# 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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### 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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### 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 ...