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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 ...
Terrie's user avatar
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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 ...
user9410's user avatar
15 votes
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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 ...
Simon Bates's user avatar
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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 ...
Cadmus's user avatar
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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 ...
elcortegano's user avatar
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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 ...
rudinable's user avatar
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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 ...
Marlon Brando's user avatar
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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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Advice Desired: Predicting US Tornado Counts Via Multi-Level Model

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. ...
FilteredFrames's user avatar
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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?
les2004's user avatar
2 votes
2 answers
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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 ...
Harry Lofi's user avatar
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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, ...
Marlon Brando's user avatar
4 votes
2 answers
251 views

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 ...
wanyancan's user avatar
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Distinguish whether time series comes from or another Poisson process

I have a time series of binary events, where the events are drawn from a Poisson process with a 50% chance of having a rate of $\lambda_1$ and a 50% change of having a rate of $\lambda_2$. Here $\...
KHAAAAAAAAN's user avatar
1 vote
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Modelling Y=min(c,X) for different c

Assume I have a random variable $X \sim Poisson(\lambda)$ which models the potential nr of people entering some room. Now consider this room has a capacity $c$ so that whenever $X > c$ we observe $...
BeechAndBirch's user avatar
5 votes
1 answer
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Questions around modelling arrival process of randomly sized groups

I have the following situation: I'm trying to model groups arriving to some location by some process. I assume the distribution on some interval $T$ is a Gamma-Poisson mixture where $\Lambda \sim ...
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Posterior distribution of shape & rate parameter in Poisson-Gamma Mixture

Currently I'm struggling to handle the following question. Suppose $x_i,(i=1,2,\dots,n)$ follows Poisson distribution: $$p(x_i|\theta) = \frac{\theta^{x_i}e^{-\theta}}{x_i!}, \quad x_i\in\mathbb N,\...
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How do I estimate the covariance matrix of a set of dependent Poisson RVs?

LeBron James has averaged 27 pts, 7 rebounds, and 7 assists per game essentially since his debut in 2003. Despite this, he has never had a game with a stat line of exactly 27/7/7. I'm interested in ...
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Poisson distribution - test per patient [duplicate]

In a positive tailed distribution (i.e. Poisson/ exponential shape), the probability a patient can have $3$ tests is $0.9$, where the chance of using $4$ tests per patient is $0.05$, $5$ tests $=0.03$ ...
Adán Osuna's user avatar
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How can one measure spatial clustering of continuous (non-count) data?

I am currently teaching an ecology class how to use the variance to mean ratio (VMR) as a method for looking at the spatial clustering of individual organisms across a landscape. This method takes the ...
Michael L's user avatar
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Conditional expectation of Poisson, conditional on Poisson sums

Consider independent Poisson random variables $X_1\sim \text{Poisson}(\alpha_1)$, $X_2\sim \text{Poisson}(\alpha_2)$, $Y\sim \text{Poisson}(\lambda)$, and suppose $Z_1=X_1+Y$ and $Z_2=X_2+Y$. I want ...
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The distribution of K until the n-th occurance of a poisson process takes place

Let's take the following scenario: Customers arrive at a shopping mall according to a Poisson process with a rate of λ per minute. The mall has a door that closes ...
Sandra Sukarieh's user avatar
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Numerical moments of a multivariate Poisson Log-normal posterior

I have a log-density of the form: $$P(\mathbf{x}) \propto \exp\left( - \mathbf{b}^{\top} e^{ \mathbf{x} } - \frac{1}{2}\mathbf{x}^{\top}A\mathbf{x} \right)$$ where $A$ is a symmetric positive definite ...
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Splitting a random variable to give another random variable from the same family

Suppose you have a Poisson distributed random variable $N$ with expectation $\mu$. You then take a conditionally binomially distributed random variable $X$ where $X \sim \textrm{Bin}(N,p)$ for some $...
Henry's user avatar
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Why following Poisson distribution can be explained as a result of chance?

