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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Poisson Regression vs. T-test for Balance

I have many subjects that were cluster-randomized to a treatment group and to a control group. I want to check the age balance of the groups following the randomization - e.g. whether there is a ...
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1answer
34 views

Removing undefined (NaN) values during log-likelihood maximization

I am trying to maximize a Poisson likelihood function for an array of values, of the form llhij = -mij + kij*ln(mij/kij). (where I use the numerical approximation ln(k!) ~ k*ln(k)). For my ...
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18 views

Question about application of GLMM with Poisson

I'm working on revising stats for a manuscript involving male reproductive success of deer. We measured three variables (body size, ...
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24 views

Comparing importance of features in different datasets in GLM

I want to compare the importance or 'predictive power' of the same feature in 2 different datasets. Specifically let $[\bf{y}_1,\bf{V}_1]$ be my output & design matrix of dataset 1 & $[\bf{y}...
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16 views

removing outliers in poisson distributed data (count data) to improve classifier accuracy

I wanted to know how to remove outliers in count data, the data i have is labeled can I remove the outliers from each class ? Or consider only 80% of the data close to the cluster center to train the ...
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3answers
176 views

Why doesn't the CLT work for $x \sim poisson(\lambda = 1) $?

So we know that a sum of $n$ poissons with parameter $\lambda$ is itself a poisson with $n\lambda$. So hypothetically, one could take $x \sim poisson(\lambda = 1) $ and say it is actually $\sum_1^n ...
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62 views

Poisson Modeling ANOVA

I'm looking to model percent change in transaction year over year for sales people grouped in certain categories (7 categories total). The percent change in transactions would be Q1 of the current ...
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1answer
27 views

Chosing the right test for weekly disease counts

I am using STATA to analyze count data (weekly disease counts), and I am trying to pick the best test between Poisson, negative binomial and zero-inflated Poisson / negative binomial but I am not sure ...
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21 views

How to test the distribution of the transcripts per million (tpm) values and analyze ASE (allele specific expression) differences between haplotypes?

I have the TPM (transcripts per million) values generated for my RNAseq data. My overall goal is to identify genes that show allele specific expression differences. In the table below the TPM values (...
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1answer
28 views

Comparing RMSE to model

I'm assessing the accuracy of the prediction of my model using the RMSE on a new data set. Now the RMSE in itself doesn't give any indication of whether it is a good model since there is no threshold ...
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1answer
25 views

Poisson regression for ordered variables

I have three waves of data, and I am trying to estimate group-based trajectories of binge drinking across the three waves. The question asked (at all three waves was): “Over/During the past 12 months, ...
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1answer
23 views

scipy.stats.poisson.interval - what confidence interval

What kind of confidence interval does scipy.stats.poisson.interval return? Is it normal approximation? I went on GitHub, but could not look it up in the code. How ...
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25 views

How can I decide weight in negative binomial regression?

I'm on my project to predict the amount of demand of products in a store. we have lot of 0 on the amount of sales of products so when I did multiple regression, predictions of the demand had negative ...
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1answer
40 views

Poisson Regression Likelihood estimation

Let $Y_1,\dots,Y_n$ independent random variables with $Y_i\sim > Poisson(\lambda_i)$. For the likelihood model $$log(\lambda_i)=\sum_{j=0}^p\beta_jx_ij$$ with $x_i=(x_{i0},\dots,x_{ip})$ where $...
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0answers
8 views

Assess what factors are associated with the duration between two events

I am working on a project where I calculate the time between two different type of treatments (e.g. A and B). I am trying to assess what factors predicts this duration (measured in days). I use SAS. ...
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2answers
192 views

Unbiased estimator of poisson parameter

The number of accidents per day is a Poisson random variable with parameter $\lambda$, on 10 randomly chosen days the number of accidents were observed as 1,0,1,1,2,0,2,0,0,1, what will be an unbiased ...
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6 views

Is it possible to derive a relation between parameters in Poisson process representation of extremes and parameters in GPD model?

I want to derive the theoretical relation between the parameters in a point process model for extremes and the parameters in the GPD model for extremes. I'm following Coles - An introduction to ...
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1answer
22 views

Poisson regression with different exposures dependent and predictor variables

I am trying to fit a Poisson regession in R, using rates: $\ln(\mathrm{rate}_i) ~= a + bx_i + c \ln(\mathrm{old\_rate})_i$ My issue is that the predictor variable $(\mathrm{old\_rate})$ is also a ...
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20 views

Idiosyncratic error term in fixed effects Poisson

Cameron and Trivedi (2013: 346) and Wooldridge (2010) suggest fixed-effects Poisson with multiplicative heterogeneity.E[y_it│x_it,α_i ]=α_i exp⁡(x_it'β), where α_i is the unobserved heterogeneity. If ...
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1answer
19 views

Poisson regression with offset vs logistic regression

I am thinking to use Poisson regression with an offset variable instead of a logistic regression in case where event is rare, since p (probability of success) is very small and n (sample size is large)...
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15 views

DIfferent zero-inflated poisson model outputs of Frequentist and Bayesian

I modeled zero-inflated poisson regression using crime data. There are 10034 obs and let assume spatial autocorrelation is not significant. For the Frequentist approach, R was used and code is ...
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16 views

How to determine counts of viruses from limiting dilution assay

My question relates to a common experiment in the field of virology. Let me give some background so you understand why I'm asking this question. When producing virus for an experiment you typically ...
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1answer
33 views

The Number of Exponential Summands in a Fixed Interval is Poisson

What is the most clever way to prove that the number of independent exponential summands in a fixed interval is distributed as a Poisson random variable? I can do it one way, but I would like to know ...
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13 views

Estimating the uncertainty in the peak of a non-stationary poisson process

I have daily counts of observed disease cases for a single location. I am interested in the peak timing of the outbreak of the disease and want to assess the uncertainty in the peak estimate. In other ...
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1answer
35 views

What is the difference between Poisson Regression and Log-linear Models in terms of their usage and which should I use?

