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

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11
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1answer
327 views

Why is a “negative binomial” random variable called that?

I don't understand why the "negative binomial" random variable has that name. What is negative about it? What is binomial about it? What is negative-binomial about it?
0
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0answers
7 views

How do you deal with overdispersion in a zero-inflated negative binomial regression AND when you expect data to have zeros?

Background: I am analyzing the effect of multiple variables (lineage, ancestral plant species, plant species reared from, larval density, body mass) on different traits: ovigeny index (initial egg ...
0
votes
0answers
12 views

Choosing between Zero Inflated Negative Binomial model versus Logistic Regression

Context: this is in the field of genome wide association studies. The norm in the field is logistic regression, but we have high quality radiographic data that gives us counts of damaged joints, so I ...
1
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0answers
15 views

Paired design and building a GLM

I am blocking a bit on the choice of a model for my data. The study is applying 2 different stimuli (S1 and S2) on some animals. Each stimuli has two 'treatments': either 'on' or 'off' (off being the ...
0
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0answers
6 views

Zero-inflated negative binomial non-integer error [migrated]

I am fitting ZINB in WinBugs using R2Winbug and this is WinBugs model code: ...
1
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3answers
111 views

Central Limit Theorem for Normal Distribution of Negative Binomial

The question is: Explain why the negative binomial distribution will be approximately normal if the parameter k is large enough. What are the parameters of this normal approximation? I have ...
4
votes
1answer
128 views

Maximum Likelihood Estimator for Negative Binomial Distribution

The question is the following: A random sample of n values is collected from a negative binomial distribution with parameter k = 3. Find the maximum likelihood estimator of the parameter ...
1
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3answers
59 views

How to deal with “non-integer” warning from negative binomial GLM?

I am trying to model the mean intensities of parasites affecting a host in R using a negative binomial model. I keep getting 50 or more warnings that say: ...
0
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0answers
23 views

Negative Binomial as weighted average?

I know the Negative Binomial distribution can be considered as the sum of r independent geometric distributions, as described here. Can it also be formulated as a weighted average of, possibly ...
0
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0answers
17 views

Distribution of sum of negative binomial parametrized with mean and aggregation parameter

From textbook, I know that: If each $X_i$ is distributed as negative binomial $(r_i,p)$ then $\sum X_i$ is distributed as negative binomial $(\sum r_i ,p)$. In R: ...
0
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0answers
13 views

Extensions of bsts and CausalImpact to non-Gaussian exponential family distributions

The bsts and CausalImpact packages implement a state space time series model with an optional regularized regression component. ...
0
votes
0answers
11 views

Comparing hurdle models to negative binomial models

I'm trying to compare the AIC or log-likelihood of a negative binomial GLM to a hurdle type approach, consisting of a binomial GLM for the presence/absence of a count and the counts modelled with a ...
4
votes
1answer
56 views

Name of rv that results from integrating over gamma in gamma product prior on poisson

If $d$ is an arbitrary random variable with parameter(s) $\Psi$ and positive support, $g \sim \mathrm{Gamma}(\alpha, \beta)$, $x \sim \mathrm{Poisson}(gd)$, and $g$ and $d$ are independent, then ...
4
votes
1answer
59 views

Sum of squared Negative Binomial probability masses

Let $(p_k)_{k=0, \dots, \infty}$ denote the probability masses of a Negative Binomial distribution with parameters $r>0$ and $p\in]0,1[$. I'm looking for the sum of their squares, ...
0
votes
1answer
48 views

Dealing with zero-inflation if the data are not count data type

In the literature I found that for the count data with a lot of zeros so-called zero-inflated distributions (models) and so-called hurdle-at-zero distributions (models) could be used. The differences ...
0
votes
0answers
20 views

How to decide whether to do regression through the origin or not (with a GLMM)?

