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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What transformation should be carried out if the count is non-integer in poisson glm in r?

My data is like this: person final sex 1 34.20 1 2 2.00 0 3 15.58 0 4 18.00 1 5 50.06 1 I am fitting ...
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1answer
31 views

How to choose between poisson regression and zero inflated models

I have data on children visiting the A&E department. I want to see which variables are associated with the numbers of visits. For instance, if genetic factors are associated with more visits to ...
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17 views

Uncertainty on ratio of integrals (correlated)?

I have a histogram, and a quantity defined as the integral of a subrange of that histogram (int_sub) divided by the integral of the full range (...
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7 views

Approach to plotting a shock model with a Poisson parameter?

I know the shock model is defined as: $$ A(t) = \sum_{i=1}^{N(t)} A0\exp[-a(t-sn)] $$ where: $a = 0.5$ N(t) is Poisson ~ lambda, and lambda = 4 $t = 5$ $A0$ is given its own uniform ...
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26 views

Bypassing exponential waiting times for Poisson simulations?

Hello StackExchange users, I am trying to figure out how do I simulate a time dependent Poisson process through N(t). However, my main problem is having trouble understanding what N is and how to go ...
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3answers
106 views

Tricky Poisson distribution question

Am new to probability and have been struggling to solve the following question. Assume $X_1, \ldots,X_4$ are IID with $X_i ∼ \text{Po}(λ)$. Let $Y = \frac{1}{4} (X_1 + \ldots + X_4)$. Find ...
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11 views

How to find F(t) in a Poisson process? [on hold]

I've been given the following scenario: There's a bar in positions "A" and position "B" that receives 6 patrons per hour. Position A has 2x the capacity has position B. Find the marked Poisson ...
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16 views

Count Data Model, Poisson Distribution and Rounding?

In doing a count data model using a Possion distribution, should the estimate (output) be rounded (or the ceiling) if your target variable is always a whole number in the input training target data ...
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188 views

Which distribution to use for a probability problem?

In a food processing plant, on average, 2 packaging machines breakdown per week. I let x be the number of processing machine breakdowns in a week. So x is Poisson(2), but one part of the question ...
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19 views

Can I use gzlm with Poisson family if counts data are treated as factors? [closed]

My data called (my data) looks like below and I have 5 DVS(dv1,dv2,dv3,dv4,dv5) note all under one column and three IVS(IV1,IV2,IV3) as a data frame. I keep getting the error below. I am trying to fit ...
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0answers
6 views

GLM to asess differences between two treatments with only one IV

I have some data that I've collected in the field while running a trial where some sites (random 50%) received a treatment and the others did not. The dependent variable is the total number of baits ...
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24 views

Poisson for percentage data if values are low?

I have percentage data for diet per area (example here.....) I have no data on the individuals contributing to this diet, only for the population as a whole for each area. I want to assess ...
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13 views

variance of data of correlated poisson means?

I want to find the mean and standard deviation for the data for the following question. We have 10 houses of known different sizes. The number of people living per square meter has a poisson ...
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0answers
15 views

I used a generalized linear model with multiple dependent variables in R [migrated]

I used a generalized linear model with multiple variables in R .my data (young) looks like below and I have 5 DVS(dv1,dv2,dv3,dv4,dv5) and three IVS(IV1,IV2,IV3) as a data frame. I keep getting the ...
2
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1answer
49 views

How do I generate two correlated Poisson random variables?

How would I simulate observations from a bivariate Poisson distribution such that they have a nonzero covariance? The hint I was given is that I need to use the fact that the sum of two Poisson random ...
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2answers
77 views

hurdle model with negative binomial distribution of counts - error message and model selection

I'm working with over-dispersed count data, which is zero inflated (~2/3 zeros). I've fit a hurdle model using hurdle from ...
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1answer
35 views

Show posterior is proper for this poisson linear model

This question is 3.12 in Andrew Gelman's Bayesian Data Analysis 3rd edition. Let $y_i|\alpha,\beta \overset{iid}{\sim} \text{Poisson}$ with mean $\alpha+\beta t_i$. Find a prior distribution that ...
2
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1answer
25 views

Can I use glm with Poisson family if counts data are treated as density?

