# 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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### How to prove overdispersion in Poisson regression?

For $Y_i$ independent $\sim \mathcal{Poisson}(λ_i)$, $i = 1, \dotsc,n$, I want to assume $λ_i$ has mean $λ$ and variance $σ^2$. With this I want to show the following, but I am not sure how to show ...
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### What is the difference between normal approximation and poisson approximation of binomial distribution?

what is the difference between Poisson distribution as an approximation of Binomial distribution and Normal (Gaussian) distribution as an approximation of Binomial distribution? Both are ...
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### How do I prove the square root is a variance stabilizing link for Poisson?

I have searched google, and wikipedia, and have come up with nothing. If there are links that you could provide to help me figure out how to prove this, that would be very beneficial. Is it possible ...
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### Pymc3 Applying a Zero Inflated Poisson Model

I'm getting started with probabilistic/Bayesian modeling and am trying to create a model for a specific scenario, and I'm running into issues achieving an acceptable outcome for the model. As a result,...
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### Time pdf of number of poisson proscces events [duplicate]

I know that the time between two events distributes exponentially with parmeter lambda, but, how will the time distributes between n events for example? I would guess there should be a simple ...
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### Poisson Distribution with variable average rate λ?

When I observe the popular times of a store / place / online shop on Google,† sometimes the bar graph has one peak (maximum) but sometimes it has two (global maximum and a local maximum). I was ...
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### Variance of scaled Poisson distribution

I teach statistics in a community college. In my class I gave an example of image noise reduction in cosmology. For example, an object is exposed for time T and we got image $C_1(i,j)$. $C_1$ is the ...
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### How to calculate the average inter-arrival time from a series of inter-arrival time?

I am currently handling count data and just look into the poisson process. It maybe a trivial question but I am really confused on it. I have collected count data and the inter-arrival time between ...
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### Simulate correlated Poisson samples

I am wondering how I can simulate Poisson data that is correlated. Let's say, I collect data at two time points. At both time points, the data is Poisson distributed, at time point 1 with $\lambda=4$, ...
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### Should I use Binomial, Poisson or Gamma distributions? With or without a log link?

I want to run a GLM to answer a few questions about differences in diet between sex and calendar year. Questions: Does frequency of occurrence (FO) of pieces eaten differ between sex or year? Does ...
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### Can Wilk's $-2\log(\Lambda)\sim \chi^2_d$ rule be used with a sample size $n=2$?

Suppose I have $X \sim \text{Poisson}(\lambda_x)$ and $Y \sim \text{Poisson}(\lambda_y)$ and they are independent. Suppose $H_0: \lambda_x =\lambda_y$ and $H_A: \lambda_x\ne\lambda_y$. My likelihood ...
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### p-values near 1.000 for all tests in a glm() (count and binary data, Poisson and binomial distributions)

I want to run multiple GLM's to answer a few questions about changes in diet between species and over time. Questions: Does frequency of occurrence (FO) of pieces eaten differ between species or ...
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### what are the parameters of a poisson term in a jump diffussion SDE

I am trying to simulate a Jump diffusion process in python and not sure what i should specify as the parameters of the poisson term. Here is what i have ...
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### Laplacian noise applications

I would like to know whether Laplacian distribution can be used to model a Poisson noise. I have met this case while checking this book and here what it says (see the picture below) As far as I ...
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### Likelihood of Poisson R.V with Bayesian Inference

In Bayesian Inference. Say I have a Poisson distributed R.V. K which denotes the observed number of some event over a specified time period. The rate of this ...
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### Bayesian Inference with Poisson Distributed R.V

In Bayesian Inference. Say I have a Poisson distributed R.V. K which denotes the observed number of some event over a specified time period. The rate of this ...
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### How to model the likelihood of an inhomogeneous Poisson process with “uncertain” event values

Using the example of an inhomogeneous Poisson process in 1 dimension for simplicity, with a varying rate parameter $\lambda (t)$. Let's say I am trying to find the form of $\lambda (t)$, using data ...
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### What is the distribution in Quasi-Poisson regression?

For Poisson regression, the assumption is that Y has a Poisson distribution. Is the same assumption true for Quasi-Poisson regression?
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### problem fitting a model with a Poisson distribution [closed]

I am working in population ecology and I am trying to write a linear regression using in JAGS. It is a simple model where I intend to relate population density with annual productivity. Population ...
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### Deriving Marginal Distribution of Poisson [duplicate]

How do you find the marginal distribution of a Poisson distribution given a gamma(a,b) prior?
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### Correlation of a poisson RV and binomial RV

My problem is something like this problem We have $X = Pois (\lambda)$ and $Y|X = binom (X , p)$ Where p is a known constant. And I want to calculate the correlation of $X$ and $Y$. I read the ...
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### Fish counts and Poisson [closed]

I am having troubles with fitting a Poisson distribution to my data, let me explain: I have fish counts of different species from a closed list, at 5 sites, 2 different depths, and across 10 years. ...
Fix $M>0$ and let $(\tau_i,\zeta_i)_{i =1}^{\infty}$ be a marked point process associated to the poisson-random measure $\mu$ on $[0,1]\times [-M,M]^2\times [0,M]\times [-M,M]$ with uniform finite-...