# 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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### Confusion on units for the Poisson distribution when it is used to model variables with units

This question stems from the comment section of this question: Bus wait time under Poisson distribution, where it seems that The properties of the Poisson don't make sense for times because the units ...
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### Bus wait time under Poisson distribution

A bus will depart every 10 minutes from the origin, and the time it takes to travel to station $A$ follows a Poisson distribution with expectation of 10 minutes. Alice arrives at station $A$ around 9:...
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### What is the conditional expectation of two random Poisson variables?

Say I have two random variables $Z^{p}_{i} \mid Y^{p}_{i} \sim \text{Poisson} \left(t^{p}_{i}Y^{p}_{i}\right)$ and $Z^{q}_{i} \mid Y^{q}_{i} \sim \text{Poisson} \left(t^{q}_{i}Y^{q}_{i}\right)$ for ...
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### How to interpret pvalue for Chi² goodness-of-fit test for Poisson distribution

I'm a bit confused about the pvalues I'd get when checking my own data against a theoretical Poisson distribution. Following e.g. this post here: https://stats.stackexchange.com/a/78175/66544 I'd ...
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### What variable type to choose for a Poisson distributed variable if software package only allows for nominal, ordinal or continuous

In the area of cluster analysis I want to calculate the dissimilarity for my data (actual use case is to feed in the dissimilarities into a plotting function to calculate so called silhouette plots). ...
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### Regression left limited dependet variable

My scope is to analyze the impact of certain variables on the change in sales. As you can see, my dependent variable is a proportion of two variables and is limited to -1 (-100%). On the other hand, ...
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### Obtaining formulae for Poisson confidence interval

I have a sample $X=(X_1,\dots,X_n)$ of $i.i.d$ Poisson variables such that $n=100,\overline{X}=8.8$. My goal is to obtain a $80\%$ confidence interval for the parameter $\lambda=\theta$. That is, the ...
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### Poisson or Binomial distribution for modeling?

I want to model the change in rate of an event in a sampled population. The populations are grouped according to some grouping variable. Each individual observation is of one organism, and the sample ...
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### Estimating Right Censored Data

I'm a newbie at Math, and I am just getting my feet wet when it comes to understanding math and statistics so please forgive my ignorance or question if it's already been answered or if materials are ...
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### VST of Poisson random variable of small lambda

https://math.stackexchange.com/questions/805550/variance-stabilization-for-poisson-data As you can see the variance is diminished when the lambda parameter closes to zero. Is there a variance ...
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### Proportional Poisson Process Problem

The alliteration is unintentional, but I was amused so I'll leave the title as is. Anyways, I am looking at a problem where we are trying to predict/justify an observed instantaneous rate by which ...
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### Modelling poisson distribution with nls() in R?

I'm trying to model the probability that somebody can do a 90 day Snapchat streak. I have some binary success data in the form of count data (the participant only reached 90 days once): I've ...