Imagine you have data of birds counted in an area - let's say, you count 18 birds in a surveyed area of 1,3 km^2. Imagine you relate this counts to 1km^2, so that you have 13.9 parrots per km^2. ...
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29 views

Since incidence rate ratios are always positive, how does one determine the sign of the effect?

I want the results from a Poisson regression to be comparable to previous OLS and Tobit regressions. To do this, I am utilizing the irr (incidence rate ratio) option in Stata. However, since all the ...
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0answers
21 views

Goodness of fit to poisson with unspecified mean

Is there a goodness of fit test for testing a series of counts against the whole family of poisson distributions? So, with the mean unspecified? Or does that not make any sense? Kinda related to ...
3
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0answers
19 views

Poisson convergences of series of random variable

Let $X_i$ be independent Poisson with mean $\lambda_i$. Show that i)$\sum_1^\infty\lambda_i<\infty$ implies $\sum_1^\infty X_i$ converges almost surely to a finite limit. ...
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2 views

How do I evaluate if an SIR model is consistent with a new-product diffusion model?

Background Susceptible-Infected-Recovered (SIR) models are used in epidemiology to determine the spread of disease. (link) The Bass models for new product diffusion are textbook in sales. (link) ...
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38 views

How to find the appropriate family for glm models?

As suggested over at stackoverflow I poste the question here instead: I have a data frame with three variables, where "Resp" is my response variable (count data), F1 is a categorical predictor (4 ...
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1answer
32 views

Relationship between Poisson generation and generalized Kullback-Leibler divergence

I have read that, in the context of matrix factorization, performing maximum likelihood estimation under the assumption that the entries are Poisson generated is equivalent to minimizing the ...
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10 views

Meta-analysis of skewed data with low event rate (single-arm studies)

I am trying to pool the data from several single-arm studies regarding the re-infection rate of a certain disease using STATA. From each study, I have obtained the no. of re-infections, and the ...
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10 views

Do the number of entries per bin of a histogram obtained out of a try and reject sampling of a pdf follow a Poisson distribution?

Imagine we have this pdf $\frac{3}{8}(1+x^2)+0.017x$ defined in $x\in[-1,1]$. Imagine we make a try and reject sampling and get many values of $x$. Imagine that with this variables we make a ...
2
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1answer
27 views

Approximation of “translated and scaled” Poisson distribution by normal distribution?

If I have a random variable $Y=a(\frac{b}{c}+\frac{X}{c})$, where $a,b,c$ are all integers and $X$ is Poisson distributed with a mean which is large enough to be approximated by the normal ...
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46 views

Distribution of ratio of Poisson distributed random variables

I am currently reading a paper and puzzling about a certain statement. I have a ratio ...
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1answer
42 views

Determine the mean and variance of X

Suppose that the number of customers who enter a post office in a 32-minute period is a Poisson random variable and that $P(X = 0) = 0.12$ How would I find the mean and variance in this case? I feel ...
2
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1answer
32 views

How to generate arrivals around a Poisson distribution

I'm interested in generating random arrivals that should simulate the call arrivals of a call center. I chose to use a Poisson distribution, but the greatest problem comes with the fact that it's a ...
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38 views

R glmer poisson for repeated measures - syntax correct?

I have for the past two days read all the questions and answers I could find regarding my problem, but as I got only more insecure, I finally decided to post a question on my own. I'd very much ...
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55 views

Poisson Regression Model - How to interpret the IRR and Base-Ratio?

By studying the Poisson regression model to analyze count data, I chanced upon the Incidence Rate Ratio (IRR). Browsing on the internet, I found different interpretations of that. For instance, ...
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38 views

Combining Poisson estimates

On average, 10 buses and 60 cars pass your house per hour. During one period of time, you count 11 buses and 40 cars passing your house. How long were you counting for? My first thought is to make ...
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2answers
740 views

Should the fumble rate of NFL teams be a normal distribution?

