# 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 does this solution relate to the actual real-life stats problem?

4.62 in Newbold (8 ed):
A new warehouse is being designed and a decision
concerning the number of loading docks is
required. There are two models based on truckarrival
assumptions for the ...

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### R: Question about central limit theorem

Hello everyone :) can you help me please, I really don't understand my teacher's videos and it is the last part of our 20-pages work :O
In the question 1 they ask us to create a Poisson distribution ...

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### How do I solve this question on poisson and exponential distribution? [closed]

The SureWin Brokerage Firm manages portfolios of common stocks. Its computers mon- itor stock prices and, when certain conditions arise, they issue buy or sell signals. These signals follow Poisson ...

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### arrival time poisson processes

The arrival times of customers in a bakery can be modeled by a Poisson process (Nt)t≥0 with some rate λ > 0. On average, there are four arrivals per unit of time.
I want to ask about the question ...

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### How pvalue is calculated internally here ? And what is the data point for which it is calculating pvalue

I got a into a question while going through poisson distribution.
Here it is:---
A nuclear pump failed 5 times out of 94.32 days.
Give a 95% confidence interval (CI) for the failure rate per day
So ...

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### How to find point estimator for $\lambda$ in Poisson distribution?

Suppose we have a random sample $(X_1,X_2,...,X_n)$ from a Poisson distribution $Poi(\lambda)$.
How to find a point estimator of $\lambda$, and compute the mean and variance of the estimator.
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### Distribution when count data have no zero counts

My data are monthly counts of samples submitted to a laboratory for testing. The data have no monthly counts of 0 for when no samples were submitted. How should this data be handled? What distribution/...

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### Alternative to Poisson process with non-independent events?

Correct me if I'm wrong but as far I know, a Poisson distribution assumes the events are independent of each other. I have a dataset of events over several years where the occurrence of an event may ...

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### How to derive the likelihood ratio test for the Poisson distribution?

I am stumped as to how to find the one-sided LRT for the Poisson distribution. The majority of the examples I am finding are for two-sided tests, which does not give all that much help. If you have ...

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### Proving Event is Poisson Distributed with parameter λγ [duplicate]

Given that in a workshop with N students, where N is Poisson distributed with parameter λ, each student attends the Monday workshop with probability γ. How do I show that the number of students ...

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### Fitting a distribution. How

First of all, i am not good at this. i need to know what distribution fits in this dataset. i though it could be a poisson due to the characteristics of the data. the data talks about forest fires.
...

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### Modeling the assembly of an icosahedral virus?

The capsids ("shell") of some viruses exhibit T=1 icosahedral symmetry. In short, this means they are assembled from 60 copies of protein subunits which form an icosahedron (a shape with 20 faces). ...

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### In R, how to detect possible outliers in right skewed data assuming Poisson distribution?

I am attempting to identify possible outliers in data which is skewed to the right and I assume it is Poisson distributed. I am a novice in all things statistics, and the following may be utterly ...

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### Poisson sufficient statistics problem

I have the following problem:
Let $Y_1, \dots, Y_n$ be a random sample from a Poisson distribution $\text{Pois}(\lambda)$. Recall, the $\text{Pois}(\lambda)$ distribution has the probability ...

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### Is there a probability distribution similar to Poisson, but with controlled variance?

Is there a probability distribution similar to Poisson, but with controlled variance?
Poisson distribution with a lambda has a fixed mean and fixed variance; both mean and variance are equal to the $\...

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### Estimate correlation in non-normally distributed (e.g. Poisson), unbalanced, repeated measures data

I have a large behavioural data set, and I would like to measure pairwise correlations between several of my outcome variables, and binned categories of outcome variables. However, I have multiple '...

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### Density Function for Time until Second Arrival with Poisson Process

Problem Statement: The number of arrivals $N$ at a supermarket checkout counter in the time interval from $0$ to $t$ follows a Poisson distribution with mean $\lambda t.$ Let $U$ denote the time until ...

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### How to fit a power curve for a glm with simr

My response variable is counts of turtles at sea surface per aerial survey (possible values: 0,1,2) and I use a Poisson distribution for it (since my data are not overdispersed neither zero inflated). ...

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### Zero offset values, glmm poisson/negative binomial distribution with

I have a data set that consists of video observations of carpenter bee nests under three treatments: a control, mothers removed and mothers and worker removed. I have counts of twenty behaviours as ...

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### What is the general process of choosing, confirming, and supporting the distribution used in a generalized linear model?

I am trying to better understand the process of choosing and validating a distribution for a generalized linear model (glm). I understand that for the most part, you can narrow it down to a few ...

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### What is the relationship between ordinary least squares and poisson model?

I am a beginner in learning Statistics with some knowledge of machine learning, some concepts really confused me recently.
Starting from the linear regression and OLS, I think the former is a model ...

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### Bayesian updating of log-normal parameter after observation of poisson process

I am trying to update my estimate of a parameter (error rate) which has a prior log-normal distribution using an observation of errors (presumed to be Poisson distributed). However, I am having some ...

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### Correct interpretation of estimates in poisson regression output

I am learning to use and validate the Poisson regression model and interpret the results. I am using some data on grassland plant diversity in response to fertilizer and light. The experimental design ...

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### Struggling with implementation of Bayesian model (R JAGS)

For more on the background of the model, see my previous question here that describes the context more clearly.
In essence, there is a particular Bayesian model that I am trying to implement. Here ...

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### Count Modelling and Rates and Zero Inflation

I am looking for some help modelling overdispersed (zero-inflated negative binomial) count data as a rate. I want to model the survivability of villages in different municipalities given guerilla ...

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### Finding the form $g(T(\mathbf{y}), \lambda) \times h(\mathbf{y})$ for sufficiency statistic examples

I'm studying some notes that present examples of sufficiency:
Let $Y_1, \dots, Y_n$ be i.i.d. $N(\mu, \sigma^2)$. Note that $\sum_{i = 1}^n (y_i - \mu)^2 = \sum_{i = 1}^n (y_i - \bar{y})^2 + n(\bar{...

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### Poisson sufficiency statistic example

I'm studying some notes that present examples of sufficiency:
Let $Y_1, \dots, Y_n$ be a i.i.d. $\text{Pois}(\lambda)$. Then
$$\begin{align} L(\lambda; \mathbf{y}) &= \prod_{i = 1}^n e^{-\...

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### Joint distribution of correlated poisson random variables [duplicate]

Say $X_0, X_1$ and $X_2$ are independent Poisson random variables with means $\lambda_0, \lambda_1$ and $\lambda_2$, respectively. Define $Y_1 = X_0+X_1$ and $Y_2 = X_0 + X_2$.
How would I find an ...

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### When it is necessary to assume distribution to calculate probability? [duplicate]

I hope that my question is clear enough to understand.
If we need to calculate the probability of an event and we have historical data regarding our parameter of interest - When we have to assume ...

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### Detect what is wrong with the R program for a Poisson Q-Q-plot?

I have a big vector, $x$, of observations constituted by integers 0-5 that represents how many claims occurred during a certain insurance-contract (111408 elements).
I want to make a Q-Q-plot to show ...

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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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### “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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### 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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### Sample size calculation for correlated count data

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 ...