I'm currently analyzing a data set from an experiment, where participants could give one of three types of answers: 1) Correct, 2) incorrect-congruent, 3) incorrect-incongruent. The priming ...
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22 views

Distinguishing between Poisson distribution and a similar distribution w/ small mean

I have an experiment where if all is going well the measured distribution should be Poisson (to very good approximation) with mean $\lambda \sim .1$, but if something goes wrong the distribution will ...
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1answer
74 views

log ratio of Poisson means versus logit of binomial probability

Assume that two observed counts C1 and C2 are independent realizations of two Poisson processes: ...
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24 views

Expectation of y given u when it follows Poisson distribution

So I was reading Generalized Linear Models with Random Effects by Youngjo Lee, in chapter 6 about Hierarchical GLMs there's this example: Suppose $y|u$ is Poisson with mean $\mu = E(y|u) = exp(X\beta)...
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16 views

how to interpret interaction in Poisson regression using SAS

I tried to run Poisson regression models using SAS by including interaction terms and offset by log population. All dependent variables were categorical. In the first model, I tested the interaction ...
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28 views

Poisson regression on Lung Cancer

I am a statistic student and I'm trying to study the effects of smoking on lung cancer rates. Below you will find what I did. My question is about the homoskedasticity, I think that the assumpion is ...
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0answers
26 views

Zero-truncated Poisson model

In the theory of generalised linear models, you may use the exponential family to find the mean and variance of certain distributions. How would the mean and expectation of the zero-truncated Poisson ...
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15 views

Poisson regression residual analysis

In a three factor poisson (log-linear) model $(A*B*C)$, when the highest interaction term $(A:B:C)$ is dropped, the response/raw residuals are exactly the same for different levels of two of the ...
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22 views

Find mean of Poisson process between two known options

I think my question is simple, but somehow it's ruining my day. My problem is: I observe a Poisson process, and I want to find out which, between two known options, mean_1 or mean_2, is the true ...
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2answers
84 views

Why two 'modes' for a Poisson Distribution with $\lambda$ an integer?

Let $X\sim \operatorname{Poi}[\lambda]$ such that $\lambda\in\mathbb{N}$. $$\mathbb{P}[X=\lambda-1]=\frac{e^{-\lambda}\lambda^{\lambda-1}}{(\lambda-1)!}=\frac{e^{-\lambda}\lambda^\lambda}{\lambda!}=\...
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14 views

Confidence interval for fitted lambda from Possion distrubtion

So my question is: you are given a set of data and you know the distribution is Possion with parameter lamda > 0. I figure out xbar is 4.06, and the z value we are using is 1.96 and n=50? But how can ...
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1answer
39 views

offset in glm for poisson regression

The offset argument in the glm() quite troubles me. As below, m3 is the usage of offset that I have seen. m4 is a manually calculated analog. But the result obtained is completely different, with m3 ...
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1answer
52 views

Log-linear model, Poisson regression, categorical variable with 100 levels

I want to compare the incidence rate(asum) of 100 different cities(cityID) to see if there are significant differences among them. Given that the incidence rate is following Poisson, so it is a log-...
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48 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
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3 views

What component of the result should I look at when doing a LLM model fit?

I am running mixed effects models with poisson and negative binomial fits. To asses which of the models are better, what components of the models should I look at? Some popular methods I follow: a) ...
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10 views

Wald, LR and LM tests for Poisson distribution

Assume that $y$ is random variable which distributes: $$f(y)=\frac{e^{-\lambda}\lambda^{y}}{y!} $$ Where $\lambda=e^{\alpha+X\beta}$ and $\alpha$ and $\beta$ are unknown parameters and we assume that ...
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1answer
19 views

Generalized poisson model with time parameter

I tried finding this on the internet, but with little success. How do I get a generalized expression involving rate parameter and time parameter for the Poisson process? The expression, $P(n) = \frac{...
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0answers
9 views

Estimated values for Chi-square

To test if my point pattern is random, I am going to conduct a Chi square test. The data has 40 points divided to 3 by 3 tiles. Should I use Binomial or Poisson probability to calculate expected ...
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0answers
12 views

Can I use an offset for the maximum number of consecutive trades in an experimental market?

I have run a study where we let students interact as buyers and sellers in an experimental markt. Every period buyers can buy from one single seller and sellers can only sell to one single buyer. We ...
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18 views

Systematic component variation

The appendix of the paper of McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the ...
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1answer
143 views

Question on Poisson Distribution (Assignment Help)

I've been given the following question which was part of a past exam paper. Q3) Trains arrive at a station at the rate of 25 per hour. a) What is the probability that the time between trains ...
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1answer
58 views

Poisson Regression in R based on categorical time variables

I am trying to make a prediction on the number of visitors of a website and am wondering if it can be done based only on categorical time variables. I received some guidance on how to structure my ...
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24 views

Standardized residuals vs fitted values for Poisson regression

McCullagh and Nelder's book on glm suggest to plot standardized deviance residuals against either the linear predictor ($\hat{\eta}$) or the fitted values ($\hat{\mu}$) transformed to the constant ...
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25 views

Count data that can take only 4 values

What is a good model for estimating a regression whose count dependent variable that only has 4 values: 0, 1, 2, 3? The variable is not truncated, it is just something that can only be from 0-3. I've ...