I'm fitting a Negative Binomial GLMM (with glmmADMB), where the DV is the number of units sold of a product bundle and the IVs are count variables that indicate how many items from a specific category ...
1
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0answers
27 views

What is expected count formula for zero-inflated negative binomial regression?

My IT department wants me to translate my zero-inflated negative binomial regression model into a formula for calculating expected count which they can hard code into SQL. I'm running the model in ...
0
votes
1answer
43 views

How can I use negative binomial regression with caret?

I'd like to use negative binomial regression with caret. However in the list of supported models I can't find it. I tried to use: ...
1
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0answers
32 views

Should predictions with negative binomial regression only produce integers?

I have a dataset consisting of about 600 observations. Each observation has around 100 attributes. One of the attributes I want to predict. Since the attribute that I want to predict can only have ...
1
vote
1answer
32 views

Alternatives to Chi-Squared for Single Categorical Outcome and Single Categorical Predictor w/counts for factors [R]

I am from an applied background, where X2 and G-tests are the default ways to analyze count data (default as in, until today, I had no idea there were other ways, as I was only taught these methods). ...
3
votes
0answers
40 views

The use of the negative binomial dispersion parameter in model selection…?

I'm doing model selection, analysing the effect of a number of variables on the number of shoots browsed by deer, using the number of shoots available as an offset variable. My data distribution is ...
1
vote
1answer
23 views

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 ...
8
votes
1answer
162 views

Why is the Quasipoisson in glm not treated as a special case of Negative Binomial?

I'm trying to fit generalized linear models to some sets of count data that might or might not be overdispersed. The two canonical distributions that apply here are the Poisson and Negative Binomial ...
0
votes
0answers
15 views

Comparing different estimation approaches — poisson vs negative binomial vs FE?

What's the appropriate way to compare two different estimation approaches? I've got a panel data model (balanced with states as panels and years as time) -- but it's over dispersed with a lot of ...
1
vote
0answers
28 views

Interpreting scaled betas for quadratic terms in a negative binomial regression

I created a negative binomial model where the final model included 5 quadratic predictors (each with a corresponding linear term). I am considering two ways to interpret the beta coefficients for each ...
0
votes
0answers
16 views

High Value of Incidence-Rate Ratio

after running several negative binomial models, the IRR for one of my ivars has returned consistently high IRR values ranging from 18 to 365.... All the other ivars return 'normal' IRR values and I am ...
1
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0answers
48 views

Estimating probability of observing greater than X events based on a current population and historical rates

Let's say I have a population that varies from month to month, and per month, there are X number of failures. Based on historical rates, I am trying to find the probability of observing Y or greater ...
0
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0answers
16 views

using mgfs to find limiting distribution

Can someone help me out with proving that the limiting distribution of a negative binomial (k,p) distributed variable is poisson if we let k -> infinity and p->1. I am just learning about limiting ...
1
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0answers
35 views

interpretation negative binomial

I have a question towards an analysis of purchasing decisions. I have a data set where I investigate the amount of previous purchases last week (predictor) on the amount of purchases today (response ...
0
votes
0answers
13 views

How do I model chapter-verse references?

Context: I am part of an 8-person group in which each person posts a Bible verse every day. For those who don't know, that is of the format "Psalm 30:1" where first we reference the chapter, then the ...
2
votes
1answer
205 views

Negative-binomial why the answer is 0.288?

In a negative-binomial experiment with three independent trials, if I want the probability for 2 successes before the first failure. The probability of each trial is 0.6. ...
2
votes
1answer
56 views

Poisson and NB results

i did a regression with poisson model, and since the dependant variable is overdispersed (0.13) , i have also tried negative binomial. The problem is that my explanatory variable "repeated partner" is ...
0
votes
0answers
31 views

