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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Expected value of the impact of an event based on Poisson Distribution [closed]

I am using Poisson Distribution to calculate the following, Suppose we are measuring that a distribution company has on average 10 truck accidents per year, on average each accident costs 25.000$ ...
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“near-birthday problem” example of Poisson paradigm

I have an example from page 460 of the textbook Introduction to Probability (second edition) by Blitzstein and Hwang: For example, suppose there are 14 people in a room. How likely is it that there ...
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Number of events calculation during fixed time interval [closed]

During a fixed interval of time let's just say one month, I want to predict occurrence of certain event. These events are mixture of dependent and independent prior events. Because of this criteria ...
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Determining overdispersion of count variable in bayesian model (brms)

I am trying to determine whether my response count data are too overdispersed for a (brms) Bayesian poisson model. I constructed a poisson-generated response variable with low and high levels of noise/...
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Poisson Regression with overload of zeroes SAS

I am testing different models for the best fit and most robust statistics to my data. My dataset contains over 50000 observations, approx. over 99.3% of the data are zeroes - such 0.7% are actual ...
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Calculating confidence intervals for poisson distribution given standardised rate and standard error

I am trying to calculate 95% confidence intervals for standardised incidence rates. I do have the standard error, the direct standardized rate, and the crude rate. Is that possible? I am assuming a ...
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Covariance of conditional poisson random variable sequence

Suppose $X_0,X_1,\cdots$ are iid $Poisson(\theta)$ r.v. Define $Y_k = X_k I_{\{ X_{k-1} = 0 \}}$ for $k=1,2,3,\cdots$ Find the limit of $Var(\sqrt{n}\overline{Y_n})$ and asymptotic distribution of $...
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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. ...
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How to Simulate Pure-Jump Process associated Marked Point Process in R

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-...
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Exercise on Poisson model: how to get fitted values?

Setting: Let $C_{it}$ denote the number of claims of individual $i$ in a certain period $t$. Assume that $C_{it}$ is distributed as a Poisson with claim rate (mean) $\gamma_{it}$. Let $\log(\...
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Is the Poisson Distribution Correct?

I've conducted a study to see if an intervention has decreased the number of detentions a sample of students obtains. Out of roughly 9000 students at a very large middle school I randomly selected 141....
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Is aggregated poisson-distributed data still poisson-distributed?

I want to aggregate a dataset which is Poisson-distributed in which each event that occurs is measured at a different time. The data is transformed into transactional data, aggregated on UserID. So ...
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Use Poisson or Linear Regression for Longitudinal Data?

I want to fit a regression with repeated measurements Outcome:number of cigarettes smoked in the jth month (j=1,2,3) The outcome variable DOES NOT follow a normal distribution. The outcome values ...
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The Poisson Regression - The Equidispersion Property

I wondered if someone would take the time to provide a simple numerical example of the equidispersion property. When it is likely to arise. And the type of data that would satisfy this property. I ...
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Poisson Distribution vs Binomial Distribution

I have a specific problem here. It is stated as: "Assume that 30% of students in a university take public transportation daily to commute to their college. Suppose 10 of the students are randomly ...
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Predict satisfaction score given a shift of Service Level Agreement

I would like to make predictions for Overall Satisfaction based on a shift of Service Level Agreement (SLA). I have number of days taken to complete a single ...
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How can I show convergence in distribution to the normal?

Consider the following model: $$Y|N \sim \mathcal{X}^2_{2N} \quad \quad \quad N \sim \text{Pois}(\theta).$$ and define the standardised statistic: $$Z = \frac{Y-\mathbb{E}(Y)}{\sqrt{\mathbb{V}(Y)}...
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Assess quality of a Poisson regression model on R

we did a Poisson regression because we figured out that our data are count data. Could you kindly explain us where we have to look at in order to understand the quality of our Poisson regression? ...
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Poisson-Gamma conjunction - calculating posterior [duplicate]

How to calculate posterior distribution step-by-step while given: some observed numbers of customers from the last days that number of clients is distributed by Poisson($\lambda$) ($\lambda$ is not ...
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Estimate mean of Poisson from binary data

If you assume that counts in sample units would be distributed according to a Poisson distribution, but the data that you have are observations of only presence (count would be 1 or more) or absence (...
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Deriving winning probability from expected score

I have a GLM model which predicts the outcome (score) of a sport game. Given that, is there a formula to predict/derive the win/loss/tie probabilities? Currently I get these probabilities by ...
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Is there a closed-form expression for the Poisson Lognormal pmf?

Suppose the $\lambda$ parameter of a Poisson distribution is generated from a $LogNormal(\mu, \sigma)$ distribution. Can the final pmf be expressed with only elementary functions? $$f(x;\mu,\sigma)=\...
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Can I fit a Poisson model to ln transformed data? [closed]

This is my first question in stats Stack Exchange and I would say that it is an easy one, but hard to find around! I have a set of fish counts which should follow a Poisson Distribution (right ? ). ...
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Can we consider arrival of pest outbreaks reports as Poisson Process?

I have a scenario where given a geographical region, farmers within that region can generate pest outbreak reports (like twitter messages) using a mobile phone. Also, a particular pest can spread to ...
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How many beds should the hospital have so that the probability that a student will be turned away for lack of bed is less than $0.01 $

At a certain men's college, the probability that a student selected at random on a given day will require a hospital bed is $\dfrac {1}{5000}.$ If there are $8000$ students, how many beds should the ...
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Estimating the uncertainty on a single sample drawn from a Poisson distribution

Consider the following example section of a time series, which shows a continuous signal in voltage, and a discrimination threshold. Each time the signal upwardly crosses the threshold counts as an ...
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Choosing the right model: Poisson, Quasi-Poisson and Negative Binomial?

[Edit] I am working in R. I am investigating the effects of weather on restaurant demand. My DV is the number of restaurant visitors per hour, my IVs are five weather variables and all other ...
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Bayesian inference problem with three parameters

Assume that I observe a yearly time series for the number of certain events occurring per year. Also, assume that the data points come from a Poisson process with parameter $\lambda$. The dataset in ...
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how to prove the probability distribution of a Poisson random distribution over a time?

My question may seem so simple but I have problem to prove it. Suppose that $X$ follows a Poisson distribution with parameter $\lambda$ which is defined per each period of time. How we can prove that ...

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