've been using a negative binomial model to compare the number of particles in the ocean of different sizes to their abundance. My gam, in r code looks like this ...
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Variance of a gamma distribution being proportional to its mean - a vacuously true statement?

I used to believe that the negative binomial distribution (for count data) and Gamma distribution (for continuous data) shared the property that the variance can take arbitrary values regardless of ...
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1answer
130 views

Negative-Binomial Method of moments with an offset

Given the method-of-moments approach to estimate the parameters of the NB-2 distribution $\mu$ and $\phi$: $$ \mu = \bar{y} $$ $$ \phi = \frac{\bar{y}^2}{s^2 -\bar{y}} $$ How can this be extended to ...
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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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1answer
73 views

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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12 views

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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1answer
29 views

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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1answer
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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 ...
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I don't need a full solution but i need guidance for the solution [closed]

I don't need a full solution but I need guidance for the solution.
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Negative multinomial notation doubt

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 ...

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