I'm reading a journal article which applies Poisson distribution in determining how many factors can be regarded as beyond the poverty threshold. My question is: why applying Poisson distribution and ...
ronzenith's user avatar
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Interpretation of a zero-inflated poisson model

I have the following data ...
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Success of Bernoulli trials with different probabilities, but a probability is only changed after success

I would like to compute the Bernoulli trials with different probabilities, but the probability is only changed after success. Such as here, all probability, p, is different at each state, s, in the ...
K-John's user avatar
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1 answer
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Is there a formula for the 95% confidence interval for the Skellam distribution or difference of two Poisson r.v.'s?

I have two independent Poisson random variables and want to assess the confidence bounds for X - Y. I know there is a closed form solution for Poisson confidence bounds, but need the difference. Can I ...
Bluegreen17's user avatar
3 votes
1 answer
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transforming a continous respond variable into a discrete one

I am visually estimating fish length underwater to convert it in fish biomass by means of proper length-weight relationships. Obviously, my accuracy is not perfect. When making hypothesis about ...
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Poisson distribution in two disconnected region

Suppose $N$ is a RV such that$$N\sim Pois(\lambda)$$ and $N_{1}$ and $N_{2}$ are two Random Variable distributed in two disconnected region called $R_{1}$ and $R_{2}$ respectively and $N=N_{1}+N_{2}$ ...
Rust32627's user avatar
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Optimal three parameter variable stabilizing transformation of a Poisson

In the paper: "On the classical choice of variance stabilizing transformations and an application for a Poisson variate", Shaul K. Bar-Lev and Peter Enis give an optimal two parameter ...
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Bacteria split each second according to a Poisson distribution, what is the distribution of the number of bacteria at some time $n$?

Each bacteria splits each second into some number of bacteria that is Poisson distributed with the same parameter for all bacteria. All the splits are not correlated. What would be the distribution of ...
mrepic1123's user avatar
1 vote
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50 views

Does the confidence interval for Poisson rate contain the sample mean?

Let $X_1, X_2, \dots, X_N$ be iid random variables from $Poisson(\lambda)$. The confidence interval for $\lambda$ with confidence level $1-\alpha$ is $$ \frac{1}{2N} \chi^2 \left(\alpha/2; 2 \sum_{i=...
mathslover's user avatar
2 votes
1 answer
60 views

Is it ok to use the log-normal approximation for incidence rates?

I have a dataset with counts of events, population and time, and need to perform a meta-analysis of incidence rates (IRs) per person-month. By assuming random effects (thus, allowing for heterogeneity ...
Federico Tedeschi's user avatar
4 votes
1 answer
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Count data multiple groups. How to define if particular groups are enriched for tumor counts or not?

I have counts (from multiple cell types) here only tumor is shown. I want to quantitatively define the clusters below as tumor rich/tumor poor based on tumor count. Tumor count represents no. of tumor ...
Saad Khan's user avatar
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Poisson Percentile Bootstrap Intervals

In Efron and Hastie's Computer Age Statistical Inference, they consider the problem of deriving confidence intervals for an estimated Poisson parameter. $\hat{\theta}=10$, where $\hat{\theta}\sim Pois(...
user1848065's user avatar
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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 ...
SemiActive's user avatar
8 votes
5 answers
1k views

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 $M^k(0)=\mathbb{E}(X^k)$ ...
Kai's user avatar
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2 votes
2 answers
78 views

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 ...
Quorthon's user avatar
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2 votes
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52 views

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 ...
KHAAAAAAAAN's user avatar
2 votes
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Why not always use covariate instead of offset in Poisson Regression? [duplicate]

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)} &...
John Katsantas's user avatar
2 votes
0 answers
27 views

What is the appropriate normalization for finding correlations between Poisson distributions? [closed]

I am interested in using this algorithm, glm-pca, to find a lower dimensional embedding in time series data, specifically neuronal spiking data, which is Poisson distributed. I have looked at some ...
Angus Campbell's user avatar

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