There's a lot of garbage statistics going around the internet regarding the Patriots, but I was just curious what the well-versed in statistics have to say about this. The main question is - in what ...
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61 views

Edited: Glmer model won't run all factor levels due to multicolinearity - can you have pseudo-multicolinearity?

I have a repeated measures design in which I have tested 112 individuals each with three different 20 second playback stimuli. I used a random block design where an individual was assigned to 1 of 6 ...
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28 views

what is the meaning and purpose of modeling a data?

Background: I collected a whole years access logs of my website, counted visit frequency for every user, and the numbers of user at each unique frequency, I got a distribution: $n_w \tilde\ D_w(f_w ; ...
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49 views

MonteCarlo simulations to test light curve variability

I have an average orbital light curve for a source, that is, binned count rate vs orbital phase, where the count rate are averaged over a number of orbit. I want to run MonteCarlo simulations to find ...
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0answers
23 views

Poisson regression with underdispersed and truncuated/censored upper bound

I'm analysing data from an experiment in which participants, over a number of trials, were presented with 8 boxes - 7 containing gold coins, and 1 containing a pirate. Their task was to open as many ...
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2answers
57 views

When is calculating probability based on a poisson distribution preferred over a binomial distribution?

I'm trying to understand why a poisson distribution may be preferred over a binomial one when modeling binary cases. Is there a case where you can't use a binomial distribution to solve a problem ...
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32 views

density function of the mixture of two NHPP

I'd like to know how can I calculate the density function of the mixture of two non-homogeneous Poisson process? I should mention that I have the kernel densities of those NHPP s. I can also describe ...
2
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0answers
29 views

ML classification problem for matrix and distribution estimate for each cell in the matrix

I am trying to think about a machine learning/statistical learning related problem. But would love to get idea from people in the forum about related problem/work/resource. So, the problem idea is ...
2
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0answers
110 views

What's the Mode of a Bivariate Poisson Distribution?

I have been looking at the bivariate Poisson distribution and I am wondering if there is close form expression for the mode of this distribution. I know the mode of the univariate Poisson distribution ...
2
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1answer
42 views

Poisson or Normal distribution?

In this problem: The respiratory disturbance index (RDI), a measure of sleep disturbance, for a specific population has a mean of 15 (sleep events per hour) and a standard deviation of 10. They ...
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53 views

Poisson distribution is a submartingale

Assuming that $s<t$, the poisson process is known to be a submartingale since only positive occurrence will happen as stating: $$E(X_t | \{ \mathcal{F}_s \}) = E(X_s | \{ \mathcal{F}_s \} ) + ...
2
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1answer
67 views

Overdispersion in poisson glm

When calculating the dispersion deviance/degrees freedom I get the value 1.8. Is it absolutly necessary to carry out the glm using quasipoisson? What is deemed 'significantly overdispersed' ?
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28 views

Distribution of “priority” emails among agents with different speeds (strange question)

but I figure if someone knows how to answer it, it may be someone here. Basically I have this weird distribution where the customer service agent speed (in terms of contacts per hour) is very ...
3
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2answers
34 views

Hierarchical Gamma-Poisson CDF?

What is the most computationally efficient way to evaluate the CDF $$P(X \leq x | r,v)$$ where $$ X \sim Poisson(\lambda)$$ and $$ \lambda \sim Gamma(r,v)$$ I can't see the next obvious step after ...
3
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2answers
49 views

Can categorical variables be treated as count data?

In a questionnaire study, I asked for the frequency of certain behaviors using a 5-point scale. Originally, I planned to treat it as categorical, however, distribution of the answers (N=1000) turns ...
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24 views

Understanding Poisson Point Process [closed]

Could someone explain the Poisson Point Process? Is it simply an Integration over a Poisson Process for higher dimensions? If so, how do you derive the function, say in two-dimensional space, and ...
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19 views

Multiple poisson processes ?

I'm just trying to get my head around Poisson processes, as they're fairly new to me, and I've had a thought experiment that has been annoying me a little. Imagine a volume of some mixture hit by ...