# 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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### Multiple poisson regression with one count and one continuous IV?

As one of my independent variables is a continuous variable and the other is a count variable, would I still be able to do a multiple Poisson regression?
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### Geom_smooth of predicted count warnings [closed]

I am currently writing an update of an article on vulture population trends (Vulture article) and looking at regular feeding at four long-term vulture restaurant sites from July 2016 to December 2023. ...
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### Why am I getting Negative Marginal Effects for Coefficients that are Positive?

I've run a hurdle Poisson model in R on the pscl package and used the marginaleffects package for the marginals and I'm getting ...
1 vote
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### Interpretation of Poisson regression model (outcome variable - dietary diversity)

I would like to get some insights on how to interpret the Poisson model using the results shown in the picture. This is how I interpreted it: For every one unit increase in the number of cooked food ...
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### How to model pixel shot noise

I'm interested in modelling the effect of shot noise on images. When taking a picture with a camera, the number of photons incident upon each pixel during the exposure time is (I believe) a ...
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### Am I using the right method to model my zero-inflated data?

I have a dataset of workplace permits, sample size n=3000. The data is collected between 2012-2020, so if a permit was active some time between 2012-2020, I included it in my analyses. My exposure of ...
485 views

### What distribution should I use to predict three possible outcomes

I am 70, left school at 14 but took to maths a few years back to ward off dementia so please excuse the naivety of my question. I have been using Poisson distribution to solve my problem but I dont ...
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### How to perform a power analysis for poisson distributed data

I want to perform a simplified power analysis to determine how many cells (samples) to have in control and experimental conditions (assume equal n across conditions). For an alpha level of 0.05, 0.95 ...
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### Is a Poisson minus a constant still a Poisson?

I am working with a process in which I expect my variable to be Poisson distributed. For reasons that have to do with the scale, however, the values I obtain have a minimum of 11. I have noted than ...
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### Exponential function for Poisson intensity

I'm getting confused on estimating the intensity for a Poisson process. My background in the subject is weak. Suppose I'm interested in modelling the probability of an event occurring given some input ...
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### Which log-likelihood is to be maximized for left-truncated count data?

What is to be done, if the count data is missing the counts on the zeros (i.e. left truncated data)? Say one wants to estimate a Poisson regression and the goal is to derive the log-likelihood to be ...
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### Confused between Multiple Random Variables and Likelihood Function [closed]

I am confused between the two at a very fundamental level. Following is the problem: I take observations $\vec{x}$ and create a histogram $\mathbf{n} = (n_1,\ldots,n_N)$ out of it with $N$ bins. ...
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I wish you good health and the best in life (whatever that means for you in particular). Context I want to model aggregated (monthly) tornado counts in the United States for a question on Metaculus. ...
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### Gaussian Field of Poisson distributed Random Variables

Can it be that the spatial process is a Gaussian field even if the observations are Poisson distributed? How does any finite combination of them follow a multivariate normal distribution?
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### Help with choosing stats test for bird count data

I am a university student working on analyzing some data, and am looking for a little bit of statistics help and guidance. Data overview: I am doing a research project on birds, and am trying to ...
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### Am I Doing Things Right? / negative binomial test

I have a dataset consisting of social media comments about a particular context from 1999 to 2024.The topic titles of the comments were annotated into two categorial variables = 0 and 1. I am aiming ...
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### What is special about the Poisson/Binomial distributions such that they have special regression estimation techniques?

You can use maximum likelihood estimation to estimate the regression parameters for a random variable with Poisson or Binomial distributions, but I haven't heard of a chi-squared regression or a Gamma ...
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### Confirmation that 0-inflated poisson model is specified correctly in jagsUI package

I have data representing counts of roads within a given cell of a raster (value) and I want to examine how it responds to a fixed effect of year (scaled, year_sc) and two random effects of cell ID and ...
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### potential measurement errors

I am working on a dataset for a practice problem and was given a dataset containing information on food items such as kcal (kilocalories), Potassium, Protein, etc. We were asked to analyze the dataset ...
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### How to derive standard errors of regressors in quasi-Poisson regression?

Suppose I want to relax a Poisson Regression to allow for overdispersion and apply a quasi-likelihood approach: $$E[y_i|x_i] = exp(x_i^T \beta)$$ $$Var[y_i|x_i] = \phi \cdot \mu_i$$ In other words, ...
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### What is the interleaved probability like when two Gamma distribution processes fired together?

As opposed to the similar question here: Is there a probabilistic (not analytical) argument for why the sum of independent Poissons is Poisson? The difference is to consider the interval between two ...
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### Distribution of Outcomes From Many Independent Events With Varied Associated Probabilities

I have a problem in which I need to visualize the distribution of possible outcomes from a large number of independent Bernoulli events with varying probabilities among those events in python (summing ...
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### How can we efficiently find the fourth moment of a Poisson distribution?

Suppose we have $X\sim \textrm{Poisson}(\lambda)$ and we know that moment generating function $M(t)=\mathbb{E}(e^{tX})$. How do we use the moment generating function property $M^k(0)=\mathbb{E}(X^k)$ ...
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### What does the following mean with regards to Poisson distribution?

A text I'm reading says the following, Consider the occurrence of any uncertain event over time or space in such a way that the average occurrence of the event over unit time or space is m. We may ...
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### Determine if Poisson process rate changes

Imagine a person, P, calls into a call center multiple times an hour. With 50% probability, P will call with some low rate (like an average of ~3 calls an hour) the whole time. With 50% probability, P ...
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I've just started studying Poisson regression and came across the two models:  \begin{align*} \log{\mathbb{E}(count)} &= \beta_0 + \beta_1x_1 + \beta_2x_2 + \log(T) \\\\ \log{\mathbb{E}(count)} &...