Negative Binomial Regression 0 Problem

I am dealing with a count data set. I am trying to predict the amount of purchasers per day by the amount of previous purchasers for different products, counting the amount of purchases per day. ...
1
vote
1answer
48 views

glm.nb fails to converge when adding one zero

I have a problem where glm.nb (R version 3.1.0, MASS version 7.3.33) converges on some data, but adding only one 0 it does not converge any more. This is the data ...
0
votes
1answer
30 views

Standard error of Poisson and negative binomial regression

In Poisson and negative binomial regression, the response is assumed have Poisson and negative binomial distributions respectively. When we test the significance of the parameter $\beta$, which is ...
0
votes
0answers
49 views

Can I use SAS Copula procedure or Matlab copulafit to fit count data (Poisson or Negative Binomial)

I want to simulate data (x,y) with dependency using copula. Matlab has the function for t copula, Clayton, Frank, and Gumbel bivariate Archimedean copulas. But I am not sure if these functions could ...
1
vote
0answers
52 views

Multiple starting value/convergence warnings when running glm.nb in R

I'm running a negative binomial GLM in R. Running the model with the pooled dataset works just fine, but I'm encountering several warning messages when I attempt to run the same model for some of the ...
0
votes
0answers
74 views

WinBUGS/JAGS code for calculating Bayesian p-value from negative binomial model

I have a working negative binomial model written in BUGS code, but am not sure about the appropriate Bayesian p-value code to test goodness of fit. Specifically, I would like to calculate Pearson's ...
1
vote
0answers
21 views

How to model the following dependent variable? [closed]

If I got a dataset which the (count data) dependent variable has the following distribution, how should I model it? I am aware of the zero inflated model and the negative binomial model, but are ...
2
votes
1answer
47 views

Exploring effect of treatment on count data

I've collected data on animal visitation at four different points in time. The four time points represent the total animal visitations over a three day period, i.e. 3 days of monitoring at four ...
2
votes
1answer
45 views

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 ...
3
votes
0answers
108 views

simulating birth death process with random numbers from negative binomial

I am trying to generate random deviates for the population size at time $t$ for a birth-death process with constant birth and death rates per individual and initial size $N_0 \gt 0$. For the simple ...
2
votes
1answer
139 views

Is it meaningful to calculate predicted marginal effects of a count data model with an interaction effect?

In a little regression model of mine, I estimate the following formula a a negative binomial regression type (it would hold for a Poisson regression as well): $$ y = \beta * var1 + \gamma * var1 * ...
2
votes
1answer
39 views

Finding how many times I need to perform an action before I have an x% chance of a specific outcome in r

Non-specific question: There is an action that can be performed that has multiple outcomes. Each outcome has a different probably, p, of occurring. How many times, n, do I need to do the action before ...
1
vote
1answer
239 views

Choosing reasonable parameters for a negative binomial distribution

My data is a list of observations and a count for each observation. The data is overdispersed, the mean is ~1,200 and the variance is ~18,000,000. I want to use a negative binomial model to assign ...
0
votes
0answers
108 views

Zero Inflated Poisson or Negative Binomial Regression model in Panel Data

I am using the Stata version 13.1. My data is count in nature and also it is a balanced panel. However, my data suffers from the problem of excess zeros and also suffers the problem of overdispersion. ...
0
votes
0answers
79 views

Negative binomial mixed effect model for repeated measures with R - prediction and plotting

I have a dataset to analyze in which a response was recorded at the ends of months 1,3,4,5,6 in 187 patients. All patients had the responses recorded in each week, and all patients started a treatment ...
0
votes
1answer
34 views

Random Coefficient Negative Binomial Model

I have a crash count data and i want to build a random coefficient negative binomial model in R. The dependent variable will be the crash counts and covariates will be Lane width, AADT, shoulder width ...
2
votes
0answers
127 views

Modeling discrete count data with a gamma distribution

I've encountered a statistical model in which discrete count data are modeled with a gamma distribution (supported on nonnegative reals). The model relies on the property of the gamma that a sum of ...
1
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0answers
64 views

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. ...