# 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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### Very different scale parameter estimates in Poisson regression

The background: I'm analysing survival data using a Poisson model. I've splitted the data on 2 time-scales (attained age and calendar year). Attained age is modelled using flexible parametric ...
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### Poisson regression for binary data

I've been trying to read up on Poisson regression models, and it looks like it is possible to estimate such a model with a binary outcome. This has come up before on this site here (and somewhat here ...
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### Bayesian inference on mean of statistic from population

Suppose that a collection of time intervals $t_i$ have occurred, for $i=1,...,n$. These should be considered as samples from a population governed by some distribution. During these time intervals, ...
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### Conditional probability update for correlated Poisson variables

Some background: I am trying to estimate the number of failures in two related machine populations. I model machine failures in a year as a correlated Poisson process as such: $Y_0,\ Y_1$ and $Y_2$ ...
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### Credit Risk and Concentration

I am working with a UK credit-union and we are looking to build a model to assess our credit risk and changes to this over time. We have a number of loans to borrowers who each have a credit rating (...
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### Rule of thumb - number of predictors - Poisson regression rates

I am interested in estimating a Poisson regression for mortality rates, with number of deaths as the dependent variable and log(population size) as the offset. I have 50 observations (states). I am ...
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### Basic idea of zero inflated two part models(hurdel) and application to big data (machine learning)

I'm currently working on the data which has 90% 0s in response variable. Based on my research, it seems zero inflated models could be a solution to this. However, while I was reading related documents,...
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### Dependent thinning Poisson process

If $N_1$ and $N_2$ are independent Poisson processes then the superposition is a Poisson process. Is it possible to construct two dependent Poisson processes such that the superposition is a Poisson ...
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### Are Poisson distributions with low mean heavy-tailed?

It is very apparent to me how using the normal distribution to estimate the probability of large, Poisson-distributed events may lead to significant underestimates of the probability of these events, ...
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### What is the best way to deal with over-dispersion in a poisson GLMM?

I am currently in the process of trying to complete a poisson GLMM analysis with two fixed (with an interaction) and two random effects using the glmer() function of the lme4 package. Using the ...
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### Mean of non-central Poisson deviance distribution is lower than that of the associated central distribution

We have observed some strange behaviour regarding distributions of Poisson deviance statistics. In short, we find for certain Poisson parameters, that the non-central deviances are smaller than the ...
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### Can we mix conclusions from Poisson and Quasi-Poisson?

Currently I'm working with ecological studies, where my response is a count variable. I need to estimate several models, each one represents a city. Afterwards I aggregate them to obtain meta-analysis ...
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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 $\lambda=4$, ...