# Questions tagged [poisson-distribution]

A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.

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### Is there a boxplot variant for Poisson distributed data?

I'd like to know if there is a boxplot variant adapted to Poisson distributed data (or possibly other distributions)? With a Gaussian distribution, whiskers placed at L = Q1 - 1.5 IQR and U = Q3 + 1....
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### The Number of Exponential Summands in a Fixed Interval is Poisson

What is the most clever way to prove that the number of independent exponential summands in a fixed interval is distributed as a Poisson random variable? I can do it one way, but I would like to know ...
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### How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression? Assume the following example: ...
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### Checking if two Poisson samples have the same mean

This is an elementary question, but I wasn't able to find the answer. I have two measurements: n1 events in time t1 and n2 events in time t2, both produced (say) by Poisson processes with possibly-...
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### Relationship between poisson and exponential distribution

The waiting times for poisson distribution is an exponential distribution with parameter lambda. But I don't understand it. Poisson models the number of arrivals per unit of time for example. How is ...
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### Why is the square root transformation recommended for count data?

It is often recommended to take the square root when you have count data. (For some examples on CV, see @HarveyMotulsky's answer here, or @whuber's answer here.) On the other hand, when fitting a ...
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### How does a Poisson distribution work when modeling continuous data and does it result in information loss?

A co-worker is analyzing some biological data for her dissertation with some nasty Heteroscedasticity (figure below). She's analyzing it with a mixed model but is still having trouble with the ...
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### Poisson regression to estimate relative risk for binary outcomes

Brief Summary Why is it more common for logistic regression (with odds ratios) to be used in cohort studies with binary outcomes, as opposed to Poisson regression (with relative risks)? Background ...
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### How to calculate a confidence level for a Poisson distribution?

Would like to know how confident I can be in my $\lambda$. Anyone know of a way to set upper and lower confidence levels for a Poisson distribution? Observations ($n$) = 88 Sample mean ($\lambda$) =...
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### Error metrics for cross-validating Poisson models

I'm cross validating a model that's trying to predict a count. If this was a binary classification problem, I'd calculate out-of-fold AUC, and if this was a regression problem I'd calculate out-of-...
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### Should I use an offset for my Poisson GLM?

I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then ...
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### Time series for count data, with counts < 20

I recently started working for a tuberculosis clinic. We meet periodically to discuss the number of TB cases we're currently treating, the number of tests administered, etc. I'd like to start ...
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### How can I test if given samples are taken from a Poisson distribution?

I know of normality tests, but how do I test for "Poisson-ness"? I have sample of ~1000 non-negative integers, which I suspect are taken from a Poisson distribution, and I would like to test that.
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### How do I interpret the 'correlations of fixed effects' in my glmer output?

I have the following output: ...
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### How do I fit a multilevel model for over-dispersed poisson outcomes?

I want to fit a multilevel GLMM with a Poisson distribution (with over-dispersion) using R. At the moment I am using lme4 but I noticed that recently the ...
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### Why is the probability zero for any given value of a normal distribution?

I noticed that in the Normal distribution, the probability $P(x=c)$ equals zero, while for the Poisson distribution, it will not equal zero when $c$ is a non-negative integer. My question is: Does ...
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### Scaling vs Offsetting in Quasi-Poisson GLM

I recently modeled insurance claim frequency assuming a Quasi-Poisson distribution in R. My frequency dependent variable was calculated, in advance of modeling, as the number of claims per underlying ...
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### How is it possible that Poisson GLM accepts non-integer numbers?

I am really stunned by the fact that the Poisson GLM accepts non-integer numbers! Look: Data (contents of data.txt): ...
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### Strategy for deciding appropriate model for count data

What is the appropriate strategy for deciding which model to use with count data? I have count data that i need to model as a multilevel model and it was recommended to me (on this site) that the ...
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### What is the appropriate model for underdispersed count data?

I am trying to model count data in R that is apparently underdispersed (Dispersion Parameter ~ .40). This is probably why a glm with ...
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### Resolving heteroscedasticity in Poisson GLMM

I have long-term collection data, and I'd like to test, whether the number of animals collected is influenced by weather effects. My model looks like below: ...
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### Can I treat a counting response variable as a continuous variable and run OLS?

What I learned from book is predicting counting is different from predicting a continuous variable. For example, if we want to predict how many mails a person get per day, we may use Poisson ...
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### What is a statistical significance test for two Poisson distributions?

Say that I have two Poisson distributions. These were modelling after count data. How would I determine statistical significance between these two distributions? That is, how would I determine ...
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### Determining confidence interval with one observation (for Poisson distribution)

When you make only one measurement, how do you determine 95% confidence interval for the Poisson distribution? Let's say that I make one measurement of a quantity $x$ and obtain $x=10$. Also it is ...
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### Is there a probabilistic (not analytical) argument for why the sum of independent Poissons is Poisson?

I was just wondering if there was a simple probabilistic argument for why a Poisson random variable with parameter $\lambda_1$ plus a Poisson random variable with parameter $\lambda_2$ (both ...
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### poisson glm to observe whether effects of artificial light on the number of bat passes in each location were significant

I am a university student looking for help with analysis for my dissertation, I do not have the best knowledge of R studios or statistics in general so please bear with me! I would like to perform a ...
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### Poisson regression - dealing with widely different population sizes

I have a dataset of counts (responses to a marketing campaign), collected at the zipcode level. I am trying to use a poisson regression to determine underlying response rate of each zipcode. How do ...
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### How to know if a data follows a Poisson Distribution in R?

I am an undergrad student and I have a project for my probability class. Basically, I have a dataset about the hurricanes that impacted my country for a series of years. In my probability Book, (...
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