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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Update gamma prior with new rate parameter instead of observations

From wikipedia: In Bayesian inference, the conjugate prior for the rate parameter $λ$ of the Poisson distribution is the gamma distribution. Let $$\lambda \sim \mathrm{Gamma}(\alpha, \beta)$...
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Estimation of stochastic parameters in bivariate Poisson model

I need to estimate parameters in bivariate Poisson model. Formulas for parameters: $\lambda_1= exp (\alpha_i-\beta_i+\delta)$ $\lambda_2= exp (\alpha_j-\beta_j)$ where delta is some constant, alpha ...
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33 views

Should OLS always have a lower RMSE than Poisson Regression?

I'm working on building a predictive model for the number of singles a hitter in baseball generates over the course of a single game. Since the number of singles a hitter scores per game is count data ...
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51 views

R: Using Poisson statistics to predict terrorist attacks in France [closed]

I am a French data analyst and am pretty certain that a statistical description of the terrorist attacks would be possible, and even useful. As "rare" events, I would choose the Poisson probability ...
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49 views

model for non-linear data with repeated measurements

I have to do a model for non-linear data with repeated measurements. I worked with predatory insects. I did an experiment with 4 treatments, where per each treatment predators received a different ...
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1answer
11 views

Is OLS Unbiased on Count Data in the Positive, Real Domain?

On the domain of positive real number is OLS on count data a consistent estimator of coefficients? I am trying to understand if the estimator is inefficient or produces biased SEs but is nevertheless ...
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340 views

Should I use Poisson distribution for non-integer, count-like data?

It's my first question here, I hope I'll ask it correctly. I am trying to find out how to analyse non-integer, count data (yes!). I am looking at the effect of a given treatment on habitat suitability ...
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31 views

How to test for group differences in poisson distributed variables with unequal length?

I would like to test group differences in poisson distributed variables. However, I'm struggle to find appropriate approach(using R), which encounters unequal ...
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17 views

Poisson process (discrete counts) measured over varying time interval with many zeros

I am modeling forest inventory data. Forest plots are visited every 5-10 years. New trees that cross some threshold diameter between census intervals are classified as 'recruits' and counted. ...
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30 views

How to analyse a “Check all that Apply” question

I have survey that asks respondents about the number of barriers they've experienced. The question lists different types of barriers, and respondents are asked to check each one they've experienced (...
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25 views

Confidence interval for Poisson distribution

Let $y_1, y_2, \ldots,y_n$ be a simple random sample from a random variable $Y \sim Po(\lambda)$. I should calculate: $\mathbb{E}(S_n)$ and $\mathbb{Var}(S_n)$, where $S_n=\sum_{i=1}^{n}Y_i$ and $...
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48 views

Relationship between Poisson, binomial, negative binomial distributions and normal distribution

When we have to define discrete counts distributions, we usually use : Poisson distribution, if mean = variance Binomial distribution, if mean > variance Negative binomial distribution, if mean <...
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13 views

Can you use the Poisson GLM if there is an upper limit?

I'm analyzing social network data where roughly 10 groups of 100 people are split into different sized teams. (For example, there are 10 schools, but some of the schools have 5 "classrooms" while ...
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13 views

Threshold to segment count data following different distribution

I have a dataset D, wherein $ D = \{x_i, x_{i+1}, \ldots, x_n\} $. each data point in D is a discrete count data and since this is spatial data, one can expect dependence between contiguous data-...
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17 views

Freeman & Tukey interval [duplicate]

If $Y$ is $\text{Poisson}(λ)$ distributed, how do we obtain this confidence interval for $λ$: $\:l=\frac14 [(\sqrt{Y}+\sqrt{Y+1}-z_{α/2} )^2-1]$ $u=\frac14 [(\sqrt{Y}+\sqrt{Y+1}+z_{α/2} )^2-1]$
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Application of Wilks' theorem to poisson data

My parametrized astrophysical model predicts a mean bin count $e_i(\theta_1,\ldots,\theta_p)$ for each of $N$ non-overlapping energy regions. For a set of observed counts $k_i$ the joint likelihood is ...
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24 views

Poisson normal approximation for comparing means of count data

I'm trying to compare the values of two counts from an A/B test, $c_1$ and $c_2$. If I assume the data is Poisson distributed then the mean and variance are $\lambda$ and the standard error is $\...
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28 views

Probability of a Blizzard - Poison vs Binomial vs Bayesian

My goal is to model data I have collected to compute the probability of a severe blizzard occurring in a given set of states (region). Assume the US is broken into 3 regions that categorize the ...
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15 views

List Experiments as Right-Truncated Poisson?

A common scenario for the analysis of list experiments: Note: the standard list experiment is also known as the Item Count Technique (see Imai 2011: http://imai.princeton.edu/research/list.html) ...
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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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40 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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42 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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212 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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65 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
31 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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29 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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31 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
30 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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29 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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29 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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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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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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195 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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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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25 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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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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20 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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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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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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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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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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36 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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77 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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25 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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29 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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27 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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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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23 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 ...